Process Intensification for Compact and Micro Heat Exchangers

Review pubs.acs.org/IECR

Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Process Intensification for Compact and Micro Heat Exchangers through Innovative Technologies: A Review Jogender Singh,*,† Alejandro Montesinos-Castellanos,*,† and K. D. P. Nigam*,†,‡ †

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Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, Ave. Eugenio Garza Sada 2501, Monterrey, Nuevo León 64849, México ‡ Department of Chemical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, Delhi 110016 India ABSTRACT: This Review offers quantitative and qualitative analyses of various compact and micro heat exchangers (CMHXs) in terms of the friction factor, Nusselt number, and heat transfer augmentation mechanism. The C-MHXs, which have already been implemented in industry, are analyzed along with brand-new heat transfer technologies. Pressure drop and Nusselt number are used to characterize the performance of the heat transfer technologies and specifically to ascertain their appropriateness in analyzing C-MHXs. A precise analysis of the correlations reveals that the design parameters must be carefully examined before selecting a suitable correlation. In addition to the quantitative and qualitative analyses, computational fluid dynamics analysis used to design the C-MHXs is also compared with experimental analysis found in the literature. This review of C-MHX technologies will hopefully encourage and motivate more in-depth research into energy-efficient heat transfer devices. dynamic conditions and the smaller quantity of fluid being handled. This results in safer conditions for the heat exchanger and the improved control reduces the loss of raw material, energy consumption, and waste disposal. d. Fouling: clogging via gas bubbles in a C-MHX is an additional category of fouling along with others caused by crystallization, particulates, chemical reaction, corrosion, and biological growth. Determining the fundamentals of fouling in a C-MHX requires experimental studies of all sequential events and influencing factors.

1. INTRODUCTION Efficient design and optimum process parameters are the main source of the augmented performance and reliable mechanical characteristics of compact and micro heat exchangers (CMHXs).1−6 Moreover, the geometric design and smaller foot print of C-MHXs is of utmost importance for their potential application in chemical, electronic, refrigeration and heat pump industries. The larger area density is a core characteristic of CMHXs; it signifies a smaller hydraulic diameter, which results in higher heat efficiency with significant reduction in volume and material as compared to those of conventional heat exchangers. In addition to exhibiting higher heat transfer coefficients, the C-MHX technology primarily provides opportunities in four areas: a. Cost: C-MHX technologies offer significant reduction in cost as compared to that of conventional heat exchangers, especially in initial investment costs (e.g., smaller foot-print, reduced material), utility costs (e.g., energy), and the stream processing cost (lower stream loss due to smaller volumes). b. Process safety: C-MHXs may significantly improve the process safety especially in heat transfer processes with chemical reactions. For chemical reactions in C-MHXs, the hazardous material content will be significantly lower, thus leading to safer process conditions. c. Process control: failure to efficiently control heat transfer may lead to hazardous conditions. In comparison with a conventional heat exchanger, a C-MHX provides better heat transfer control due to its augmented hydro© XXXX American Chemical Society

Therefore, C-MHX technologies may offer solutions for next generation heat exchangers for the chemical, electronic, refrigeration and heat pump industries. In addition to the pressure drop and convective heat transfer, process safety is also equally important for the chemical reactions in CMHXs.7−13 For instance, Rodrı ́guez-Guerra et al.14 presented a simple procedure to design a heat exchanger microreactor for exothermic reactions with a hotspot inside the reactor. To predict the hotspot temperature, a relationship between the fluid properties, heat transfer and chemical reaction kinetics was proposed for a heat exchanger reactor with tube diameters of 0.5−10 mm. The fundamentals of heat transfer and hydrodynamics in microchannels are well explained in the Received: Revised: Accepted: Published: A

April 16, 2019 June 30, 2019 July 3, 2019 July 3, 2019 DOI: 10.1021/acs.iecr.9b02082 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Review

Industrial & Engineering Chemistry Research

Figure 1. Illustrated overview of the Review.

Figure 2. Applications of C-MHXs in science and engineering (SCOPUS and ISI Web of Science).

a rather limited discussion related to the combined effect of geometrical configuration and design parameters of C-MHXs. This Review presents quantitative and qualitative analyses of C-MHXs technologies and organized in four different sections, as shown in Figure 1. The applications of C-MHXs, classification of heat exchange technologies, and the type of microchannel cross sections are highlighted in Figures 2−4.

recent book on next generation microchannel heat exchangers.15 The various applications of C-MHXs in different industries such as the food, pharma and electronic industries were discussed in terms of improved heat transfer coefficients.7−13 Several other studies have demonstrated the applications of C-MHXs for additive manufacturing in automotive, and aerospace industries.16−19 However, there is B

DOI: 10.1021/acs.iecr.9b02082 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Review


Figure 3. Classification of various types of heat exchangers.

be MHEs with an area density of 17 500 m2/m3, which is equivalent to that of a tube of 0.19 mm diameter. Some MHEs are even more compact, having hydraulic diameters in the range of 1 μm ≤ dh ≤ 100 μm.39−42 A heat exchanger with a surface area density greater than 700 m2/m3 for gas−gas and gas−liquid streams, and 300 m2/m3 for liquid−liquid streams, is arbitrarily referred to as a compact heat exchanger. So, any heat exchanger, that satisfies the criteria of surface area density may be referred as a compact heat exchanger. Due to their compactness, C-MHXs have almost completely replaced circular tubes in automotive condensers and heat exchangers with hydraulic diameters of approximately 1000 μm.43 C-MHXs have been successfully applied to microelectronics, fuel cells, and automotive air conditioning systems.20,44,45 However, the higher pressure drop, higher pumping power, intricate fabrication, and high-grade filtering of the working fluids are key challenges of C-MHX technology. Therefore, in the next two sections, the quantitative and qualitative analyses of pressure drop and heat transfer in CMHXs are presented.

Section 2 introduces a critical quantitative comparison of various C-MHXs in terms of the normalized friction constant (C*) (Figures 5−7) and Nusselt number (Figures 8 and 9). In addition to the quantitative analysis, a qualitative analysis of emerging C-MHXs is equally important and may reveal avenues for the development of novel compact and efficient heat exchangers. Thus, a qualitative analysis of various emerging C-MHXs along with their geometrical design and design parameters is presented in section 3. Furthermore, computational fluid dynamics (CFD) has been employed to investigate the fluid flow maldistribution, pressure drop, and thermal analysis of various heat exchangers.10,20−26 Therefore, in section 4, applications of CFD are analyzed considering different aspects such as hydrodynamics and design parameters of C-MHXs. The aim of this Review is to comprehensively review C-MHXs technologies along with their geometrical design and design parameters. The thermo-hydrodynamic performance of microfluidic devices has been widely investigated by various researchers.20,27−35 The growth of research articles on C-MHXs has been quantified from 1955 to 2017; an analysis of the publications accomplished via Scopus (https://www.scopus. com) and ISI Web of Science (http://apps.isiknowledge.com) showing the spectrum of the applications of CHEs technologies in various fields is presented in Figure 2. Applications of C-MHXs are found in all important branches of engineering, accounting for 53% of all applications, 16% of which are in chemical engineering alone. The rapid growth of publications, which feature C-MHXs as micropumps and microheat pipes are published in highly specialized fields such as bioengineering and microfabricated fluidic systems, validates the wide practical application of C-MHXs.2,36−38 Various heat exchangers including tubular, extended surface, regenerative, and plate and frame heat exchanger (PHE) are classified in Figure 3. The difference between the compact and micro heat exchangers is largely a feature of the hydraulic diameter of the channel. C-MHXs can be characterized by their higher area density (i.e., higher ratio of heat transfer surface area to volume of heat exchanger). Typically, the area densities of micro heat exchangers (MHEs) are greater than 700 and 300 m2/m3 for gas−gas and gas−liquid (two-phase) streams, respectively.39,40 Human lungs can be considered to

2. QUANTITATIVE ANALYSIS OF C-MHX TECHNOLOGIES C-MHXs rely on process intensification by utilizing smaller fluid channels with larger surface area per unit volume. The small diameters of the C-MHXs have two effects on hydrodynamics, namely, the tendency for laminar flow and a higher pressure drop, as compared to those of C-MHXs with conventional diameter (≥3 mm). Laminar flow is associated with lower heat transfer (Nusselt number (Nu) = 3.36 for uniform heat flux at wall and Nu = 3.66 for uniform temperature at the wall), and hence, the heat transfer efficiency can be improved by various heat transfer augmentation techniques.11,46−65 This section of the Review presents quantitative analysis of the pressure drops and thermal characteristics in different C-MHXs, considering their corresponding heat transfer mechanisms. 2.1. Pressure Drop Analysis. The pressure drop in CMHXs and the effect of different design parameters, namely inlet type, inlet temperature, length of the channel, hydraulic diameter, Reynolds number (Re), and the type of fluid, have C


D

E

E

E

E

N

E, N

T, E

E

E

E

E

E

74

75

76

69

21

72

73

98

99

87

95

100

C2H6O2H2O sol., air H2O

air, H2O, R-134a

He

H2O

N2

air

H2O

H2O and CO2 (g)

H2O, CH3OH N2, H2O

Si, gl

900−15000

65−130

752−3165

1200−3800

500−4000

Al

Si

Si, gl

Si

SS

cer

−

50−4000

Z

−

rect

circ

circ

rect

rect

trap

rect

S

circ

SS

Si

rect

circ

rect

sq

type of channelc

100−1500 (H2O), 1500−15000 (CO2) 700−1400

250−20000

SS

Si

≤20000

200−2500

Si

≤300

n-propanol

N2

SS

MOCb

10−3300

Re

H2O

test fluid

−

− 180− 300

−

−

500

1.33

100− 300

30−60

500

300

1350

−

700

−

100− 200 −

H (μm)

52.25

200− 400

130

1000− 10400 2800

12000

200− 800 −

−

100− 200 −

W (μm)

264.71− 375

1000

173− 4010

2.59

133−367

55−76

848.48

275−500

2426.96

311.11− 746.67 19−102

3−81

1.6−65

100−200

dh (μm)

geometrical design parameters

−

32000

610000

−

−

15000− 25 1000000

7500

22−44

−

−

50000

750

−

5.15− 85.15

−

10−35

−

−

−

Ti (°C)

−

27000

90780

−

45000

24−52

−

−

L (μm)

I-type heat exchanger offers lower pressure drop as compared to the S-type.

ij 1.01612 yzz (−0.268 + 0.3293 x/D ) zzRe fapp = jjj0.0929 + j x /D z{ k The Colburn factor (ja) was attained in the range from 0.0026 to 0.0086 ja = 0.874Re−0.716

The pressure drop versus flow rate trends were similar to the conventional theory and followed power function profiles, but they were higher by 34−70%. The model was in good agreement with experimental results. For higher Re, the pumping loss was significantly higher (up to 60 at Re = 1000 as compared to 0.001 at Re = 10). Friction factor in glass channels was 3−5 times higher than that of smooth-pipe predictions. f = (110 ± 8)/Re for 900 ≤ Re ≤ 3000 f = 0.165(3.48 − log Re)0.24 + (0.081 ± 0.007) for 3000 ≤ Re ≤ 15000 Flow transitions zone at Re = 200−700 f = C/Re1.98, laminar range f = C/Re1.72, turbulent range, C = C vs Re plot81 Flow rates measured and compared with theoretical models. Mass flow−pressure relationship modeled by including a slip flow boundary condition at the wall. f = 0.316Re−0.25

The pressure drop was in good agreement with conventional theory. Microfabrication procedure may be important in MHEs. For larger cross-sectional areas, the experimental friction factor agreed well with theoretical results. f = C/Re, C = C vs Re plot 81 for laminar conditions f = 64/Re[1 + 30(v/dtca)]−1, laminar (Re < 2000) f = 0.14Re−0.182, turbulent (2000 < Re < 20000) In microchannels the transition takes place at a lower value of Re (400−1000) as compared to conventional channels. f = 50.13/Re, laminar (Re < 2000) f = 0.302/Re0.25, turbulent (6000 < Re < 20000) The pressure drop in S-shaped fin configuration (100 kPa/m) was about one-fifth of the conventional zigzag configuration (500 kPa/m).

remarks/ friction factor correlations

↑

↑

↑

↓

↑

↑

↑

↑

↓

↓

↓ ↓ ↓

↓

≈

f/ ΔP

a Type of study: E, experimental; N, numerical; and T, theoretical. bMaterial of construction: SS, stainless steel; Si, silicon, cer, ceramic; gl, glass; A;, aluminum. cMicrochannel cross section (see Figure 4): sq, square; rect, rectangular; circ, circular; trap, trapezoidal; tri, triangular; Z, zigzag; S, S-shaped. dSymbols “≈”, “↑”, and “↓” mean that f/Re is similar to, higher than, or lower than that estimated by classical/conventional theory.

E

E

3

101

studya

ref

Table 1. Pressure Drop Studies in C-MHXs

Industrial & Engineering Chemistry Research Review


Review


Figure 4. Types of microchannel cross sections: (a) circular, (b) semicircular, (c) elliptical, (d) triangular, (e) square, (f) rectangular, (g) rhombic, (h) trapezoidal, (i) pentagonal, and (j) hexagonal.

Figure 5. Normalized friction constant (C*) vs Reynolds number (Re) of gas flow in microchannels (10 < Re < 20 000, 25 < dh < 508 μm).

been widely studied.3,21,59,66−80 Table 1 presents an overview of the experimental and theoretical studies carried out under laminar, turbulent, and transitional flow ranges in microchannels of different inlet cross sections (circular, rectangular, triangular, S-shaped, etc.), using different fluids. The different cross sections of the microchannels are shown in Figure 4. Air, nitrogen, helium, and argon were the main fluids considered in gases, whereas in liquids, the isomers of alcohols, oil, refrigerants, and water were tested. The hydraulic diameter was varied from 1.6 to 2427 μm. A careful assessment of Table 1 suggests that there is no pressure drop trend in micro-

channels. A similar conclusion may be drawn upon observing the pressure drop analysis for gas (Figures 5 and 6) and water flow (Figure 7) in microchannels. The pressure drop analysis was performed in terms of the normalized friction constant (C*), by using pressure drop data from the literature,34,59,66−71,74,75,77,78,80−86 where C* is defined as the ratio of the experimental Poiseuille number (Poexp) to the theoretical Poiseuille number (Potheory), as follows: C* = E

Poexp Potheory

,

where Po = fRe , and Re =

ρνdh μ

(1)


Review


Figure 6. Friction factor (f) vs Reynolds number (Re) of gas flow in both smooth and rough microchannels (100 < Re < 10 000, 29.9 < dh < 2490 μm).

Figure 7. Normalized friction constant (C*) vs Reynolds number (Re) of liquid flow in microchannels (0.001 < Re < 10 000, 25.4 < dh < 1000 μm).

The pressure drop for gas flow in microchannels was found to be higher, lower, similar, or inconclusive (i.e., simultaneously lower, and higher) in comparison to that observed in

classical theory, as shown in Figure 5. It has been argued in the literature that for gas flow, the friction factor (f) decreases with the Knudsen number (Kn) and increases with the Mach F


Review


increase in f occurred due to the entrance effects, which were not adjusted appropriately for a lower length-to-diameter (L/ dh) ratio of the tested channels. Judy et al.68 experimentally studied the water flow in the circular and rectangular microchannels with hydraulic diameters from 14 to 149 mm under laminar flow conditions and showed a good agreement between the experimental results and data calculated from the conventional theory. For higher Re (1000 ≤ Re ≤ 10 000), the deviation of C* data from conventional theory decreases with increasing Re and hydraulic diameters of the channels. For a smooth tube, good agreement was reported between the experimental data and the conventional theory (for Re ≤ 2100), whereas the experimental friction factor values in rough microchannels were higher than those of conventional theory.91 Most of the studies reported the transition from laminar to turbulent flow in both rough and smooth microchannels for an Re range of 1900 ≤ Re ≤ 2500, which is in good agreement with the conventionally sized channels. However, a few studies reported discrepancies with conventional theory. Barlak et al.70 experimentally investigated the friction factor for water (distilled) flow in microtubes with dh ranging from 200 to 589 μm, Re from 100 to 10 000, and length-to-diameter ratios (L/d) from 16 to 265. Two different mechanisms (smooth and abrupt) were observed for the transition from laminar to turbulent flow. The friction factor values were in good agreement with the classical theory. The friction factor was significantly affected by the length-to-diameter ratio for L/d < 100. Pfahler et al.74,83 investigated liquid flow in microchannels and reported that friction factors decrease with decreasing channel depths. They reported a good agreement between the experimental and theoretical results for a larger size channel (100 μm × 17 μm); however, a significant deviation from conventional theory was reported for a smaller channel (100 μm × 8 μm). Therefore, it may be argued that channel parameters such as width and depth may have significant effects on experimental friction factor results. In single-phase microchannel flow, the values of f fluctuate about 0.5−5 times that of conventional pressure drops for the given range of hydraulic diameters (1.6−2427 μm). The pressure drop in metal microchannels was lower than that in a silica glass tube with the same design parameters,102 due to the electric surface potential, which attracts counterions in the liquid and causes formation of an electric double layer on the wall. The anomaly in the pressure drop results may be attributed to the roughness, material of construction (MOC) of the microchannel, error in measuring the channel dimensions, and the lack of well-controlled surface structure, as most of the channels are fabricated by bonding silicon and glass. Unfortunately, the ability to fabricate channels for microfluidic testing has been limited until recently. A new domain of techniques for precise fabrication of microscale channels has emerged with the advent of micromachining. However, the capability for precision fabrication of microchannels has not been achieved yet. Despite significant effort invested into understanding the microfluidic effects, it remains an unresolved issue. Several other phenomena, such as twoand three-dimensional transport effects, are normally neglected at the microscale. However, these phenomena may exist in microchannels as well. Another microscale effect is the temperature gradient in the transport fluid, which may cause a significant variation in fluid properties (e.g., apparent fluid viscosity) throughout a microsystem, thus invalidating the

numbers (Ma < 0.3) and can be attributed to either gas compressibility and rarefaction effects or both.75,87 The discrepancy in the transition from laminar to turbulent flow is noticeable in the inset of Figure 6, a zoomed-in section of the data. An early transition from laminar to turbulent flow may be noted in Figure 6 for Re ranging from 1400 to 1800. The discrepancies in the experimental results may be caused by incorrect hydraulic diameters provided by the vendors (these are generally not measured before calculating f) and by not considering the entrance/exit losses in calculation of the friction factors. However, the results do not show any discrepancies when entrance/exit losses were accounted for and hydraulic diameters were measured before calculating the friction factor.84,85 It is well known that f is affected by relative roughness in conventional pipe flow under turbulent flow regime. Some studies have reported that in microchannels, f depends on roughness for laminar flow as well.75,79,88−91 However, the experimentally measured roughness was negligibly small (15 nm) in comparison to the height (68.2 or 23.7 μm) of the microchannel.88,89 A comprehensive review and experimental studies showed that the presence of surface roughness affects the velocity and decreases the value of the transitional Re.85,86,92−96 In turbulent flow, the Blasius correlation ( f = 0.079Re−0.25) for the friction factor in conventional smooth tubes reasonably represents the f data for microchannel flow. The experimental data for microchannels (dh = 1100−2490 μm) are in good agreement with the conventional Poiseuille ( f = 16/Re) and Blasius equations for laminar and turbulent flow conditions.95 However, for air flow in smaller channels, the experimental data are significantly lower than those of conventional theory. It may be noted from Figure 6 that the discrepancy between experimental results begins at Re = 4000. A previous study reported that the Blasius equation developed for the incompressible flow was inappropriate for prediction of the friction factor.95 The analysis of the experimental data for turbulent flow (Re = 4000) and at higher Mach number is challenging due to the combined effects of compressibility and turbulence. A modified correlation for f was proposed for determining the apparent friction factor as a function of Re, which is believed to cover both the developed and developing turbulent flows in conventional tubes.95 The experimental friction factor data for single-phase liquid flow in microchannels are analyzed for different cross sections (circular, rectangular, trapezoidal, etc.), hydraulic diameters (8.0−1700 μm), Reynolds number (Re = 0.001−10000), and fluids (water, alcohols, silicon oil, refrigerants, etc.). It may be noted from Figure 7 that for liquid flow the data obtained by most studies are in good agreement with conventional theory (most of the C* data falls within 20%). However, a few studies have revealed significant deviation between the experimental results and the results predicted by conventional theory. A large data set over the wide ranges of Re and dh is analyzed in Figure 7; it can be discussed in three different sets, i.e., lower Re (≤10), intermediate Re (10 ≤ Re ≤ 1000), and higher Re (1000 ≤ Re ≤ 10 000). For lower values of Re (0.001−10), the experimental results were higher than those of the conventional theory, likely due to the smaller values of Re and dh.78 Experimental values of the friction factor were in good agreement (within 20%) with the classical theory for Re ranging between 10 and 1000, except for the data reported by Jiang et al.97 The friction factors reported by Jiang et al.97 were 1.15−1.75 times higher than those of the smaller channels. The G


studya

E

E

N

T

E E, N

T, E

E

E

E, N

E E

E

E

E

E

E

E

E

E

ref

1

3

21

44

69 72

73

75

76

90

98 100

101

H

105

111

115

116

117

118

119

trap circ

Cu

Si, gl Si

139−162 (q = 100 W/cm2) 385−1289 (q = 200 W/cm2) 900−15000 752−3165

SS Si

2600−23000

−

−

H2O

H2O, CH3OH H2O

50−4000

Cu

50−4000

H2O

H2O

−

−

H2O

SS

SS

SS

1500−7500

H2O

N2 C2H6O2− H2O sol., air H2O Al

rect

SS

200−2500

H2O, CH3OH H2O

65−130

rect

Si

≤20000

N2

rect

rect

rect

circ

rect

trap

rect

rect

circ

rect

cer

air

−

circ Z

rect

S

sq

rect

inlet typec

Si −

Si

SS

SS

Cu

MOCb

250−20000 700−1400

N2, H2O H2O

air

CO2

100−1500 (H2O), 1500−15000 (CO2) −

10−3300

H2O

H2O,

60−3000

Re

H2O

test fluid

Table 2. Heat Transfer Studies in C-MHXs

−

−

−

1000

176− 325 −

700

−

−

200−800

−

180− 300 700

30−60 −

713

700

−

−

600

500

130 −

231

200−800

−

− 300

− 10000− 10400 2800 500

10000

100− 200 1350

100− 1600

H (μm)

130−250

12000

100−200

200

W (μm)

133−367

−

−

102−1090

133−367

690

264.71− 375 −

remarks/correlations

50000

46000

−

−

50000

22−44

10−35 14−19 −

−

22−44

−

30−60

− −

The S-type provides higher heat flux as compared to the I-type, even though the performance indices of both heat exchangers were essentially the same. In single-phase heat convection, the value of heat flux for microchannels was higher than that for conventional tubes. Nu = 8.39Re0.5 − 1.33Re2/3, laminar Nu = 4.73Re0.5 − 0.22Re2/3, turbulent Nu = 0.1165(dh/P)0.81(H/W)−0.79Re0.62Pr0.33, laminar Nu = 0.72(dh/P)1.15(1 − 2.421(z−0.5)2Re0.8Pr0.33, turbulent Nu = NuGn(1 + F), where NuGn = ( f/8)(Re − 1000)Pr/[1 + 12.7( f/8)] f = [1.82 log(Re) − 1.64]−2, C = 7.6 × 10−5, dt = 1164 μm Turbulent convection starts at Re = 1000−1500. Nu = 0.00805Re4/5Pr1/3 The Nusselt number for developing laminar flow is higher than that predicted from analytical solutions. Fully convective conditions reached at Re = 400−1500. Nu = Ch,lRe0.62Pr1/3, laminar Nu = Ch,tRe0.8Pr1/3, turbulent, C = C vs Re plot 81

−

32000

The conventional Navier−Stokes and energy equations can adequately predict the fluid flow and heat transfer characteristics of microchannel heat sinks.

Compact heat sinks are efficient and desirable as compared to conventional air circulation heat sinks. Nu = 0.007Re1.2Pr0.2, turbulent (6000 < Re < 20000) The experimental fluid temperature distribution was found to be in good agreement with the numerical results at lower flow rate. The heat transfer coefficient dominates at low Re. However, at high Re number, the pumping loss can become higher. Nu = 0.000972Re1.17Pr1/3, laminar (Re < 2000) Nu = 3.82 × 10−6Re1.96Pr1/3, turbulent (2000 < Re < 20000) Liquid temperature, velocity, Re, and size of the microchannel were the important parameters for the transition zone and heat transfer.

Nu = 0.207Re0.627Pr0.34, for CO2 (hot side, 1500 < Re < 15000, 1 < Pr < 3)

Nu = 0.0022Re1.09Pr0.4, turbulent (Re > 3000) A power-law correlation for Nu and Re was proposed for higher heat transfer performance. Nu = 0.792Re0.281

10−35 14−19 −

−

750

− −

−

+

Nu = 0.52(e ) , for e < 0.05 Nu = 2.02(e+)−0.31, for e+ < 0.05, where e+ = RePrdh/L The heat transfer results show discrepancies with the available models and correlations in the literature for low values of Re. Nu = 0.253Re0.597Pr0.349, for water (cold side, 100 < Re < 1500, 2 < Pr < 11)

+ −0.62

− −

− 610000

500− 44764

−

55−76 1000

45000

24000− 52000

−

− 27000

−

5.15− 85.15

−

− 90780

15

Ti (°C)

20000

L (μm)

311.11− 746.67

3−81

848.48

19−102 275−500

−

2426.96

100−200

20−65

dh (μm)


↓

↑

↓

↑

↓

↑

↓

↑

↑ ↑

≈

↑ ↑ ↓

↑

↑ ↑

↑

↑

↓

↑

Nu/hd



I

E

126

SS

15−1450

1000 − 17000

FC-84

H2O

H2O

H2O

R134a

Si

40−9000

− CuZn37 Cu

100−800

−

−

Cu,

SS,

R134a,

circ

−

tri, trap

rect

circ

circ

rect, circ, trap, tri

trap

−

10−2600

10−450

circ

rhom

rect

inlet typec

Al

Cu

SS

MOCb

H2Osurfactant H2O,

10−20000

10−50

H2O

H2O

911−4807 70−170 9−103

Re

FC-72, oil H2O

test fluid

−

−

−

800

−

−

800

−

−

−

−

−

−

−

−

−

−

−

100− 580

H (μm)

146−234

W (μm)

231−279.5

−

125.4−500

62.3− 168.9 800−1700

125.4 − 1070 133−2000

1070

69.2−160

710 − 740

100−1300

−

dh (μm)


−

53000− 250000 42000

325000

25− 325.13 30.13

53−335

600000

115500 − 116200 −

−

35000

L (μm)

12−68

27

−

−

−

−

−

−

50

−

Ti (°C)

laminar (10 ≤ Re ≤ 100) Nu = C1Re0.946Pr0.488(1 − c/a)3.547(ε/dh)0.041γ−3.577(dh/L)1.369 turbulent (2000 ≤ Re ≤ 20000) Nu = C2Re0.148Pr0.163(1 − c/a)0.908(ε/dh)0.033γ−1.001(dh/L)0.798 The experimental values of Nu were significantly lower than theoretical values of Nu for water flow in a straight tube. Two heat transfer regimes were predicted under laminar flow conditions. The first regime takes place at Re > 150. The heat transfer through the solid substrate was neglected. The second one occurs at Re < 150. Under this condition, the heat transfer through the solid substrate was considered. In microchannels, the effect of energy dissipation on heat transfer is negligible under laminar flow. The experimental data were in good agreement with the classical correlations. However, the microscale correlations did not agree with the experimental data. The local value of Nu is in good agreement with conventional theories including at the entrance region. The heat transfer coefficient of the ring-shaped microchannel plate with guide vanes was higher than that of the system without guide vanes at lower flow rates. The thermal model is validated for both balanced and unbalanced flow conditions for a parallel-flow trapezoidal microchannel heat exchanger.

Nusselt number correlation for the two liquids. Nu = 0.429Re0.583Pr1/3x/2H)0.349(B/2H)−0.494 Experimental Nu well-predicted by the Gnielinski correlation.110 The dh of 1−2 mm was proposed as a lower limit for the applicability of standard Nu correlations to non-circular channels. Laminar flow data found to correlate well using the Brinkman number.

remarks/correlations

↑

↑

≈

≈

≈

↓

↑

↓

≈

↑

Nu/hd

Type of study: E, experimental; N, numerical; and T, theoretical. bMaterial of construction: Cu, copper; SS, stainless steel; Si, silicon, cer, ceramic; gl, glass; Al, aluminum. cMicrochannel cross section (see Figure 4): sq, square; rect, rectangular; circ, circular; trap, trapezoidal; tri, triangular; Z, zigzag; S, S-shaped; rhom, rhombic. dSymbols “≈”, “↑”, and “↓” mean that f/Re is similar to, higher than, or lower than that estimated by classical/conventional theory.

a

E, T, N

125

E

E

124

129

E

123

E, N

E

122

128

E

121

E

E

120

127

studya

ref

Table 2. continued



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correlations proposed by Choi et al.,75 Yu et al.,69 Petukhov et al.,109 and Wu and Little98 were compared with that from the conventional Dittus−Boelter107 and Gnielinski110 correlations. It may be noted that in the turbulent regime, the correlations of Petukhov,109 Choi et al.,75 Yu et al.,69 and Wu and Little98 predict higher Nu than those of the theoretical correlations of Dittus−Boelter107 and the Gnielinski.110 The main reasons for the augmented values of Nu were the dominance of the eddy motion in the radial direction due to the small diameters of the microchannels and the effects of geometrical parameters such as relative length-to-diameter ratio, zigzag angle, and the radius of curvature. Eddy motion or current is the swirling of a fluid and the reverse current created either by the turbulent flow or geometrical design parameters. The moving fluid generates a void space on the downstream side and the fluid behind the obstacle flows into the void creating a swirl on the edge of the obstacle, followed by a small reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. The Nu correlations for laminar liquid flow (Pr = 3) proposed by Tsuzuki et al.,21 Nguyen et al.,111 Lee,112 Tang et al.,113 Seo et al.,114 and Peng and Peterson115 are compared with the Hausen correlation107 in Figure 9. It may be noted that for laminar flow conditions, the proposed correlations are neither in agreement with each other, nor with the Hausen correlation.107 The value of Nu predicted by all the correlations significantly increases with increasing Re under laminar flow conditions, which signifies the dominating effect of the geometrical design parameters (such as tube diameter and type of cross section) on the heat transfer performance of the microchannel heat exchangers. The hydraulic diameter of the microchannels ranges from 3 to 2426.66 μm, with various types of cross sections including circular, square, rectangular, and trapezoidal. In the turbulent flow regime, the correlations from Petukhov et al.,109 Nguyen et al.,111 Tang et al.,113 Peng and Peterson,115 Adams et al.,116 and Wang and Peng117 are compared with those of Dittus−Boelter107 and Gnielinski.110 The correlations of Peng and Peterson,115 Wang and Peng,117 Petukhov et al.,109 and Tang et al.113 show trends similar to those of the conventional Dittus−Boelter107 and Gnielinski110 correlations. It may also be noted that the correlations of Peng and Peterson115 and Wang and Peng117 predict lower values of Nu, whereas those of Petukhov et al.,109 Nguyen et al.,111 Tang et al.,113 and Adams et al.116 predict higher values of Nu in comparison to Nu values predicted by the Dittus−Boelter107 and Gnielinski110 correlations. The geometrical design parameters (hydraulic diameter 3 μm ≤ dh ≤ 2426.66 μm and type of cross section) were the main cause of enhanced heat transfer performance of the microchannel under turbulent flow. Comparing the single-phase convective heat transfer correlations in microchannels suggests that further systematic studies are required to demystify the physics of the transport mechanism of various flow structures responsible for the variation in heat transfer. Experimental data are required for possible extrapolation of the deviation between the behavior of fluid through microchannels with respect to that in conventional channels. The data from the older studies may not result in effective analysis as significant improvement in the microfabrication techniques is needed along with reduced surface roughness in microchannels with appropriate cross sections. The present analysis confirms that the understanding of fluid flow and heat transfer mechanisms in microchannels must be considered an open scientific problem, and more

often-used assumption of constant properties. Questions regarding the scale effects in microchannel fluid flow have not yet been satisfactorily answered, due to either difficulty in precisely carrying out measurements at the microscale or other factors like fabrication. Consequently, much work remains to be done in this area so that a complete understanding of fluid dynamics in microchannels can be realized. 2.2. Heat Transfer Analysis. Heat transfer in conventional geometries has been extensively studied over the past five decades, and there are well-established correlations for heat transfer coefficients in conventional geometries. Nusselt number is constant for fully developed laminar flow and depends on the boundary conditions and type of cross-sections of the geometry. For circular tubes, Nu = 3.66 and 4.36 for an isothermal wall and constant heat flux boundary conditions, respectively.103 In microchannels, the experimental results of many studies were predicted adequately by conventional correlations.90,104 However, other experimental studies revealed considerable deviations from conventional theory for heat transfer.105,106 A summary of different heat transfer studies is presented in Table 2. Several heat transfer correlations have been proposed for gas and liquid flow in mini- and microchannels based on experimental investigations. The Nu correlations for gas and liquid flow in microchannels are compared with the conventional heat transfer correlations in laminar and turbulent flow regimes as shown in Figures 8 and 9, respectively.

Figure 8. Nu correlations in C-MHXs for laminar and turbulent gas flow (Pr = 0.7).

For laminar gas flow (Pr = 0.7), the correlations proposed by Choi et al.,75 predict lower values of Nu as compared to the Hausen correlation.107 As can be seen in Figure 8, Nu increases with increasing Re faster than it does in conventional laminar flow. The dominance of eddy motion in the radial direction due to the small diameter of the microchannels was the main reason behind the leading effect of Re on Nu.75 Yoon et al.108 proposed a new Nu correlation as a function of the geometric parameters necessary to evaluate the thermal hydraulic performance in a semicircular zigzag channel. It may be noted from Figure 8 that the Yoon et al.108 correlation predicts significantly higher values of Nu as compared to those of conventional correlation, likely due to the presence of the different geometrical design parameters (hydraulic diameter, relative length ratio, zigzag angle and bend radius of curvature) of the microchannels. For turbulent flow regime, the Nu J


Review


Figure 9. Nu correlations in C-MHXs for laminar and turbulent water flow (Pr = 3).

MHX. Corrugated sheets were stacked with an appropriate angle between adjacent sheet rows, which is known as the chevron angle. The thermal performance at the chevron angle with the appropriate pitch to height ratio of the corrugated surface was investigated numerically and experimentally.138 Microchannel-embedded corrugated sheets (20 in number) were stacked to form the cross-corrugated heat exchanger. Applying the microchannel pressure tapping to a crosscorrugated heat exchanger (CCHX) implies that a practical design of the CCHX is possible by numerical analysis of the unit cells, employing experimental static and stagnation pressures. However, further experimental studies must be done on pressure distribution to validate the numerical results. It is widely reported that geometrical parameters such as the aspect ratio (the ratio of width to height) and hydraulic diameter-to-pitch ratio significantly affect the heat transfer and pressure drop in laminar and transition regions.88,89,115,142 The pressure drop in microchannels was found to increase by 35% with a decrease in the hydraulic diameter from 370 to 229 μm.142 Qu et al.88,89 investigated heat transfer in silicon microchannels with trapezoidal cross sections for hydraulic diameters from 51 to 169 μm. The experimental values of the friction factor were up to 38% higher as compared to the numerically predicted friction factors due to wall roughness, which was not considered in the numerical simulations. For the Nusselt number, the opposite trend was reported: a 2-fold higher value was obtained by numerical simulations as compared to the experimental Nu values.89 Therefore, a roughness−viscosity model was proposed to interpret the experimental data. The results from the roughness−viscosity model were in better agreement with the experimental results with an error of ± 20%.130 Another study investigated the effect of viscosity and thermal resistance in four different plate C-MHXs.143 They suggested that the effect of the heat input on the fluid properties (particularly the viscosity) should be considered when calculating frictional losses, because the cold

reliable/accurate experimental data are needed in order to possibly explain the observed behavior.

3. QUALITATIVE ANALYSIS OF EMERGING C-MHX TECHNOLOGIES Energy dissipation is an increasingly important topic in various industries, including in the microelectronics industry due to high-performance computing systems. To meet the requirements of the electronics industry, many studies have been carried out on plate C-MHXs with extensive geometrical perturbation since their invention by Tuckerman and Pease.35,82,88,89,106,115,130,131 Thus, this section of the Review presents a qualitative analysis of various new designs and configurations of C-MHXs that were developed for better heat transfer via geometrical perturbation. 3.1. Plate C-MHXs. Plate-type C-MHXs containing microchannels with different cross sections have been extensively studied for enhancing heat transfer. The thermal coefficient can be increased by increasing the heat transfer area and implementing rigorous mixing via improved hydrodynamic conditions.132 Cross-corrugated heat exchangers have wide applications, including in power stations,133 aircraft engines,134,135 and ships,136 due to their high thermal coefficients. Several patterns of embossing, ribs, and herringbones have been examined to further enhance the heat transfer coefficient.137,138 Bier, Schubert et al., and Bier et al.2,139,140 studied a cross-flow C-MHX with a volume of 1 cm3, surface density of 14200 m2/m3, and 4000 channels per cubic centimeter. They reported that a volumetric thermal power of 18 000 MW/m3 could be achieved with an overall heat transfer coefficient of 20 kW/m2 °C for gas (N2, He, and Ar) under constant solid temperature, i.e., homogeneous conditions. The pressure drop in C-MHXs is equally important to the heat transfer coefficient, as it correlates with the pumping cost. Thus, Ahn et al.141 suggested a new method for measuring pressure distribution in a cross-corrugated CK


Review

Industrial & Engineering Chemistry Research flow conditions can lead to over prediction (up to 23%) of the frictional losses. Adams et al.116 studied water flow in circular microchannels and observed that the microchannels with smaller diameter (102 μm) exhibited approximately 2-fold higher values of Nu as compared to those of the larger diameter (1090 μm) microchannels. Based on such trends, we suggest that one must consider the change in the geometrical parameters and fluid properties due to the change in the average bulk temperature. To optimize the performance of the plate C-MHXs, a threedimensional conjugate heat transfer model was proposed with different cross sections of the plate C-MHXs, as shown in Figure 10.82 At a specified channel length and for constant

thermo-hydrodynamic characterization of C-MHXs.144 A good agreement between micro-PIV and CFD data was reported; however, modeling was not precise. Missaggia et al.,145 Patel et al.,146 and Benett et al.147 have investigated the use of laser diode arrays for heat transfer enhancement. Missaggia et al.145 experimentally investigated the use of a parallel microchannel for heat dissipation from a twodimensional diode laser array. A water flow rate of 1.2 L/ min in microchannels having a width and height equal to 100 and 575 μm was used for the experiments. Thermal resistance was as low as 0.04 °C cm2/W at a constant heat flux of 500 W/ cm2. Patel et al.146 experimentally examined both the heat transfer and fluid flow performance of a microchannel for arrays of diode laser bars requiring rejection of 60 W of the waste heat. The total thermal impedance of the microchannel and laser bar package was found to be 0.33 cm2/W for flow rates between 120 and 480 mL/min. Benett et al.147 developed a plate C-MHX for diode laser bars using parallel silicon microchannels having a hydraulic diameter of 43 μm. A thermal impedance of 0.014 °C cm2/W was achieved experimentally. Dix and Jokar72 investigated the heat transfer performance of the plate C-MHX for high-power diode laser applications, as shown in Figure 11. Dimensions of the

Figure 10. Silicon parallel-flow C-MHX: (a) computational domain and (b) schematic illustration of the flow.

fluid properties, reducing the thermal resistance leads to an optimal design because thermal resistance is a function of the number of microchannels and dimensionless temperature. Thus, global thermal resistance was calculated using a classical definition (eq 2) in terms of non-dimensionless temperature (eq 3). RT =

max(Tw ) − Ti qLxLz

max(θw ) Rθ = NLx λl

Figure 11. Schematic diagram of the flow in a C-MHX with a microchannel cooling system. Reprinted with permission from ref 72. Copyright 2010 Elsevier.

(2)

microchannels were 1.5 × 10 × 27 mm with a minimum hydraulic diameter of 275 μm for the heat flux input region, which included 14 parallel zigzag channels consisting a depth of 300 μm. The hydraulic diameter was larger (500 μm) for the outside heat flux input region, which helped to decrease the pressure drop across the system. The straight microchannel design exhibited a 60% reduction in the pressure drop as compared to that of the symmetric design of equal diameter (240 μm) and approximately the same heat transfer performance (Nu = 8). In addition, the straight microchannel with hydraulic diameters of 150 to 240 μm resulted in optimal performance regarding heat transfer and pressure drop. Kang et al.148 developed a theoretical model to predict the hydrodynamic and thermal characteristics of a micro crossflow heat exchanger. The schematic structure and crosssectional view of a plate C-MHX reported by Kang et al.148 are shown in Figure 12. The average temperature of the hot and

(3)

For a water-cooled microplate C-MHX, a channel with width, depth, and pitch equal to 60, 700, and 100 μm, respectively, was optimized for conjugate heat transfer under constant power of 0.05 W.82 The heat transfer in the optimized C-MHX was enhanced by 20% as compared to that of the configurations designed by Tuckerman and Pease.130 Tuckerman and Pease130 demonstrated microchannel cold plates for the first time, resulting in a cooling performance of C-MHX, up to 790 W/cm2. However, higher pressure drops, higher cost, and manufacturing difficulties delayed the implementation of microchannel plates in electronics applications. A new technique called microresolution particle image velocimetry (micro-PIV) was used along with CFD for L


Review


Figure 12. Cross-flow C-MHX: (a) cross-sectional flow and (b) schematic structure showing the dimensions. Reprinted with permission from ref 148. Copyright 2007 Elsevier.

cold fluids was observed an important parameter, having a significant effect on the pressure drop and heat transfer rate (increases up to 40% for higher temperature). The heat transfer rate and pressure drop were also affected by the MOC and effectiveness due to higher thermal conductivity (2.7 times) of copper in comparison to that of silicon. The performance of a counter-flow C-MHX was investigated experimentally and numerically by Kee et al.73 Figure 13 illustrates the design of the internal manifold and the temperature of the fluid and solid, respectively. Each flow layer contained 10 microchannels, and the overall area of a microchannel was equal to 5000 mm2. The longitudinal conduction in the counter-flow arrangement reduced the heat transfer performance, particularly for high-effectiveness designs.41,149 In the counter-flow C-MHX, the axial gap between the microchannels allowed for pressure equalization due to improved flow distribution and reduced longitudinal wall conduction. Thus, a thermal model was developed to predict the thermal fields of solid material in addition to the hydrodynamics.73 Dang and Teng101,150 studied two different microchannel geometries; the S- and I-type geometries are shown in Figure 14. The effect of two different substrate thicknesses was investigated for the same microchannel with an identical means of connecting it to the manifolds. The increasing inlet temperature on the hot side was explained in detail. However, pressure drop and the performance index of

Figure 14. Different design configurations of the microchannels: (a) S- and (b) I-type. Reprinted with permission from refs 101 and 150. Copyright 2011 Elsevier and 2010 IEEE.

the heat exchangers were not discussed. A detailed analysis of fluid properties and geometrical design parameters were presented in terms of the pressure drop and performance index of S- and I-type microchannels for changes in temperature.101,151 The performance index is defined as the ratio of heat flux to total pressure drop in the C-MHX. The effect of the hydraulic diameter on the performance index was more significant (2-fold increase at dh = 300 μm as compared to dh = 180 μm) than that of the substrate thickness (13% higher at 2000 μm as compared to that at 1200 μm). It demonstrates that the lower the hydraulic diameter is, the higher the heat flux and the pressure drop will be. The heat flux and pressure drop in the S-type device were higher than those of the I-type despite the performance indices of both heat exchangers being essentially the same. Therefore, the microchannel design, dimensions, and inlet/outlet locations may greatly affect the hydrodynamics and heat transfer performance

Figure 13. Counter-flow microchannel heat exchanger: (a) design of the internal manifold and channel structure, (b) the flow arrangement, and (c) the solid body temperature. Reprinted with permission from ref 73. Copyright 2011 Elsevier. M


Review

Industrial & Engineering Chemistry Research of heat exchangers and should be carefully considered in heat exchanger design. The pressure drop, thermal oscillations, and density-wave are three main instabilities in flow boiling systems under reversed flow conditions.152 Qu and Mudawar153 studied the hydrodynamic instability in 21 parallel copper microchannels and reported that the pressure drop oscillations caused by growing number of bubbles in a narrow channel could be eliminated by throttling the upstream flow. Chang and Pan154 explored the two-phase flow instability in 15 parallel microchannels with a hydraulic diameter of 86.3 μm. Liu et al.155 experimentally studied the two-phase flow in a co- and counter-current C-MHX with gas heating. The top view of the C-MHX and a schematic diagram of the test section are shown in Figure 15. The cold side of the flow plate consists of 18

Figure 16. Vapor venting parallel-flow C-MHX. Reprinted with permission from ref 158. Copyright 2011 Elsevier.

advantage of VVMHE is that different types of membranes could be used due to the easy insertion and removal of membranes. So, the membranes could be studied to determine the impact of wear and fouling. However, reducing the steadystate pressure drop is one of the key requirements vapor venting technology. Entrance effects and conjugate heat transfer are generally considered in the design of a recuperator. However, a simplified design model is desired within an acceptable error range. Wang and Peterson proposed a simplified model (without considering conjugate heat transfer and entrance effects) for a new thermally activated cooling system made by integrating an organic Rankine cycle and vapor compression cooling cycle.31 The thermally activated cooling system and integrated microchannel boiler/recuperator (374.65 × 133.35 × 66.294 mm) are shown in Figure 17. Oil was used as the heat source with a temperature up to 200 °C.

Figure 15. Two-phase co- and counter-current microchannel heat exchangers: (a) top view and (b) schematic diagram of the test section. Reprinted with permission from ref 155. Copyright 2012 Elsevier.

microchannels in a diverging cross section design, which may enhance the stability of flow boiling and heat transfer efficiency.154,156,157 The mean hydraulic diameter was 240 μm. The two-phase flow patterns, flow instability, and efficiency were investigated using two-phase gas−liquid flow over the hot and cold sides of the microchannel heat exchanger. Four different flow patterns, specifically bubbly elongated slug flow, annular flow, dry out, and annular flow with liquid film breakup, were observed. The heat transfer efficiency (ratio of heat transfer rates of methanol to helium) was significantly enhanced by increasing the thermal power (from 0.2 at 1 W to 0.8 at 9 W) for both the single- and twophase flow, whereas the effect of thermal power was lower for the co-current C-MHXs. David et al. proposed a C-MHX with vapor venting parallel microchannels (VVMHE) for a 60% improvement in pressure drop with 4.4 °C reduction in the temperature over a nonventing device operating under the same conditions.158 The design and assembly of the VVMHE is shown in Figure 16. The heat transfer area was 19 mm × 5.5 mm, contained 19 microchannels, and measured 130 μm × 134 μm. The liquid and vapor microchannels were fabricated in a 2.4 mm thick copper plate. In the proposed two-phase flow system, the removal of vapor was the primary source of the pressure drop, which resulted an increase in the mass flux of the vapor. The model proposed by David et al.158 does not capture this complex behavior and hence under-predicts the increase in pressure drop with increase in mass fluxes. The major

Figure 17. Thermally activated cooling system: (a) integrated microchannel boiler/recuperator and (b) microchannel condenser. Reprinted with permission from ref 31. Copyright 2011 Elsevier.

The actual heat transfer effectiveness of the recuperator was significantly higher than the designed value of 85% due to a relatively conservative design approach.31 The thermally activated cooling system with integrated microchannels achieved a heat flux of over 5 kW with an overall coefficient of performance equal to 0.8. The thermally activated systems offer various advantages such as higher energy efficiency, higher indoor air quality, lower air emissions, and lower peak N


Review


Figure 18. Brazed microplate heat exchangers (BMPHE). Reprinted with permission from the Danfoss Group, www.danfoss.com.

Figure 19. Schematic diagrams of the different types of fin surfaces.

ment. Han et al.163 experimentally investigated the performance of a BMPHE with different chevron angles (45°, 35°, and 20°) by using different refrigerants (R410A and R22). The heat transfer coefficient decreased from 4000 to 2500 kW/m2 K with an increase in the chevron angle from 20° to 45°. They observed that for a given value of mass flux, the heat transfer coefficient increased with increasing vapor quantity and decreasing evaporating temperature. In addition, the heat transfer coefficients for R410A were found to be 33% higher than those of R22. The pressure drop increased with increasing mass flux and with decreasing evaporating temperature, and chevron angle, the pressure drops of R410A were less than those of R22. A novel microplate design for higher heat transfer rate in a BMPHE was proposed by the Danfoss Group. Microplate CMHXs are ideal for use in heat pumps, chillers, and closed-loop control systems with cooling capacities up to 400 kW. The fluid across the plate moves with a relatively uniform velocity and results in better mixing and a higher heat transfer rate (40%). The pressure drop decreases up to 35% as compared to that of a conventional brazed heat exchanger due to the uniform velocity. This results in less energy being required to drive the water around the system which consequently lowers operating costs. In addition to this, the improved plate design resulted in an enhanced flow within the heat exchanger that leads to less fouling and scaling. The Danfoss Group has

electricity demand. However, more efficient, reliable, and focused thermally activated technologies are required; these should be operated using a variety of energy sources including integration with lower waste of heat, combined heat and power (CHP) systems, clean fossil fuels, biomass, and eventually hydrogen. In another attempt to enhance a plate C-MHX, brazed microplate heat exchangers (BMPHEs) were investigated for compactness and higher heat transfer.159−163 The BMPHE comprised a brazed stack of aligned plates that enabled cocurrent or counter-current flow as shown in Figure 18. The higher turbulence in BMPHE leads to lower fouling rates and an enhancement in the heat transfer for a lower heat transfer area. Recently, brazing techniques have allowed the use of BMHEs for two-phase flow applications due to the realization of higher pressure (40 bar) and temperature (200 °C) capabilities. Our literature review showed that one BMHE can replace several shell-and-tube heat exchangers for refrigeration processes.159−161 An experimental study for quantifying the performance of a BMPHE whose vertical position was changed from the designed vertical position was reported by Kedzierski.162 It was reported that the R22 BMPHE condenser provides better heat transfer performance in the horizontal position as compared to that in the vertical position.162 However, quantifying the performance associated with inclination was limited and requires a detailed measureO


Review

Industrial & Engineering Chemistry Research reported many advantages of the microplate design. However, there is no comparative study available for the microplate design proposed by Danfoss, because there is a lack of details available regarding the geometrical design parameters. A comparative study based on detailed geometrical parameters (chevron type, chevron angles and mass flow rates) is necessary to improve the understanding. A careful review of this section reveals that heat transfer performance of C-MHXs can be evaluated by different experimental, numerical, theoretical, and micro-PIV techniques. We found that the performance of plate type C-MHXs depends on various parameters such as the type of geometry, geometrical parameters (such as channel width, height, and length as well as the hydraulic diameter), properties of the fluid (at constant or varying temperature) and the MOC of the channel. Similar to the conventional channel, the heat transfer efficiency of co-current C-MHXs with lower mass flux at a given gas flow rate is better for an evaporator, whereas for higher gas flow rates, the counter-current C-MHX is the better design. The counter-current C-MHX is recommended for application in a fuel cell due to its preferable performance characteristics. 3.2. Fin and Plate C-MHXs. C-MHXs with fin arrangement offer reliability with different combinations of gas, liquid, and two-phase fluids. As shown in Figure 19, different types of fin surfaces have been used in various types of C-MHXs. It is well accepted that louver-directed flow is important for heat transfer augmentation.45,164−169 However, there is limited information available to deal with the frosting, defrosting, and the design of louvered-fin C-MHX. This section of the Review analyzes different type of fins and their effect on the thermal and hydrodynamic performance of the C-MHXs. When designing a C-MHX and considering the frosting process, it is essential to investigate the effects the geometrical parameters have on air flow rate. Several studies observed a significant effect of the properties and growth mechanism of frost on plate-fin heat exchangers.166,168,170,171 Kondepudi and O’Neal165 reviewed the literature on finned-tube heat exchanger (fin on tube) performance and conducted frost growth research on louver-fin-round tube heat exchangers. Yan et al.166 investigated the performance of frosted finned-tube heat exchangers with plain fins, single-bank louvered fins, and multilouvered fins. The heat transfer coefficients were reduced up to 20% due to the frost formation. Kim and Groll167 reported a comparison between microchannel and fin-tube heat exchangers to investigate the effect of the geometrical design parameters including the number of fins per inch and heat exchanger inclination. In the C-MHX, the frosting time was observed 6.75% less than that of the fin-tube heat exchangers.167 A further decrease in the frosting time was observed with each cycle due to retained residual water at the end of each defrost cycle. Xia et al.168 studied the effects of frost, defrost, and refrost on the air-side thermo-hydraulic performance of a louvered-fin, flat tube heat exchanger using the experimentally validated numerical model for computing the frost thickness and blockage ratio. Padhmanabhan et al.169 compared the frost and defrost performance of a louvered-fin C-MHX with those of a fin-tube C-MHX that had straight fins employed as outdoor coils of a heat pump system. The S-shaped fin configuration was proposed for lower pressure drops such that the same heat transfer performance could be achieved.21 The S-shaped fin, microchannel plate, and a prototype of the C-MHX are shown in Figure 20. The

Figure 20. Microchannel heat exchanger: (a) S-shaped fin, (b) schematic illustration of the microchannel, and (c) a prototype of the C-MHX. Reprinted with permission from ref 21. Copyright 2009 Elsevier.

pressure drop in the S-shaped fin configuration was 5 times lower than that of the zigzag configuration and varied from 11.7 to 95 kPa/m with changes in the fin angle from 0° to 57°.171 The heat transfer rate of the S-shaped fin was identical (20.9−31.1 MW/m3) to that of the zigzag configuration.171 Nikitin et al.172 and Ngo et al.173 experimentally investigated the advantages of the S-shaped fin configuration in the recuperators for a CO2 gas turbine and CO2 heat pump system, respectively. Utamura and Nikitin10,174 made a specific comparison between a recuperator12 and a hot water supplier,167 both with S-shaped fins. Good agreement (within an experimental error of 5%) between the numerical and experimental results was reported. The flow stream was separated around the channel, since the S-shaped fin configuration comprises many discontinuous fins located in the flow channel. Therefore, the water flow in the S-shaped fin configuration was not a fully developed laminar flow. Hence, new correlations of the Nusselt number have been proposed for the S-shaped fin configuration, as summarized in Table 2. The correlations were obtained using generalized mean temperature differences instead of the logarithmic mean temperature difference. The proposed correlations showed a good agreement with the experimental results. A uniform flow profile was observed in the S-shaped fin heat exchanger due to the geometrical configuration. Consequently, the fluid velocity in S-shaped fin configurations was smaller than that in the other configurations; the discontinuous fins in the S-shaped configuration initiates turbulent flow conditions. Therefore, the S-shaped fin configuration has special characteristics for increasing heat transfer performance, and the effect of the Reynolds number on the Nusselt number correlations becomes weaker. The improvement in the microchannel heat exchanger design is accompanied with higher pressure drop. The Sshaped fin configuration was considered to be better than conventional zigzag-type fin because it provides practically the same heat transfer coefficient with a 7 times lower pressure drop.21,171 Jungi et al.175 experimentally studied the effect of varying the pitch of the fin, lengths, and heights, all subject to a constant tube-side water flow rate. A total of 16 different offset strip fins were tested, with the air-side Re ranging from 500 to 7500. The air-side thermal performance data were analyzed using the P


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complete plate assembly. Three designs, V1, V2, and V3, with varying fin thicknesses were modeled for three different porosity levels, 59%, 52%, and 46%. The model predictions agreed well with experimental data. As shown in Figure 22, the pressure drop increases exponentially for a transition from V1 to V3, with values of 550, 800, and 1000 Pa for V1, V2, and V3, respectively, at a given flow rate (10 mL/min). The heat transfer coefficient increases by a factor of 2 from 60 000 W m−2 K−1 at 2 mL/min to 120 000 W m−2 K−1 at 12 mL/min for the V1 design. Furthermore, the different designs (V1, V2, and V3) showed a significant improvement in the convective performance at a given flow rate. Heat transfer coefficients of 135 000 and 146 000 W m−2 K−1 were observed for V2 and V3 at a flow rate of 12 mL/min, respectively. Although finer heat transfer mesh results in higher heat transfer, it is at the expense of higher frictional losses. Hasan et al.183 studied the effect that shape and size of the cross section have on water flow in a counter-flow plate and fin type C-MHX. The heat exchanger effectiveness and pressure drop increased with decreasing microchannel size. The circular cross section was evaluated to be the best shape for the CMHX with a counter-flow arrangement, as it intensified the hydrodynamic and thermal performance. The schematic design of a plate and fin C-MHX proposed by Garcia-Hernando et al.3 is shown in Figure 23. The metallic plate and methacrylate square section were enclosed by the micro heat exchanger. Two different microchannel prototypes, one consisting of 100 microchannels with a 100 μm side and the other consisting of 50 microchannels with a 200 μm side, were designed and characterized. The friction factor f was experimentally calculated for a wide range of Re from 10 to 10000 and compared with the empirical values of f from classical and analytical correlations (eqs 4 and 5). The analytical equation includes a fully developed flow term (f fd) and the Hagenbach factor, K(x),184 evaluated for the entire length of the microchannels.66,185

effectiveness-number of transfer units (NTU) method. It was reported that heat transfer coefficients and pressure drop decrease with increasing pitch, height, and length of the fin. The friction (f) and Colburn (j) factors were also observed to decrease with increasing Re. Jungi et al.175 successfully highlighted the effect of geometrical design parameters. Nuntaphan et al.176 carried out a similar study on cross-flow heat exchangers with crimped spiral fins. The effects of the tube diameter, fin spacing, tube pitch, and tube arrangement were also studied. The heat transfer coefficient increased by 32% with a 36% reduction in the tube diameter at a constant flow rate. For an inline arrangement, an increase in the fin height increased the pressure drop and decreased the heat transfer coefficient significantly (approximately by half).176 However, the effect of height was prominent for a staggered fin arrangement. This was caused by the airflow blockage pressure drop term dominating over other pressure drop contributions in the staggered fin arrangement. Park and Jacobi177 studied the air-side thermal−hydraulic performance of a flat tube heat exchanger constructed with serpentine louvered, wavy, and plain fins. A significant effect of the fin spacing was observed on the f and j factors for both dry and wet conditions. The effect of fin spacing becomes more prominent at higher Reynolds numbers. Tang and Yang113 experimentally investigated the thermal performance of a single-row fin-and-tube heat exchanger. The experimental data were correlated using the Chilton−Colburn j-factor analogy, in combination with the least-squares power-law method. The air- and water-side Nu correlations were separately developed as a function of Re and Pr. Another complex design of a plate and fin C-MHX was constructed using micromachining in silicon with a threedimensional microchannel plate (20 × 20 mm2). A thermal impedance up to 15.9 C mm2 W−1 was achieved at a flow rate of 1.25 L/m with a pressure drop of 0.4 bar.178 A direct water jet for cooling the backside of an electronic chip was also reported with a thermal impedance and pressure drop of up to 15 C mm2 W−1 and 35 bar, respectively, for a given flow rate equal to 2.5 L/m.45,178,179 However, direct contact between the microprocessor and fluid is not desirable, as it necessitates advanced sealing and assembling. Specific numerical models were recommended for special types of C-MHX. For example, a numerical model was developed to compute the air-side heat transfer coefficient in an MHE for cross-flow conditions by Taler.180 Similarly, Wang et al.181,182 recommended a specific data reduction method to analyze the air-side performance of a fin-and-tube C-MHX. To solve the conjugate heat transfer in a unit cell stack, a new CFD model was proposed.24 Figure 21 shows the mesh element, the entire unit cell, as well as the

fexp =

2dh Lρv 2

2(fapp Re) dh

2

=

ΔP

(4)

2(ffd Re)μvL dh

2

+

K (x )ρ v 2 2

(5)

The experimental results were compared and found to agree well with classical theory. and no special effect was observed to be related to the small dimension (200 and 100 μm) of the channels. Similarly, there was no practical difference between the experimental heat transfer results and that derived from classical theory for medium and higher values of Re (400− 1000).184 However, the experimental results showed discrepancies with the classical correlations for lower values of Re due to overestimated values of the convection coefficients. An experimental investigation on a sinusoidal wavy C-MHX with a square cross section found that a wavy C-MHX provides a 4.5 times higher heat transfer coefficient as compared to that of the straight C-MHX.186 The literature review for this section reveals that different types of plate and fin arrangements have been studied for heat transfer enhancement. Most of the studies reported a higher heat transfer rate for fin C-MHXs. However, very limited work has been done to investigate the effects geometrical parameters such as triangular, square, rhombic, trapezoidal, pentagonal, and hexagonal cross sections except for rectangular C-MHXs. Therefore, more work must

Figure 21. Schematic diagram of a higher heat flux C-MHX for cooling and the assembly of the plate. Reprinted with permission from ref 24. Copyright 2010 Elsevier. Q


Review


Figure 22. Pressure drop and heat transfer coefficient vs flow rate per unit cell. Reprinted with permission from ref 24. Copyright 2010 Elsevier.

Figure 23. Plate and fin C-MHX: (a) schematic design and (b) a prototype with a 100 μm side. Reprinted with permission from ref 3. Copyright 2009 Elsevier.

be done to optimize the geometrical and flow parameters, the Reynolds number, and the heat flux to achieve enhancement via intensification of the role of the microchannels with different shapes. 3.3. Curved Tube C-MHXs. The design of heat exchangers with enhanced thermal efficiency has been a practical goal for decades. Microfluidics in combination with complex geometries offer new challenges and opportunities for heat transfer augmentation. A significant amount of work was carried out in an effort to enhance mixing and heat transfer by using curved geometries such as bent coil, spiral coil, helical coil, and coiled flow inverter.11,23,29,46,57,61,96,187−198 In passive techniques, the heat transfer augmentation depends mainly on efficient mixing and large heat transfer area. The curved tube is one of the passive techniques and provides prominent mixing with enhanced heat transfer caused by secondary flow in the transverse plane. The different curved geometries studied in the C-MHXs are shown in Figure 24. In curved C-MHXs, the heat transfer not only is a function of Re and Pr but also depends on the geometrical design parameters. The pressure losses and heat transfer in bent (L bend, T bend, and forkshaped) C-MHXs were investigated for Re ranging from 10 to 3000.29 In bent C-MHXs, the heat transfer effectiveness has been enhanced but with only a relative increase in the pressure drop. A ring-shaped C-MHX with a guide vane was designed based on the turning process for improved hydrodynamics.128 The guide vanes in C-MHXs can greatly enhance the flow distribution uniformity among the microchannels and, hence,

Figure 24. Different types of curved C-MHXs: (a) C-shaped, (b) T bend, (c) L bend, (d) Y-shaped, (e) S-shaped, (f) spiral coil, (g) helical coil, and (h) coiled flow inverter.

the heat transfer is enhanced for both the counter-current and co-current flow arrangements. Another curved geometry investigated for improving hydrodynamics and heat transfer is a wavy C-MHX with rectangular cross sections.193 Wavy CMHXs provided much better heat transfer performance as compared to the straight C-MHXs with the same cross section. The relative pressure drop in the wavy microchannels was negligible in comparison to the heat transfer enhancement. In R


1−900 − 200 rect

E, N E, N

N

191 192

202

a

E, N E N E 57 61 189 190

C

200−400 − rect circ

E, N 46

U U-coil

200 150−300 200 sq rect semi circ

E 96

U U C C

200 sq

N 11

serp

circ

circ

studya ref

geometryb

inlet typec

b

79

−

3.3−10.3 151 − − 150 −

− 1000

10 000), the heat transfer coefficients in the CFI were augmented up to 13% with a marginal increase in the pressure drop (2%−9%) as compared to those of a helical coil.50,52 The CFI heat exchanger was also compared with shell and tube (SHE) and plate heat exchangers (PHE). The CFI with At = 0.22 m2 provided 2.2−4.5 and 2−3.6 times higher overall heat transfer coefficient as compared to that from the SHE and PHE of At = 1.76 m2, respectively.58 The NTU in CFI was 3.7−7.5 times higher than that of SHE and 2−2.5 times higher than that of PHE. In addition to being implemented as a heat exchanger, the CFI could also be utilized as a continuous sterilizer,56 as a membrane absorber for CO2,53 and in simultaneous heat and mass transfer applications. Therefore, chaotic advection, which is the production of chaotic paths in the laminar regime, is a passive technique for increasing heat transfer. The chaotic trajectories are the main mechanism of enhancement of mixing and heat transfer in the chaotic advection regime. A recent study highlighted opportunities for the intensification of CFI design with a better utilization of the centrally located space shown in Figure 24.203 Thus, more studies are needed to design novel devices with the practical applications to the simultaneous heat and mass transfer operations.

Type of study: E, experimental; N, numerical. Geometries of micro heat exchangers (see Figure 24 for some types): str, straight tube; MHC, micro helical coil; MCFI, micro coiled flow inverter; U, Ushaped tube; serp, serpentine; C, C-shaped tube. cMicrochannel cross section (see Figure 4): sq, square; rect, rectangular; circ, circular; semi, semicircular; trap, trapezoidal.

Review



T

rectangular channel

microchannels

227

228

counter-flow microchannel heat exchangers

ridge/V/shield/straight slot groove/plain surface shaped microchannel heat exchanger

230

231

232

microchannel heat sink

229

226

224 225

microchannel with S-shaped fin rectangular straight/curved microchannel microchannel cold plates microchannel with triangular manifolds starfish-shaped microchannel micro gas turbine recuperator printed circuit with S-shaped fin plate-fin microdevices

microchannel separate heat pipe with louvered fin flow channel bifurcation integrated fin and microchannel compact heat exchanger

219

211

173

37

26

24 25

23

21

11 20

8 10

5

type of heat exchanger

multifunctional heat exchangers/reactors ceramic micro heat exchangers microchannels as heat sinks microchannel heat exchanger with S-shaped fins MST, MHC, MCFI microchannels as heat sinks

ref

4

CFD methodology

ANSYS FLUENT

CAN method: (CFD + ANN + NSGA-II) CFD: unsteady state model, SIMPLEC CFD model coupled with Navier−Stokes equation OpenFOAM: Eulerian and Lagrangian approaches thermal model based on the principles of continuum CFD and lattice Boltzmann approach

FLUENT: QUICK FLUENT

FLUENT, VISUAL BASIC ANSYS FLUENT

FLUENT

CFD: volume of fluid method FLUENT

ANSYS ICEM COMSOL

FLUENT

FLUENT

SIMPLEC, CFD-ACE FLUENT k-ε RNG Enhanced, RSM FLUENT FLUENT

TwoPorFlow code

FLUENT

good agreement

good agreement

good agreement

close agreement

good agreement

close agreement

close agreement

close agreement close agreement

good agreement

−

good agreement

good agreement

close agreement

close agreement good agreement

close agreement

good agreement agree with experimental data224 close agreement

close agreement close agreement

close agreement

close agreement

comparison to experimental results remarks

A satisfactory approximation of the heat exchanger performance was reported along with reduced computational time and resources.

The CFD and lattice Boltzmann methods were found appropriate to describe the effects of shape geometry and thermo-physical properties of liquid flow in microchannels.

Analytical equations are proposed for predicting the temperature and effectiveness of hot and cold fluids in counter-flow microchannel heat exchangers with non-adiabatic walls.

Simulations demonstrated that the pressure difference, inlet geometry, and wall heat flux are important parameters for the effectiveness of the micro heat exchanger. The results showed that a numerical method can predict the fiber web formation at the entrance of a microchannel heat sink. An auxiliary structured mesh and the neighbor cells reduced the computational time.

A relation between the Colburn factor and Fanning friction factor for the triangle fin geometry was developed using CFD coupled with artificial neural network. CFD techniques can predict the exact number of operational parameters at any point in membrane modules.

CFD was able to analyze and predict the effects of the flow channel bifurcation structure and dimensions on the flow uniformity. The flow characteristics of the integrated fin and microchannel heat exchanger were analyzed by three-dimensional numerical simulation.

Higher heat exchanger effectiveness was achieved when pressure drop occurred as a result of increased pipe length rather than pipe diameter combination. The thermal−hydraulic performances for the CO2 side and H2O side in fin and plate configurations were evaluated using three-dimensional CFD simulations. A new CFD-based optimization method was developed by integrating the model and mesh generator with the CFD simulator. The CFD results verified that the magnification of the outlet manifold area makes the flow distribution uniform. The volume of fluid method was applied to simulate the interfaces and two-phase flow in a microchannel separate heat pipe with louvered fin.

The experimental and numerically computed liquid volume fractions in the capillary region were in good agreement. with a relative error of ±10%.

Obtained analytical results were found to be in good agreement (error < 0%) with the three-dimensional CFD model for a wide range of studied parameters. The model can accurately predict the hydrodynamic and thermal performance of a microchannel cold plate. A methodical approach was presented to ascertain a design that balances low manifold volume and maintenance of flow uniformity.

The Nusselt number correlations were obtained based on numerical results for both the cold and hot sides.

Two approaches: one combines CFD analysis with an analytical method, and the other uses multiobjective genetic algorithms in combination with CFD. The temperature distributions, heat load, and overall heat transfer coefficient were predicted by CFD simulations with an accuracy of 11%, which was within the experimental data uncertainty. The effect of chaotic flow and flow inversion on the hydrodynamics and heat transfer can be demonstrated and analyzed using CFD. The numerical methods and procedures were validated by comparing the numerical and experimental data of laminar flow velocities from flow channels in a flow distributor.224

The flow of the liquid and gaseous fluids inside the one-dimensional channels was described by using a two-fluid model.

The turbulence models reproduce the experimental results very well, especially in the shear region (0 < r/R < 0.7) and flow core (0 < r/R < 0.4).

Table 4. Applications of CFD for Thermal and Hydrodynamic Analysis of C-MHXs



Review

not in agreement FLUENT: two-dimensional axis-symmetric CFD model 222

220 221

223

4.1. Hydrodynamics. Experimental results represent the real behavior of any heat transfer device with specific measuring errors. However, measuring the flow maldistribution in complex multiphase devices is difficult. The uniformity of fluid flow maldistribution is key for mixing and heat transfer augmentation since non-uniformity leads to poor heat exchanger performance, which is attributed to the improper design of the inlet, outlet, header configuration, distributor construction, and plate corrugations. CFD has proven to be an effective tool to adequately predict and analyze the flow maldistribution.9,11,206,212−217 Various possible models that might be used to carry out simulations on a plate heat exchanger with different corrugations are found in the literature, which validates the potential and possibility of CFD to undertake various issues encountered in heat exchangers.213,214 Perrotin et al.43 carried out two- and three-dimensional simulations of louvered fin and flat tube heat exchangers and observed that the space between the successive louvers was blocked at a low value of Re (78.6) due to the thin boundary layer between the air and the louver. The temperature of the air in that local region increased due to the hampered airflow path, which subsequently reduced the overall heat transfer rate. On the contrary, at higher Re, the boundary layer was found to be thin, and the air velocity aligned with the louvers. The flow parameters of the louvered fin and flat tube heat exchangers were analyzed using a fin angle-alignment factor for different configurations and Reynolds numbers.218 A decrease in the fin angle produced a uniform flow, resulting in increases in f and j. Recirculation zones were observed at the inclined section of the fin, indicating that inclined louvered fins give better results than slit or louvered fins. To simulate the interfaces and two-phase flow in a microchannel with louvered fins, the volume of fluid method was successfully applied.219 The cooling capacity increased (up to 4087 W) with the filling ratio (at 78%). Shah et al.215 successfully employed a three-block CFD model to investigate the hydrodynamics and heat transfer characteristics of a vertical mantle heat exchanger of a solar water heater. The computed results revealed that the recirculation produced by buoyancy significantly affects the fluid distribution along the mantle. In a similar heat exchanger, Knudsen et al.216 elucidated the mixed flow in the mantle close to the inlet via CFD investigation of the flow pattern inside the tank and mantle of the heat exchanger. Fernandes et al.217 studied a double sine−chevron plate heat exchanger for a range of corrugation angles (30°−85°) and channel aspect ratios (0.38−0.76) and demonstrated that the shape factor and tortuosity coefficient depend on the corrugation angle and channel aspect ratios. Several other authors11,219−223 emphasize the significance of CFD to visualize the flow maldistribution and its effect in various types of heat exchangers. The effect of chaotic flow and flow inversion on hydrodynamics and heat transfer in a microCFI was demonstrated and analyzed by using CFD.11 The effect of secondary flow was lower for shorter axial length, whereas with an increased axial distance, the centrifugal force pushed the fluid outward, making secondary flow maximize across the walls of the inner tube in the micro-CFI. In an another study,220 three-dimensional CFD simulations were successfully applied to develop a novel microchannel heat exchanger with S-shaped fins for the recuperator of CO2 gas turbine nuclear reactors. The review of the available literature

The temperature outlet histories were used in CFD to match the experimental data and the direct curve using least-squares criteria. The hydrodynamics and heat transfer properties of the three-dimensional rectangular microchannel heat sinks were computed numerically by solving the appropriate governing equations. The discrepancies were due to a difference between the operating frequency (144 Hz) and the resonant frequency (140 Hz) for the micro linear compressor, thus decreasing the motor efficiency. Second, in the CFD model, the mismatch of the axial temperature profiles between the regenerator and the pulse tube was ignored. good agreement good agreement COMSOL Multiphysics ANSYS CFX

good agreement FLUENT

good agreement

remarks CFD methodology type of heat exchanger

counter-flow micro heat exchanger microchannel heat exchangers with S-shaped and zigzag fin mini-channel regenerative rectangular microchannel heat sinks micro coaxial Stirling-type pulse tube cryocooler

ref

233

ANSYS FLUENT

comparison to experimental results

Table 4. continued

Temperature profiles measured in two dimensions inside the heat exchanger were in good agreement with profiles predicted by CFD. The temperature variation was correctly predicted along the axial and transverse directions (between channels). Three-dimensional CFD simulations were successfully applied to develop a novel microchannel heat exchanger with S-shaped fins for recuperators of CO2 gas turbine nuclear reactors.


U


Review


software packages are readily accessible and have met the requirements of researching various heat exchangers, for example plate, shell and tube, vertical mantle, compact, and printed circuit board exchangers. The simulations generally yield results that agree well with the results of experimental studies, with discrepancy ranging from 2% to 10%, though in some exceptional cases, it may vary up to 36%. When large deviations occur, user-defined sub-routines specific to the design problem may become necessary. The reliability of CFD results makes CFD an integral part of the design process, leading toward the elimination of prerequisite prototyping.

shows that CFD has been a strong tool for successfully establishing the flow maldistribution in a variety of complex heat exchangers. In experimentation, it is challenging and expensive to find the flow maldistribution in complex geometries. On the other hand, CFD is not only cheaper, but it is also an effective technique for studying the flow maldistribution as compared to experimentation. 4.2. Pressure Drop and Heat Transfer. The pressure drop and heat transfer in microchannel heat exchangers were already explained in detail in sections 2.1 and 2.2, respectively. Table 4 presents a variety of CFD models used to investigate the heat transfer and pressure drop performance in various geometries of MHEs. CFD has been utilized to address the hydrodynamics and thermal characteristics of MHEs by using two approaches, the thermal coefficients and effect of physical parameters. It can be noted that most models adequately predict the pressure drop and heat transfer. The computational results were found to agree well with experimental results. Researchers have pointed out that an adequate model must be selected according to various study parameters such as singlephase or multiphase, viscous or non-viscous, and laminar or turbulent flow conditions. 4.3. Fouling. MHEs offer process intensification and lower investment. However, the process stability of these miniaturized devices is not yet industrially viable. MHEs are extremely sensitive to undesirable deposition on the surface, which is known as fouling. Fouling results in a lower heat transfer coefficient and higher pressure drop, and it alters the residence time and flow maldistribution. Several studies have recognized the importance of CFD in determining the different parameters responsible for fouling in microchannel heat exchangers.48,149,205,214,234−239 The temperature difference between the wall and working media was one of the major sources of fouling in the food processing industry, which was explained by visualizing the weak temperature regions via CFD.214 The effect of corrugations and their position on fouling rates was also investigated for a microplate heat exchanger.205 A novel MHE with a smaller heat transfer area and a 92.6% reduced deposition rate, though with the same heat transfer duty, was proposed to establish the prospect of an unconventional MHE for food processing. Kockmann240 pointed out that enhanced mass flow rate is the key to enhancing transport processes and maintaining the efficient mixing performance with reduced fouling in microchannels (100−1000 μm). Another study238 reported a significant increase in the fouling rate (1 g for Re = 1700 and almost 22 g for Re = 3700) for increases in Re over a given time period. In general, the fouling in microscale devices is comparable to that at the macroscale. Mayer et al.239 investigated the impact of crystallization fouling on the heat transfer performance of a MHE. The fouling developed heterogeneously in microchannels due to supersaturated solution (CaCO3) and caused a decrease in the heat transfer performance along with an adverse increase in the pressure drop. Artificial neural networks can be employed for predicting the fouling factor by measuring a few variables, since experimental measurement of the degree of fouling is difficult, time-consuming, and is not accurate.241 Therefore, based on the discussion above, it may be argued that CFD is an effective tool for addressing the fouling problem in a wide variety of MHEs. CFD has emerged as a fast and cost-effective alternative to conventional methods, which are often tedious and expensive, for the design and optimization of MHEs. Commercial CFD

5. CONCLUSIONS A wide range of C-MHXs have been designed and developed to meet industrial requirements and application. This Review provides quantitative and qualitative analyses of the different types of C-MHXs. The conclusions drawn from the current Review are as follows. i. The experimental results in C-MHXs (1100 ≤ dh ≤ 2490) agree well with the conventional Poiseuille and Blasius correlations for the friction factor under laminar and turbulent flow. However, for gas flow in smaller channels, the experimental data in the turbulent regime were significantly lower than the conventional correlation. ii. The frictional pressure drop data show an early transition from laminar to turbulent flow at 1700 ≤ Re ≤ 1800 in both rough and smooth microchannels. The disparity in the results may be due to incorrect values of diameters provided by the vendor and overlooking or ignoring the entrance and exit effects in the friction factor calculations. However, experimental results considering the entrance and exit effect with experimentally measured values of diameters were found to agree well with classical theory. iii. For laminar flow conditions, the Nusselt number correlations proposed by different authors are neither in agreement with each other nor with the Hausen correlation. The value of Nu predicted by all the correlations significantly increases with increasing Re under laminar flow conditions, which signifies the dominant effect of the geometrical design parameters (such as tube diameter and type of cross sections) on the heat transfer performance of microchannel heat exchangers. iv. In microchannel heat exchangers, the difference between the classical theory and experimental results was caused by several new microfluidic phenomena acting simultaneously. Some of these factors are vortex initiation and the transition from laminar to turbulent flow at lower values of Re than that in the conventional size tubes. Other factors, such as slip effect, viscous dissipation, and compressible flow, are significantly important for microchannel devices, though these are usually neglected for conventional dimensions. Considering the importance of the microfluidic phenomena, new calculation methods should be developed that consider these processes at the micro level. v. Plate microchannel heat exchangers are promising MHEs, as the plate geometry significantly affects the fluid flow in the channels. V


Review

Industrial & Engineering Chemistry Research k Kn L Ma Nu Nux NuGn p Po Pr Pt PT ΔPexp ΔPpred Q q qm,p

vi. Passive techniques like chaotic mixing in a spiral coil or helical coil due to enhanced centrifugal force and flow inversion in a CFI due to a 90° bend are promising features that are otherwise not available in conventional heat exchangers. vii. C-MHXs technologies have common characteristics, e.g., safer operating conditions, compactness, enhanced heat transfer coefficient and selectivity, and energy savings. However, only a few C-MHXs have been implemented in industry; most have been developed at the laboratory scale, and thus scalability remains an important parameter to study. viii. Careful review of the literature confirms that CFD has emerged as a fast and cost-effective alternative to conventional methods used for the design and optimization of MHEs, which are often tedious and expensive. The reliability of CFD results makes it an integral part of the design process, leading toward elimination of the prerequisite of prototyping. In general, MHEs have limited industrial applications, and a better understanding of their characteristics is required before they can be scaled up. Technological advancements (such as three-dimensional printing) are expected to enable the development of more compact heat exchangers that will have industrial applications in the future.

■

R Re Recri RT t Ti Tw v V W Wc We WT w

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] or [email protected]. *E-mail: [email protected]. *E-mail: [email protected] or [email protected]. ORCID

Jogender Singh: 0000-0002-0630-6890 Alejandro Montesinos-Castellanos: 0000-0001-9249-8878

wc

Notes

X x

The authors declare no competing financial interest.

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■

ACKNOWLEDGMENTS This research is a product of the Project 266632 “Laboratorio Binacional para la Gestión Inteligente de la Sustentabilidad Energética y la Formación Tecnológica” [“Bi-National Laboratory on Smart Sustainable Energy Management and Technology Training”], funded by the CONACYT SENER Fund for Energy Sustainability (Agreement: S0019-2014-01).

μ ν θ Φ σ ρ λ δij ξc

■

NOMENCLATURE A area, m2 a channel aspect ratio [H/2W] Am amplitude of wavy microchannel, m B width of the slot nozzle for liquid impingement, m C, Cp specific heat, kJ/kg·K C* normalized friction constant c speed of sound, m/s Dc curvature diameter, m De Dean number dh, dt hydraulic diameter, m f friction factor G mass velocity, kg/m2·s h heat transfer coefficient, W/m2·K H, Hc microchannel height, m hfg latent heat of vaporization, J/kg j Colburn J-factor [hc·Pr2/3/VρCp]

■

thermal conductivity, W/m·K Knudsen number microchannel length m Mach number [V/c] Nusselt number local Nusselt number Nusselt number from Gnielinski correlation pressure, N/m2 Poiseuille number Prandtl number channel pitch pumping power, W experimental pressure drop, N/m2 predicted pressure drop, N/m2 volumetric flow rate, L/min heat flux, W/m2 critical heat flux based on heated channel inside area, W/m2 thermal resistance of a cross section, K/W Reynolds number transition Reynolds number thermal resistance, K/W tube wall thickness, m inlet temperature, K wall temperature, K inlet velocity, m/s fluid velocity, m/s microchannel width, m center-to-center distance of microchannel, m Weber number [ρv2L/σ] chip width, m half-distance between adjacent channels, non-dimensionalized with channel height half-channel width, non-dimensionalized with channel height mole fraction lateral distance from stagnation point, m

GREEK SYMBOLS dynamic viscosity, kg/(m·s) kinematic viscosity angular coordinate, deg enhancement ratio surface tension, N/m density of fluid, kg/m3 curvature ratio (Dc/dt) Dirac delta function zeta potential, V REFERENCES

(1) Jiang, P. X.; Fan, M.-H.; Si, G.-S.; Ren, Z.-P. Thermal−Hydraulic Performance of Small Scale Micro-Channel and Porous-Media HeatExchangers. Int. J. Heat Mass Transfer 2001, 44, 1039. (2) Bier, W.; Keller, W.; Linder, G.; Seidel, D.; Schubert, K.; Martin, H. Gas to Gas Heat Transfer in Micro Heat Exchangers. Chem. Eng. Process. 1993, 32, 33. (3) García-Hernando, N.; Acosta-Iborra, A.; Ruiz-Rivas, U.; Izquierdo, M. Experimental Investigation of Fluid Flow and Heat Transfer in a Single-Phase Liquid Flow Micro-Heat Exchanger. Int. J. Heat Mass Transfer 2009, 52, 5433. (4) Habchi, C.; Lemenand, T.; Valle, D. D.; Peerhossaini, H. Turbulent Mixing and Residence Time Distribution in Novel Multifunctional Heat Exchangers−Reactors. Chem. Eng. Process. 2010, 49, 1066.

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Process Intensification for Compact and Micro Heat Exchangers

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