GasâLiquid Sensible Heat Transfer in Spray and Packed Bed under a

Article pubs.acs.org/IECR

Gas−Liquid Sensible Heat Transfer in Spray and Packed Bed under a Centrifugal Field Abhijit Mondal, Avijit Bhowal,* and Siddhartha Datta Department of Chemical Engineering, Jadavpur University, Kolkata 700032, India ABSTRACT: Sensible heat transfer rates between a heated liquid (dibutyl phthalate) and an air stream in direct contact have been studied in different contactor configurations (spray, spray with liquid redistribution, and packed bed) wherein the liquid flows under the influence of centrifugal force rather than terrestrial gravity as in traditional equipments. Experiments were carried out by contacting the phases counter-currently between two coaxial circular rotating disks. The cooling range of the liquid in these contactors was obtained by varying mass flux of liquid and air, and the rotational speed between 0.35 and 0.67 kg/m2·s, 0.26 and 0.52 kg/m2·s, and 300 and 900 rpm, respectively. The cooling range in the spray mode of operation increased with rotational speed. The ratio of the cooling range obtained in rotating packed bed and spray operation decreased at higher rotational speed (other conditions remaining same). Below a critical rotational speed, the cooling range in spray operation could be further extended by redistributing the liquid in the spray zone. The overall volumetric heat transfer coefficients in these three contactors determined by simple mathematical models monotonically increased with centrifugal acceleration and were between 5 and 10 times higher than in traditional ones.

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terrestrial gravity has been exploited9−11 to reduce liquid film thickness, and permit use of high surface area packing for intensifying mass transfer rates in gas−liquid systems. The studies indicate that higher values of volumetric coefficients could be achieved and equipment size reduced for direct contact gas−liquid heat transfer as compared to traditional spray and packed bed contactors, if the liquid flow is dictated by centrifugal force. In view of the above-mentioned possibility of intensification in heat transfer rates, it is necessary to obtain comprehensive information on direct contact gas−liquid heat transfer rates achievable under centrifugal acceleration for potential industrial applications. However, no attempt appears to have been made in this direction. The objective of the present study was (i) examining the effect of rotational speed on the sensible heat transfer characteristics, and (ii) determining the volumetric heat transfer coefficient, in different contactor configurations.

INTRODUCTION Direct contact heat exchangers involve heat transfer between hot and cold streams of two phases in the absence of a separating wall. The process offers an attractive approach for energy recovery as compared to conventional heat exchangers because of manifold advantages such as higher effective heattransfer coefficients, absence of surface scaling, operation at low temperature differentials, among others. Existing technologies for direct contact gas−liquid heat exchange rely largely on spray columns, and columns with packing or trays. The operation is carried out in a vertical vessel. The liquid flows downward in these equipments under the influence of terrestrial gravity. Data involving purely sensible heat transfer for air−liquid system are not abundant. Fair1,2 proposed design correlations for several direct contact heat exchange devices such as packed column, sieve tray, and spray column. Spiegel et al.3 reported that overall heat transfer coefficient in packed (Mellapak 250.X) bed varied between 20 and 50 W/m2·K (liquid flow rate 3−25 m3/m2·h, air F-factor 0.9−2.2 m/s(kg/m3)0.5) for the dibutyl phthalate/air system. Designing efficient equipments is one of the most promising challenges for this process. Bruckner and Mattick4 conceptualized a direct contact liquid drop/gas heat exchanger for thermal management in space wherein a vortex chamber served the dual purpose of heat exchanger and separation of the fine droplets from the gas stream. Hattori et al.5 theoretically examined the thermal efficiency of a device in which the liquid flowed down wires suspended in the gaseous stream. The thermal energy recovery was shown to be higher than that accomplished by direct spraying of the liquid. Several researchers6,7 have studied the breakup of liquid jets from a rotating orifice. Drops produced were noted to become smaller with the increase of the rotational speed. The gas− liquid heat transfer coefficient increases with decrease of drop diameter according to available correlations.8 In recent years, rotating packed bed operating at hundreds of times the © 2012 American Chemical Society

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EXPERIMENTAL SECTION The system selected for the study was air/dibutylpthalate (DBP). The liquid has a very low vapor pressure, and hence the data can be used for directly evaluating the volumetric heat transfer coefficients.3 A general diagram of the experimental setup is shown in Figure 1. Heat transfer studies between dibutyl phthalate (DBP) and air flowing counter-currently were carried out between two coaxial stainless steel disks. Each of the disks was rotated by an AC motor through a shaft. The outer diameter of the disks and the distance between them were 0.32 and 0.03 m, respectively. The diameter of the cylindrical shaped stationary Received: Revised: Accepted: Published: 499

April 30, 2012 December 5, 2012 December 12, 2012 December 12, 2012 dx.doi.org/10.1021/ie301116s | Ind. Eng. Chem. Res. 2013, 52, 499−506

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of the experimental setup.

The temperatures were determined by Pt100 thermoresistors. All thermocouples were calibrated before use. The thermocouples were placed in the pipelines transporting the contacting phases into and out of the device. The inlet temperature of the liquid was maintained at 52 °C, while that of air was 25 °C. Experiments were continued until the outlet temperature fluctuations were within ±0.1 °C. Parameters were estimated from the average of two runs at the same experimental conditions. Heat capacity of DBP at 39.5 and 49.5 °C is 1.76 and 1.78 kJ/kg·K, respectively.12

casing enveloping the disks was 0.35 m. The outer surface of the casing and the disks was insulated. Air from a compressor was passed successively through a constant temperature bath and a moisture entrapment chamber before entering the contactor through three openings in the casing wall that were 120° apart. It then flowed inward between the disks and exited at a radial distance of ∼0.08 m from the rotational axis through perforations on one of the disks. The outlet of the air stream was provided ∼0.05 m radially outward from the liquid distributor to reduce its superficial velocity and extend the flow rates employable (especially in spray operations). DBP was stored in a reservoir with the provision of heating and agitation. It was pumped through coils immersed in a constant water bath into the contactor through a stationary distributor. The liquid was accelerated in the outward radial direction through a packed bed section rotating with the bed (indicated as W in Figure 2) to reduce mal-distribution even if the liquid jet velocity is low. The liquid was discharged from the equipment through an opening in the bottom of the casing wall. The details of the contactors studied are shown in Figure 2. In contactor A, the liquid was dispersed into the spray zone through a wire-mesh screen (100 × 100 mesh) aligned perpendicular in the flow direction. The wire diameter and percentage open area of the screen were approximately 0.1 mm and 30, respectively. In contactor B, a series of similar wire mesh screens (few of them shown in the figure) attached to the two rotating disks were placed at intervals of 1 cm in the spray zone. The wire mesh was wound over supports to provide rigidity. The wire diameter and openings of the support was ∼1.0 and 6.0 mm, respectively. The disks were rotated in the opposite direction at the same speed. In contactor C, the spray region of the previous contactors was filled by a stack of 20 circular wire meshes. The inner and outer diameters were 0.16 and 0.32 m, respectively. The packing was attached to one of the disks and rotated along with it. Both of the disks were rotated in the same direction.

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RESULTS AND DISCUSSION The heat balance in contactor A over a differential volume between the two disks may be written as dQ = (Ua)s (Tl − Ta) dV

(1)

where the differential volume element dV is (2)

dV = 2πrh dr

The term (Ua)s refers to the average overall volumetric heat transfer coefficient, Tl and Ta are the temperature of liquid and air at radial distance r, respectively, and h is the distance between the two disks. Substituting eq 2 into eq 1 and integration between the radius at which the gas enters (ro) and exits the rotor (ri) assuming (Ua)s is constant in this entire region yields (Ua)s =

1 π (ro2 − ri2)h

∫ T d−Q T l

a

QT 1 = 2 2 π (ro − ri )h (Tl − Ta)m

(3)

where (Tl − Ta)m is the mean temperature difference and QT is the thermal load. The influence of the rotational speed on (Ua)s estimated from the experimental data using eq 3 is depicted in Figure 3. The coefficient was noted to vary with rotational speed (ω), 500

dx.doi.org/10.1021/ie301116s | Ind. Eng. Chem. Res. 2013, 52, 499−506


Article

Corresponding magnitude of this quantity was determined in traditional spray columns by solution of eq 1 along with overall enthalpy balance. The volumetric gas-phase heat transfer coefficient (hga) in the latter is given by2 hg a = 0.89G 0.82L0.47 /Zsp0.38

(6)

In the estimation of (ΔTl)c, the magnitude of (Ua)s was considered to be equal to hga after neglecting the heat-transfer resistance in liquid phase. Figure 5 illustrates the ratio of (ΔTl)c in contactor A at ω = 900 rpm to that in a traditional spray column of volume and contacting zone length (Zsp) equal to that used in the present study. The volumetric coefficient in the former and latter contactor was estimated using eqs 5 and 6, respectively. The enhanced cooling range (2.5−5 times) in contactor A noted in Figure 5 is due to higher values of volumetric heat transfer coefficient achieved when terrestrial gravity is replaced by centrifugal acceleration (8−70g at ri). This is also supported by theoretical estimations of hga. The coefficient was determined to be 6.5 times higher at 70g as compared to g = 1 (L = 0.55 kg/m2 s) using eq 7 to estimate the gas-phase heat transfer coefficient8 (hg). hg =

⎛K⎞ 0.5 0.33 ⎜ ⎟(2 + 0.6Re Pr ) ⎝d⎠

(7)

The term d in the above relation was computed from the correlation given below for drops detaching from the wire mesh screen.13 ⎛ 12σ ⎞1/3 d = ⎜⎜ D⎟⎟ ⎝ πρl g ⎠

In the above equations, σ, g, d, and D represent the surface tension, terrestrial gravity (replaced by centrifugal acceleration in contactor A), diameter of liquid drops, and the wire mesh, respectively, and K, Re(dvtρa/μa), Pr, and μg are the thermal conductivity, Reynold’s number, Prandtl number, and viscosity of air, whereas vt is the terminal velocity of drops. Counter-rotation of the disk could also have a significant influence on hga. Soong et al.14 carried out flow visualization studies between two coaxial rotating disks using paraffin mist as the tracer. They noted that more turbulence was generated with counter-rotation of the disks as compared to corotation. Higher shear experienced by the gas would contribute toward increasing heat transfer rates as compared to conventional columns where such a mechanism is absent. Equations 7 and 8 suggest that volumetric coefficient larger than that depicted in Figure 3 could be achieved by fragmenting the liquid drops and increasing its terminal velocity in the spray zone. This is expected to be simulated in contactor B by the rotating wire mesh screens present in this region as the liquid is dispersed by gradually increasing centrifugal force in the radial direction (at constant rotational speed). Figure 6 compares the experimentally determined performance in terms of the ratio of the thermal load removed from the liquid phase (Ṁ lCl(ΔTl)c) in contactor B (ψsr) to that in contactor A (ψs). At the same operating conditions, ψsr/ψs is greater than 1.0 (i.e., (ΔTl)c higher in B) when the rotational speed is below 900 rpm. This points to the enhancement of the volumetric heat transfer coefficients due to liquid redistribution in contactor B. At a fixed liquid flow rate (L = 0.35 kg/m2 s), it is seen that ψsr/ψs increases with gas to liquid flow rate.

Figure 2. Details of the contactors.

liquid, and air flow rate. It was correlated to these experimental parameters by the following empirical equation: (Ua)s = e(ω 2ri)b Lc Gd

(4)

where ω ri is the centrifugal acceleration at ri, and L and G are the liquid and air mass flux at average radius, ravg = 0.5(ri + ro), respectively. The value of the exponents, b, c, d, and e, was obtained from regression analysis of experimental data. The final form of eq 4 is 2

(Ua)s = 7.14(ω 2ri)0.049 L0.234G 0.29

(8)

(5)

Figure 4 shows the parity plot of the experimental values of (Ua)s and that calculated using eq 5. The deviations are within ±10%. The cooling range of the liquid (ΔTl)c increased with rotational speed (constant G and L) in contactor A. 501



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Figure 3. Influence of rotational speed on overall volumetric heat transfer coefficient in contactor A.

Figure 4. Comparison of theoretical predictions of (Ua)s and experimental data in contactor A.

streams with ω. It was neglected in estimation of (Ua)s as the magnitude was not large enough to make any significant difference. Several simplifying assumptions were made to develop a mathematical model to determine the volumetric heat coefficient (Ua)sr in contactor B from the experimental data. It was assumed that equations used for contactor A were valid in the region between two successive redistributors at radial distance Si+1 and Si. Therefore:

Heat transfer studies have indicated15 that the adiabatic wall temperature within the region surrounding the point of liquid jet impingement exceeds the jet temperature due to frictional temperature rise from viscous dissipation. A similar phenomenon also occurs when the liquid impacts the wire-mesh screens present in the spray zone in contactor B. Thermal energy generation increases with ω as the ligaments/drops impinge on the wire mesh at a greater velocity. (This trend was verified by independent experiments in the absence of air flow.) The gradual decrease of ψsr/ψs as the rotational speed was varied from 300 to 900 rpm (Figure 6) can be attributed to added heat load exceeding the heat removed from the liquid due to expected increase of (Ua) with ω. The generation of frictional heat was also discerned in contactor A from the gradual rise in the discrepancy between enthalpy of the outlet and inlet

Ṁ l C l ΔTl, i = Ṁ a CaΔTa, i

(9)

and (Ua)sr = 502

Ṁ l C l ΔTl, i 1 π (Si2+ 1 − Si2)h (Tl − Ta)i ,m

(10)



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Figure 5. Theoretical estimation of enhancement of (ΔTl)c under centrifugal acceleration in spray mode of operation.

Figure 6. Comparison of thermal performance between contactors A and B.

where Ṁ l and Cl, Ṁ a and Ca are the mass flow rate and heat capacity of liquid and air, respectively, and ΔTl,i and ΔTa,i are the change in liquid and air temperature in this region. The redistributor surfaces were considered to be completely wetted by the liquid, and heat exchange between the streams at these surfaces was considered negligible. The frictional temperature rise of the liquid (ΔTfi) when it impacts the ith redistributor surface is given by ΔTfi =

Q̇ gi = Q̇ oSi

The constant Q̇ o was evaluated from the following equation: Q̇ g =

∑ Q̇ gi = Q̇ o ∑ Si i

i

(13)

The total frictional heat generated (Q̇ g) was assumed to occur only due to contact of liquid with the solid surface and was estimated from the enthalpy difference between the outlet and inlet streams. The volumetric heat transfer coefficient, (Ua)sr, was obtained by trial and error method such that the change of the temperature of the phases obtained by solving eqs 9−13 was equal to the experimentally determined values. The plot of (Ua)sr versus rotational speed for some of the experimental conditions is presented in Figure 7. The

Q̇ gi Ṁ l C l

(12)

(11)

The frictional heat generation at this surface (Q̇ gi) was considered to be proportional to the radial position of the redistributor, that is: 503



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Figure 7. Variation of overall volumetric heat transfer coefficient in contactor B.

Figure 8. Comparison of theoretical predictions of (Ua)sr and experimental data in contactor B.

coefficient was related to the operating parameters through the following equation: (Ua)sr = 13.83(ω 2ravg)0.1(L)0.274 (G)0.49

Table 1. Volumetric Heat Transfer Coefficient in Spray Mode of Operation volumetric heat transfer coefficient (kW/m3·K)

(14) conventional spray column conventional spray column with liquid redistribution contactor A contactor B

using the same procedure mentioned earlier for contactor A. It is seen in Figure 8 that eq 14 predicted the experimental values obtained in contactor B to within ±15%. Comparison of eqs 14 and 5 suggests that the operating parameters exert a greater influence on the volumetric coefficient when the liquid is redistributed. The range of variation of the volumetric heat transfer coefficient in contactors A, B, and traditional spray column is listed in Table 1. The coefficient for contactors A and B was estimated from the presented correlations for rotational speed, L, and G varying between 300 and 900 rpm, 0.35 and 0.67 kg/

0.47−1.12 1.0−2.5 4.7−7.5 9.0−18.2

m2·s, and 0.26 and 0.52 kg/m2·s, respectively. For the traditional device, the value of Zsp in eq 6 was taken to be 0.01 m (distance between successive wire mesh screen) when liquid is redistributed, and (ro − ri) in its absence. The magnitude of the coefficient is seen to be 7−10 times higher 504



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Figure 9. Comparison of thermal performance between contactors C and A, and B and A.

configuration similar to that used in this study. This implies that the value of the heat-transfer coefficients should be nearly the same in conventional and rotating packed bed. The magnitude of (Ua)p was determined to vary between 8.5 and 21.4 kW/m3·K. In comparison, the overall heat transfer coefficient in a conventional packed bed3 (surface area = 250 m2/m3) for DBP/air system is ∼3.50 kW/m3·K at L and G = 0.67 and 0.52 kg/m2·s, respectively. The larger values of (Ua)p obtained in contactor C as compared to that in conventional packed bed appear to be largely due to higher packing area (∼1700 m2/m3) in the former. The cooling range, that is, (ΔTl)c, was ∼1.9 times higher in rotating packed bed (experimental) as compared to that obtained theoretically in the conventional contactor. Liquid mal-distribution in rotating packed beds has been reported by Burns and Ramshaw.17 In fact, the fraction of the packing surface wetted by the liquid calculated using Onda’s relation18 is ∼0.2 only for the operating conditions. This is one of the possible reasons for the volumetric heat transfer coefficient in rotating packed bed estimated with the stated assumptions being not significantly higher than in contactor B and commensurate with the large packing surface. The analysis also suggests that heat exchange with the packing and effective thermal conductivity of the bed may have played a major role in determining the thermal performance of the rotating packed bed.

when direct heat exchange is carried out under centrifugal acceleration. The ratio of the thermal load removed from the liquid (ψp) in the rotating packed bed (C) to that in spray mode of operation (A) is illustrated in Figure 9. For comparison, the plot of this quantity determined in contactor B at identical experimental conditions (represented by open symbols and dashed lines) is also given in the same figure. The trend of the profiles is similar to that in contactor B. However, ψp is slightly higher as compared to ψsr. The heat balance over a differential element in contactor C with the consideration that the packing surface is uniformly wetted by the liquid and frictional heat per unit volume, Q̇ gv, is generated as the liquid flows in contact with the packing surface is given by Ṁ l C l

dT dTl = Ṁ a Ca a + Q̇ gv 2πrh dr dr

(15)

dTa = −(Ua)sr (Tl − Ta)2πrh dr

(16)

Ṁ a Ca

The values of the volumetric heat transfer coefficients in contactor C, (Ua)p, were determined from the experimental data by solving the above two equations. The term latter Q̇ gv was expressed as

Q̇ gv = Q̇ ′o r

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(17)

CONCLUSIONS The possibility of employing centrifugal force for enhancing direct contact sensible heat transfer between gas and liquid stream has been investigated in spray and packed column. The volumetric heat transfer coefficient in the former and latter modes of operation was estimated to vary between ∼4.5 and 7.5 kW/m2·K, and 8.5 and 21 kW/m2·K, respectively. These values are 5−10 times greater than in corresponding traditional devices, suggesting that the equipment size can be reduced by this means. In spray mode of operation under centrifugal acceleration, the volumetric heat-transfer coefficient was further enhanced by 2−3 times when liquid redistributors were employed. However, its direct translation to achieving

The constant Q̇ ′o was estimated by equating the integral Q̇ gv over the entire packed bed volume to Q̇ g, that is: Q̇ g =

∫r

i

rod

(Q̇ ′o r )2πrh dr

(18)

Further, the heat transfer in the spray region between outer radius of disks (rod) and casing wall was considered negligible. In contactor C, the disks were rotated in the same direction to prevent heat generation from contact between the packing and the counter-rotating disk. Sandilya et al.16 noted that the tangential slip velocity was negligible, and the gas undergoes solid-body-like rotation in their rotating packed bed of 505



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Greek Symbols

significantly higher cooling range of liquid is restricted by frictional heat generation due to contact of the liquid with packing surface. Flow nonidealities appear to be a major impediment toward achieving high thermal efficiency in rotating packed bed. More detailed experiments and rigorous modeling are required to determine the actual gas−liquid heat transfer coefficient by incorporating the thermal resistance of the bed as distinguished from the apparent ones reported here.

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AUTHOR INFORMATION

Corresponding Author

ρ = density (kg/m3) ω = rotational speed (rad/s) (ΔTl)c = cooling range of liquid (°C) ϕsr/s = ratio of thermal load removed from liquid (contactor B/A) σ = surface tension (N/m) μ = viscosity (kg/m s) ψ = thermal load removed from liquid (kW)

REFERENCES

(1) Fair, J. R. Designing Direct-Contact Coolers/Condensers. Chem. Eng. 1972, 40, 91−100. (2) Fair, J. R. Direct contact Gas-Liquid Heat Exchange for Energy Recovery. J. Sol. Energy Eng. 1990, 112, 112−120. (3) Spiegel, L.; Bomio, P.; Humkeler, R. Direct Heat and Mass Transfer in Structured Packings. Chem. Eng. Proc. 1996, 35, 479−485. (4) Bruckner, A. P.; Mattick, A. T. High Effectiveness Liquid Droplet/Gas Heat Exchanger for Space Power Applications. Acta Astronaut. 1984, 11, 519−526. (5) Hattori, K.; Ishikawa, M.; Mori, Y. H. String of Liquid Beads for Gas-Liquid Contact Operations. AIChE J. 1994, 40, 1983 −1992. (6) Partridge, L.; Wong, D. C. Y.; Simmons, M. J. H.; Parau, E. I.; Decent, S. P. Experimental and Theoretical Description of the Breakup of Curved Liquid Jets in the Prilling Process. Chem. Eng. Res. Des. 2005, 83, 1267−1275. (7) Wong, D. C. Y.; Simmons, M. J. H.; Decent, S. P.; Parau, E. I.; King, A. C. Break-up Dynamics and Drop Size Distributions created from Spiralling Liquid Jets. Int. J. Multiphase Flow 2004, 30, 499−520. (8) Fair, J. R.; Steinmeyer, D. E.; Penney, W. R.; Crocker, B. B. Gas Absorption and Gas-Liquid systems Design. In Perry’s Chemical Engineers’ Handbook, 7th ed.; Perry, R. H., Green, D. W., Eds.; McGraw-Hill International: Singapore, 1998; pp 14−56. (9) Ko, C.-H.; Guan, C.-Y.; Lu, P.-J.; Chern, J.-M. Ozonation of Guaiacol solution in a Rotating Packed Bed. Chem. Eng. J. 2011, 171, 1045 −1052. (10) Lin, C.-C.; Chen, B.-C. Carbon Dioxide Absorption in a CrossFlow Rotating Packed Bed. Chem. Eng. Res. Des. 2011, 89, 1722−1729. (11) Lin, C.-C.; Lin, Y.-H.; Tan, C.-S. Evaluation of Alkanolamine solutions for Carbon Dioxide Removal in Cross Flow Rotating Packed Beds. J. Hazard. Mater. 2010, 175, 344−351. (12) Rohác, V.; Fulem, M.; Schmidt, H. G.; Rùzicka, V.; Rùzicka, K.; Wolf, G. Heat Capacities of some Phthalate Esters. J. Therm. Anal. Calorim. 2002, 70, 455−466. (13) Huang, L. S.; Yao, S. C. Dripping Phenomena of Water Droplets Impacted on Horizontal Wire Screens. Int. J. Multiphase Flow 2002, 28, 93−104. (14) Soong, C.-Y.; Wu, C.-C.; Liu, T.-P. Flow Structure between Two Co-axial Disks Rotating Independently. Expt. Therm. Fluid Sci. 2003, 27, 295−311. (15) Li, D.-Y.; Guo, Z.-Y.; Ma, C.-F. Relationship between the Recovery Factor and the Viscous Dissipation in a Confined, Impinging, Circular Jet of High-Prandtl Number Liquid. Int. J. Heat Fluid Flow 1997, 18, 585−590. (16) Sandilya, P.; Rao, D. P.; Sharma, A. Gas-Phase Mass Transfer in a Centrifugal Contactor. Ind. Eng. Chem. Res. 2001, 40, 384−392. (17) Burns, J. R.; Ramshaw, C. Process Intensification: Visual Study of Liquid Maldistribution in Rotating Packed Beds. Chem. Eng. Sci. 1996, 51, 1347−1352. (18) Onda, K.; Takeuchi, H.; Okumoto, Y. Mass Transfer Coefficients Between Gas and Liquid Phases in Packed Columns. J. Chem. Eng. Jpn. 1968, 1, 56.

*Tel.: +91 033 24146378. Fax: +91 033 24137121. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial assistance provided under the UPE (Phase II) scheme of Jadavpur University is deeply appreciated.

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NOMENCLATURE C = heat capacity (kJ/kg·K) d = diameter of liquid droplets (m) D = diameter of wire mesh (m) g = terrestrial gravity (m/s2) G = mass flux of air estimated at the mean radius (kg/m2·s) h = spacing between the two rotating disks (m) hg = gas side heat transfer coefficient (kW/m2·K) hga = volumetric gas side heat transfer coefficient (kW/ m3·K) K = thermal conductivity of air (kW/m·K) L = liquid mass flux at the average radius (kg/m2·s) Ṁ = mass flow rate (kg/s) Nuh = Nusselt number based on channel height Pr = Prandtl number of air Q̇ gi = frictional heat generation at ith distributor surface in contactor B (kW/m) Q̇ o,Q̇ ′o = constants in contactors B and C, respectively Q̇ ′gv = frictional heat generation constant in contactor C (kW/m4) Q̇ g = total frictional heat generated (kW) Re = Reynolds number (dvtρa/μg) r = radial position (m) ravg = average of inner and outer radii of the contacting region (m) ri = radius at which gas exits the contactor (m) ro = outer radius of disks (m) Si = radial distance of ith wire mesh screen from rotational axis in contactor B (m) T = temperature (°C) Ua = overall volumetric heat transfer coefficient (kW/m3·K) vt = terminal velocity of liquid droplets (m/s) Zsp = height of the contacting zone in conventional spray column (m)

Subscripts

a = air l = liquid m = mean p = packed bed sr = spray with liquid redistributor s = spray 506


GasâLiquid Sensible Heat Transfer in Spray and Packed Bed under a

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