RESEARCH NOTE pubs.acs.org/IECR
Measurements of Local Nusselt Number with a Miniscale Laminar Confined Slot-Jet Impinging on a Flat Plate Dae Hee Lee* School of Mechanical and Automotive Engineering, High Safety Vehicle Core Technology Research Center, Inje University, 607 Obang-dong, Gimhae, Gyeongnam 621-749, Korea
Daniel Trainer School of Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
Jun Sik Lee and Hyun Jin Park Graduate School of Mechanical Engineering, Inje University, 607 Obang-dong, Gimhae, Gyeongnam 621-749, Korea ABSTRACT: Heat transfer characteristics in a miniscale laminar confined slot-jet on a heated plate at uniform heat flux are experimentally investigated. The effects of the jet Reynolds number (Re = 120180) on the heat transfer and flow are considered. An electrically heated gold film Intrex (a very thin gold-coated polyester substrate sheet) is used to create a uniform heat flux on the flat surface. The temperature on the surface is measured by thermochromic liquid crystals and a digital color image processing system. Recorded color images of liquid crystals are then used to determine the local Nusselt numbers along the surface. The results show a peculiar behavior in that the Nusselt number increases between Re = 120 and Re = 140, suddenly drops at around Re = 150160, and increases again beyond Re = 160. This sudden drop of Nusselt number at around Re = 150160 may be caused by a sinusoidal fluctuation of the jet flow.
1. INTRODUCTION Owing to relatively high heat transfer rates, impinging jets have been widely used in many industrial applications such as gas turbine blade cooling, electronic equipment cooling, glass tempering, papers drying, and food heating and cooling.13 The laminar impinging slot-jet at low Reynolds number has been often used for the cooling of electronic components such as MEMS (micro-electro-mechanical systems) since it creates a relatively low noise at the nozzle exit. Because the velocity-driven noise level at the nozzle exit becomes larger as Reynolds number increases, an application of the turbulent impinging jet in such MEMS devices has limitations due a high noise level caused by a high jet velocity. Heat transfer studies with confined impinging slot-jets have increased with the growing need for the cooling of MEMS devices, since the confined jets have an advantage of concentrating cooling effects in a relatively narrow area.49 Recently, a number of studies have been carried out with laminar impinging jets. Lin et al.4 performed an experimental investigation of fluid flow and heat transfer characteristics of a confined slot-jet impingement. They studied the effects of jet Reynolds number (ReD = 1901537) and ratio of nozzle-toplate distance to nozzle width (H/W = 18) on heat transfer and obtained empirical correlations for stagnation and average Nusselt numbers. They also found that the Nusselt number is significantly affected by jet Reynolds number, while it is not significantly influenced by nozzle-to-plate distance. In another experimental study, Choo et al.5 investigated heat transfer characteristics of a microscale slot-jet impinging on a flat r 2011 American Chemical Society
plate. Their experiments were carried out for Reynolds number from 150 to 5000 and nozzle-to-plate distances from 0.5 to 10. They developed empirical correlations on the stagnation and average Nusselt numbers as a fuction of Reynolds number and nozzle-to-plate spacing. They found that at Re g 2500 the heat transfer characteristics of the microscale impinging slot-jet are different from those of the macroscale impinging slot-jet. Zhou and Lee6 studied fluid flow and heat transfer characteristics of a sharp-edged rectangular air jet (aspect ratio of 4)) impinging on a heated flat plate. They studied the effects of jet Reynolds number (Re = 271525005) and nozzle-to-plate distance (Z/B = 120) on local and average Nusselt numbers. They found that jet Reynolds number, nozzle-to-plate distance, and turbulence intensity have an important influence on the heat transfer of a impinging rectangular jet, especially on the impingement region. Cho7 numerically investigated a laminar bifurcating jet impinging on a plane in a confined channel and observed intermittent, then continuous, flapping motions at Reynolds numbers between 130 and 160. Lee et al.8 used the periodic flapping motion of a bifurcating jet impinging on a V-shaped plate to build a MEMS flow sensor capable of sensing very low flow velocities. Lee et al.9 studied the unsteady two-dimensional fluid flow and heat transfer in a confined impinging slot-jet using a finite volume numerical Received: August 18, 2010 Accepted: April 19, 2011 Revised: March 26, 2011 Published: April 19, 2011 6508
dx.doi.org/10.1021/ie101738y | Ind. Eng. Chem. Res. 2011, 50, 6508–6512
Industrial & Engineering Chemistry Research
RESEARCH NOTE
Figure 1. Overall set-up of the experimental apparatus.
Figure 2. Schematic diagram of the heat transfer measurement section.
method. Their numerical studies were undertaken at Reynolds numbers (on the basis of nozzle width) between 50 and 500, and ratios of nozzle-to-plate distance to nozzle width between 2 and 5. The present research experimentally studies heat transfer characteristics in a miniscale laminar confined slot-jet on a plate wall at a uniform heat flux. The fully developed air jet issuing from a long slot-nozzle impinges perpendicularly on the wall inside the double-sides closed duct, bifurcates, and exits in two opposite directions. An electrically heated gold film Intrex (a very thin gold-coated polyester substrate sheet) is used to create a uniform heat flux on the wall. The temperature on the surface is measured by thermochromic liquid crystals and a digital color image processing system.
2. EXPERIMENTAL APPARATUS AND PROCEDURE 2.1. Experimental Apparatus. Figure 1 shows the schematic diagram of the experimental apparatus set-up. Air for the jet was
supplied from an air compressor with a line pressure set at 100 kPa. The air passed through a constant temperature water bath and an inline electric heater to adjust the jet temperature exiting from the nozzle exit to become nearly the same as the ambient temperature. The air temperature at the heater exit was monitored using an E-type thermocouple whose junction was positioned at the tube centerline. The air then passed through a flow meter equipped with a microcontrol valve. Air exiting the flow meter was led to a stagnation chamber, and finally down to a 1.3-mm slot nozzle. Figure 2 shows a schematic diagram of the heat transfer measurement section. The material used to construct the nozzle and channel was a 5-mm-thick clear acrylic. A cross-sectional area of the nozzle was 1.3 mm 100 mm with an aspect ratio of 77. The large aspect ratio between height and width eliminated a possible end effect at the nozzle and led to a situation of truly two-dimensional planar jet. The nozzle width was precisely measured by using a toolmaker’s microscope to an accuracy of (0.001 mm. 6509
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Industrial & Engineering Chemistry Research
RESEARCH NOTE
It should be noted that the nozzle had an entrance length of 100 mm, which was long enough to ensure that the jet flow at the nozzle exit had a fully developed velocity profile. A calibrated E-type thermocouple was placed near the nozzle exit to measure the jet temperature to an accuracy of (0.1 oC. The duct was 140 mm long and 100 mm wide. The impingement wall of the channel was 100 mm away from the nozzle exit. Behind the impingement wall, an air pocket was constructed as shown in Fig. 2, with an internal space of 0.01 m. This space of air pocket effectively blocked the conduction heat loss from the heated surface and the heat loss due to the conduction was assumed to be negligibly small in the Nusselt number calculation. The jet nozzle and channel were positioned so that the nozzle exit pointed upward and the impingement wall pointed downward. This vertical orientation was used to minimize thermal buoyancy effects. The test plate surface was heated with gold film Intrex (a 0.13 mm thick polyester substrate sheet on which an approximately 20 Å thick gold-coating is applied). A DC current was supplied to the Intrex via bus bars (copper tape) at opposite edges, which were connected to a power supplier. A good electrical connection between the copper and gold was made by a silver-loaded paint. The constant current passing through the Intrex created a uniform heat flux of approximately 1130 W/m2 at the surface. On the backside of the Intrex (uncoated polyester), we applied first a thin layer of black paint and second a thin layer of microencapsulated thermochromic liquid crystal using an air brush. When white light was directed onto the liquid crystal, the reflected color varied depending on the temperature. To determine quantitatively the particular color and to minimize a visual bias, an in-situ calibration technique using a digital color image processing system was used. The measurement technique in this study, described by Lee et al.,10 provides a method for determining the surface isotherms using liquid crystal. Unwanted heating of the surface by the white light was avoided by illuminating the liquid crystal-coated surface using a fiber optic lamp. Images of the liquid crystal were recorded using a macro-lens-equipped digital camera and later analyzed to obtain local heat transfer coefficients. 2.2. Experimental Procedure. The air line was pressurized and the flow meter was set to a certain flow rate that produced the desired Reynolds number at the nozzle exit, beginning with Re = 120. The Reynolds number is defined on the basis of the nozzle width (B) and determined from Re ¼
uB ν
ð1Þ
The power supply into the Intrex was adjusted until the liquid crystal color images appeared on the impingement surface. The system was allowed to run for 10 minutes in order to reach a steady-state; during this 10-minute period, the incoming air temperature was maintained at around 21 °C. Once the system reached a steady-state, photos of the liquid crystal color images on the impingement surface were taken, and the voltage and current into the Intrex were also recorded along with the jet air temperature. The Reynolds number then increased by 10 and the same measurements were repeated until a Reynolds number of 180 was reached.
3. DATA REDUCTION The data analysis was performed using MATLAB. Photos of the liquid crystal color images were loaded into the program and
Figure 3. Local Nusselt number distributions at different Reynolds numbers.
viewed using the MATLAB Image Toolbox. The toolbox allowed the image pixels to be quickly selected and their location to be viewed on an xy scale. The surface temperature data from each photo was used along with the corresponding voltage, current, and air jet temperature to calculate the local heat transfer coefficients and Nusselt numbers. Assuming that all of heat generation by the gold film Intrex was convectively transferred (we explained in the preceding section that the conduction heat loss through the back of the heated wall was effectively blocked by the air pocket), the net heat flux on the heated surface was determined from qw ¼
VI WL
ð2Þ
The local heat transfer coefficient and Nusselt number were determined from hx ¼
qw Tw Tj
Nux ¼
hx B k
ð3Þ
ð4Þ
The flow was considered to be incompressible, and its thermal properties were assumed to be constant and evaluated at the freestream temperature.
4. DISCUSSION OF RESULTS The local Nusselt number distributions are plotted in Figure 3 against the lateral distance from the stagnation point at different Reynolds numbers. It is shown that the local Nusselt number increases between Re = 120 and Re = 140, and at both Re = 150 and 160 the local Nusselt number is significantly reduced compared to Re = 140 at and near the stagnation point. The local Nusselt number then increases as the Reynolds number increases from 160 to 180. It is also observed that the Nusselt number distributions are all clustered for distance coordinates x/B > 2.0 on both sides of the confined channel. Cho7 showed in his numerical study of the same set-up as ours that as the Reynolds number increases from 130 to 140 to 150, the flow entered an impulsive intermittent state, which describes a sort of flapping motion as the flow exits the nozzle. He then stated that as the Reynolds number increases to 160 the flow enters a continuous sinusoidal flapping state. 6510
dx.doi.org/10.1021/ie101738y |Ind. Eng. Chem. Res. 2011, 50, 6508–6512
Industrial & Engineering Chemistry Research Table 1. Nusselt Number Uncertainty Analysis Xi
value
δXi
(δXi/Nu)(∂Nu/∂Xi) 100 x/B = 6
I
0.697 (A)
.005
V
8.760 (V)
.01
B L
0.73
RESEARCH NOTE
flat plate significantly alters the heat transfer characteristics with a moderate change in Reynolds number. Therefore, special care should be taken for determining the nozzle size and operating condition in the microflow sensor.
0.12
’ AUTHOR INFORMATION
0.0013 (m)
5 10
-5
3.89
5 10-4
Corresponding Author
0.09 (m)
0.56
W
0.06 (m)
5 10-4
0.84
Tw
35.23 (°C)
0.2
1.43
Tj
21.09 (°C)
0.1
0.72
total Nusselt number uncertainty
4.39
Cho’s numerical results are in good agreement with our experimental results and explain the reason why the Nusselt number decreases when the Reynolds number above 140 can lead to a loss of forward momentum in the flow. This loss of forward momentum affects heat transfer near the stagnation point, while not having a significant impact on heat transfer in the wall jet region further away from the stagnation point as shown in Figure 3. The subsequent increase of heat transfer as the Reynolds number increases beyond 160 is expected as overall flow velocities are continuing to increase. The Nusselt number uncertainty analysis has been carried out using methods suggested by Kline and McKlintock11 with a 95% confidence level of both the bias and precision errors. Table 1 shows that the Nusselt number uncertainty for x/B = 6 at Re = 180 is 4.39%. It should be noted that this uncertainty represents the maximum uncertainty in the Nusselt number under the given experimental conditions. The uncertainty due to the nozzle width is the largest contribution to the total Nusselt number uncertainty. Another important source of uncertainty is the wall temperature measured by liquid crystal. It is worthy to note that the total Nusselt number uncertainty can be reduced by more precise machining of the nozzle and more accurate measurement of its size.
5. CONCLUSIONS We experimentally studied the heat transfer characteristics of a miniscale laminar slot-jet impinging on a plane in a double-sided closed duct. The effects of the jet Reynolds numbers (Re = 120180) on the heat transfer were considered. An electrically heated gold film was used to create a uniform heat flux on the flat surface. Temperatures on the surface were measured by thermochromic liquid crystals, and a digital color image processing system captured liquid crystal color images and calculated the Nusselt numbers. The results showed a significant decrease in heat transfer near the stagnation point at Reynolds numbers of 150 and 160. Our experimental results are in good agreement with the numerical analysis by another researcher that showed a sinusoidal fluctuation (or flapping motion) of the jet flow as it exited the nozzle at the same Reynolds numbers. This flapping motion can lead to a loss of forward momentum in the flow, resulting in the significant reduction of heat transfer rate near the stagnation point. The present results can be applied to measure the velocity (or volumetric flow rate) of small amounts of flow in the microflow sensor by detecting the frequency of the jet flapping motion because the flapping motion of a confined slot-jet impinging on a
*Tel.: þ82-55-320-3185. Fax: þ82-55-324-1723. E-mail: mechdhl@ inje.ac.kr.
’ ACKNOWLEDGMENT This work was supported by a Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (No. 2009-0076596). We are grateful for the financial support for this research. ’ NOMENCLATURE B = width of the slot nozzle (m) hx = local heat transfer coefficient (W/(m2 °C)) H = nozzle-to-surface distance (m) I = electrical current through the gold film Intrex (amps) k = thermal conductivity of air (W/(m2 °C)) L = length of the gold film Intrex (m) Nux = local Nusselt number qw = net wall heat flux (W/m2) Re = Reynolds number Tw = wall temperature measured by liquid crystal (°C) Tj = jet temperature at the nozzle exit (°C) u = jet velocity at the nozzle exit (m/s) V = voltage across the gold film Intrex (v) W = width of the gold film Intrex (m) x = lateral distance from the stagnation point (m) Greek symbols
ν = kinematic viscosity of air (m2/s)
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(10) Lee, D. H.; Chung, Y. S.; Kim, D. S. Turbulent flow and heat transfer measurements on a curved surface with a fully developed round impinging jet. Int. J. Heat Fluid Flow 1997, 18, 160. (11) Kline, S. J.; McKlintock, F. A. Describing uncertainties in single sample experiments. Mech. Eng. 1953, 75, 3.
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