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Heat transfer enhancement with liquid–gas flow in microchannels and the effect of thermal boundary layer
International Journal of Heat and Mass Transfer 70 (2014) 725–733
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer enhancement with liquid–gas flow in microchannels and the effect of thermal boundary layer Farzad Houshmand, Yoav Peles ⇑ Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110, 8th street, Troy, New York 12180, USA
a r t i c l e
i n f o
Article history: Received 5 September 2013 Received in revised form 15 November 2013 Accepted 15 November 2013 Available online 12 December 2013 Keywords: Bubbles Microchannel Convective heat transfer Two-phase flow Heat transfer enhancement Thermal boundary layer
a b s t r a c t Heat transfer coefficient of air–water two-phase flow in a microchannel was experimentally studied and the effect of the thermal boundary layer on the heat transfer process was elucidated. Air stream was injected into liquid water flow in a 210 lm deep and 1.5 mm wide horizontal microchannel, and the heat transfer coefficients due to the presence of bubbles were measured through an array of heaters and resistance temperature detectors (RTDs) inside the channel. Using different configurations of heated areas in the channel, the mixing effect of the bubbles and the interaction with the thermal boundary layer were studied for a range of liquid and gas flow rates. With two-phase flow, enhancement of up to 100% in the heat transfer coefficient was observed compared to single-phase flow. The enhancement was observed to be more significant for thermally developing flow with thicker thermal boundary layers. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Convective heat transfer in microchannels, especially for electronic cooling applications, has been a topic of much interest (e.g., [1]) ever since the early work of Tuckerman and Pease [2]. Over the years, various methods were developed to enhance heat transfer at the microscale, such as impinging jets [3], shear-driven flow [4], segmented flow [5,6], and extended surfaces [7–11]. Injection of gas bubbles into liquid flow (i.e., non-boiling gas–liquid two-phase flow) is a technique that can be triggered upon demand locally or at the system level, and similar to other active techniques, holds key advantages compared to passive approaches. In addition, knowledge about the processes controlling such flow can assist revealing the interaction of vapor bubbles with liquid flow during flow boiling. Although gas–liquid two-phase flow heat transfer is common (especially in chemical engineering applications), studies at the microscale are scarce (e.g., [12,13]). In a previous study by Houshmand and Peles [14], the effect of injected immiscible air bubbles on heat transfer and flow field in a microchannel was experimentally studied. A notable difference in the heat transfer enhancement was observed relative to other gas–liquid studies, such as the study of Betz and Attinger [5]. Comparison of the micro devices and the experimental conditions suggested that the thermal boundary layer thickness in the chan⇑ Corresponding author. Tel.: +1 (518) 276 2886; fax: +1 (518) 276 2623. E-mail addresses: [email protected] (F. Houshmand), [email protected] (Y. Peles). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.053
nel was a key difference between the experiments, requiring further investigation. Independently, the effect of developing flow on heat transfer in microchannels has been discussed in previous studies [15,16], and other studies, such as [17–19], have leveraged this concept to design more efficient micro devices. In this study, a new set of micro devices was designed and fabricated to study the interaction of injected bubbles with the thermal boundary layer; its effect on the heat transfer process was carefully examined. Disruption of the thermal boundary layer brings colder liquid closer to the heated surface and, as a result, enhances heat transfer. It is believed that characterization of the thermal boundary layer in the test section and careful analysis of the associated conjugate effects help assess and compare the heat transfer measurements in different studies. 2. Experimental setup and method 2.1. Microdevice To study the interaction of the injected bubbles and the thermal boundary layer, a microchannel with multiple heaters and wall temperature sensors was designed and fabricated. With multipleheater configuration, the length of the heated area was varied, and consequently, the thickness of the thermal boundary layer was controlled. A schematic of the microdevice is shown in Fig. 1. Distilled water flowed into a 210 lm deep, 1.5 mm wide, and 22 mm long microchannel; air bubbles were injected into the microchannel
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Nomenclature a Ac AH cp Dh E h H ji keq kl Nu q00 Q_ loss Q_ net Q_ tot
half-depth of the channel (m) cross sectional area (m2) heater area (m2) specific heat (J/kgK) hydraulic diameter (m) enhancement factor (–) heat transfer coefficient (W/mK) channel depth (m) superficial velocity of fluid i (m/s) equivalent thermal conductivity (W/mK) liquid thermal conductivity (W/mk) Nusselt number (–) heat flux (W/m2) power loss (W) net power (W) total power (W)
through a 250 lm diameter orifice located 13.9 mm (x = 10.4 mm) downstream of the inlet manifold. Titanium heaters and resistance temperature detectors (RTDs) were embedded in the channel to dissipate heat to the flow and directly measure the wall temperature, respectively. Heater #1 (located 3.5 mm downstream of the inlet manifold) served as a pre-heater; it allowed the thermal boundary layer, upstream of the bubble injection orifice, to grow. The flow temperature upstream of the bubbles was also controlled through the power delivered to Heater #1, and the corresponding wall temperature was measured by RTD #1. Heater #4 was the main test section of the channel, where the other four RTDs were located. The micro device consisted of two processed Pyrex substrates and a patterned double-side adhesive-coated vinyl layer that bonded them together (Fig. 2). Four 120 nm thick and 1 mm wide heaters, and five 70 nm thick RTDs (Table 1) were formed on the bottom Pyrex substrate through a sequence of deposition and wet etching steps in a cleanroom environment. Initially, the four heaters were formed on the substrate, and after depositing a 1 lm thick layer of silicon dioxide—to electrically insulate the RTDs from the heaters beneath—the five RTDs were planted on top of the heaters. A 250 nm thick layer of silicon dioxide as well as a 150 nm thick layer of silicon nitride were also deposited on the top to electrically insulate the RTDs from the water. Subsequently, insulating layers on top of the contact pads were etched away to provide contact between the device and the electrical loop through spring loaded probe pins. Finally, the inlet and outlet
Fig. 1. A schematic of the microdevice (top Pyrex layer removed).
Re teq T0 TRTD Tw U u W x y
a Ci dt
li t q
Reynolds number (–) equivalent thickness (m) inlet temperature (C) RTD temperature (C) wall temperature (C) mid-plane (maximum) velocity (m/s) average velocity (m/s) channel width (m) axial length (m) vertical distance from wall (m) thermal diffusivity (m2/s) volumetric flow rate of fluid i (m3/s) thermal boundary layer thickness (m) viscosity of fluid i (kg/ms) kinematic viscosity (m2/s) density (kg/m3)
manifolds (D = 1 mm), as well as the bubble injection orifice, were drilled through the bottom substrate. To form the heaters and the RTDs, a layer of titanium followed by a layer of aluminum were sputtered on the surface. The electric vias and pads were covered with patterned photoresist and the remaining aluminum was removed. After rinsing the photoresist, the heater area and the aluminum patches were covered and the rest of the titanium was etched away. As a result, the exposed titanium area formed the heaters and RTDs and the low-resistance layer of aluminum composed the electric pads and vias. The final cross-section of the bottom Pyrex substrate is shown in Fig. 3 for the heaters (left) and the RTDs (right). The vinyl layer was patterned with a laser-cutting machine (Hurricane 80 W) to form the microchannel and the access holes for the probe pins over the contact pads. Similar holes were also drilled in the Pyrex substrate that formed the top wall of the microchannel. The transparent Pyrex layer on the top enables flow visualization during experiments. After aligning and bonding the three substrates, individual devices were cut out using a diesaw.
2.2. Device packaging To connect the micro device to the fluid lines and the measurement apparatus, a two-piece packaging system was designed and Ò built (Fig. 4). The micro device sits in the groove on the Delrin block, which connects the inlet and outlet ports of the microchannel to the supply connector and the drain pipe; it also connects the bubble injection orifice to the syringe pump. A set of miniature Orings were used in the grooves beneath the fluidic ports to seal the connections between the device and the package. A set of similar O-rings was placed beneath the device to provide a uniform and elastic support and to provide an air gap between the device and the package to minimize heat loss. The cover plate (Fig. 4(b) and (c)) consisted of a printed circuit board (PCB) substrate with soldered gold-plated probe pins and a male insulation-displacement connector (IDC) supported by a reinÒ forcing Delrin piece. The cover plate provided the electrical connections between the contact pads on the micro device, power supplies, and data acquisition system (DAQ) through the IDC ribbon cables. It also supported the micro device and compressed the O-rings to ensure proper sealing of the device. A window was machined in the center of the cover plate to enable flow visualization during the experiments. It should be noted that the overall
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Table 1 Dimensions and locations of the heaters and RTDs; (center point is used for RTD locations).
Heater #1 Heater #2 Heater #3 Heater #4 RTD #1 RTD #2 RTD #3 RTD #4 RTD #5
Dimension
location
10 mm 1 mm 0.94 mm 1 mm 1 mm 1 mm 3 mm 1 mm 600 lm 20 lm 200 lm 15 lm 200 lm 15 lm 200 lm 15 lm 200 lm 15 lm
x = 0 to 3 mm x = 10.03 to 10.97 mm x = 11 to 12 mm x = 12.03 to 15.03 mm x = 9.51 mm x = 12.07 mm x = 12.75 mm x = 13.50 mm x = 14.85 mm
RTDs’ wires to measure the resistance of the RTDs. All the measurements were recorded in a personal computer (PC) through National Instrument (NI) LabView interface. The package was held horizontally over an inverted microscope (Zeiss Observer Z1m) to visualize the flow. The test section was illuminated by a halogen lamp, and the images were recorded by a high speed Complementary Metal-Oxide-Semiconductor (CMOS) camera (Phantom V4.2). 2.4. Experimental procedure and data reduction
Fig. 2. Microdevice details.
thickness of the cover plate was constrained by the minimum working distance of the objective lenses (9 mm). 2.3. Experimental apparatus The schematic of the experimental setup is shown in Fig. 5. A pressurized tank propelled distilled water in the main line and a Ò FL-3600 series rotameter from Omega was used to measure the flow rate, which was controlled by a metering valve upstream of the package. The bubbles were generated by a gas stream injected through a controllable syringe pump made by Harvard apparatus. The heaters and RTDs in the micro device were connected to a terminal block through the cover plate and the ribbon cables. The terminal block connected electrical wires to a series of DC power supplies while the voltage and current were measured by two digital multimeters (HP 3457A and Agilent 34401A) to calculate the power delivered to the heaters. A current excitation module and an isolated analog input module were connected to the
In order to use the RTDs to measure local temperatures, the resistance of the RTDs was determined at different temperatures. The calibration process was carried out in a controllable oven and the resistances of the RTDs were recorded at different temperatures. A 6 mm thick copper block was machined to seat the devices and to fasten the cover plate on the device. Two calibrated thermocouples were also attached to the bottom of the device through the copper block to measure the temperature of the device. The entire assembly was placed in the oven, and the ribbon cables and the thermocouples were connected to the terminal block and the DAQ through the insulated opening of the oven. The oven temperature was set, and after reaching steady state temperature in the device (variations less than 0.1 °C), resistances and temperatures were recorded and a calibration curve was plotted for each RTD (e.g., Fig. 6). To estimate the heat loss to the substrate, the device was vacuumed and the temperatures of the RTDs were measured for a range of heaters’ powers. Assuming negligible natural convection and radiation in the channel, the recorded power was used to estimate the heat loss during the experiments based on the temperature of the RTDs. The procedure was performed for the two combinations of powered heaters during experiments (Cases I and II) to minimize the effect of discrepancy in the axial conduction pattern on the heat loss estimate between the two cases. Once the RTD calibration curves and heat loss estimations were obtained, time-averaged steady state heat transfer coefficient for single-phase flow and bubbly flow was calculated for various liquid and gas flow rates at different RTD locations on Heater #4. The experiments were performed and compared for two cases of thermally developing flow: (1) only Heater #4 turned on, and (2)
Fig. 3. Cross-section of the deposited layers; heaters (left), RTDs (right).
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a
b Cover plate
c Delrin block
Fig. 4. Device packaging; (a) exploded view, (b) cover plate (top), (c) cover plate (bottom).
Fig. 5. A Schematic of the experimental setup.
all heaters turned on. To prevent cavitation of the dissolved gas in the microchannel, the tank containing distilled water was degassed using a vacuum pump, and subsequently pressurized helium— which is insoluble gas in water (15 mg/kg)— was introduced into the tank. The bubble formation and trajectory over Heaters #3 and #4 were captured by the high speed camera through a 2.5 objective lens while the test section was illuminated by a halogen lamp. To quantify the flow rates in the two-phase regime, superficial velocities of liquid and gas phases were used:
100.0 90.0 80.0 T ( C)
70.0 60.0 50.0
ji ¼
40.0 30.0 20.0 285
290
295
300
305
310
315
320
R (Ω) Fig. 6. An example of RTD calibration curve; (RTD #2).
325
Ci Ac
ð1Þ
where i specifies the phase (i.e., liquid or gas), Ci (m3/s) is the volumetric flow rate of fluid i, and Ac (m2) is the cross-sectional area of the microchannel. Reynolds number was defined as:
Re ¼
quDh l
ð2Þ
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where q (kg/m3) is the density, l (kg/m s) is the dynamic viscosity, (m/s) is the average liquid velocity, and Dh (m) is the hydraulic u diameter of the channel. The thermophysical properties were calculated at the inlet temperature. The local heat transfer coefficient at each RTD was calculated based on the convective heat transfer equation:
q00net ¼ hðT w T 0 Þ
ð3Þ
where Tw is the calculated wall temperature at the RTD, T0 is the inlet channel temperature and q00net is the effective heat flux of the hea ter: Q_ tot Q_ loss =AH . Because of the insulating layers on the RTDs, the wall temperature is slightly lower than the RTD temperature, which was corrected through a one-dimensional conduction analysis: T w ¼ T RTD q00 t eq =keq where teq and keq are the equivalent thickness and thermal conductivity of the composite insulation layer, respectively. However, this estimated temperature difference in the present study was calculated and found to be very small (<0.1 °C). The effect of bubbles on the heat transfer coefficient was quantified by introducing enhancement factor, E, which compares the heat transfer coefficient of the bubbly flow to that of the singlephase liquid flow at the same liquid flow rate:
E¼
hb hsp hsp
ð4Þ
hb and hsp denote bubbly flow and single-phase heat transfer coefficients at a same RTD, respectively. 2.5. Heat loss and uncertainties The conjugate conduction/convection effect, which is a result of a non-ideal insulating substrate, is an important factor that should be considered in microscale convective heat transfer experiments. The conduction is a three-dimensional process, which can be divided into depth-wise direction (y) and planar direction (z, x; transverse and axial). Depth-wise conduction is mainly through the Pyrex, and the planar conduction mainly occurs near the heater edges through the composite structure made of Al, Ti, and Pyrex layers. In the present study, the method used to estimate the heat loss—through conduction—at each RTD location is based on the temperature of the RTD. The surface temperature corresponding to conduction heat transfer to the substrate (assuming no convection and radiation and uniform heat generation in the heater) was obtained through the vacuum test. Therefore, if the temperature of the RTD is known during the experiments, the combined value of the heat loss can be estimated. A concern arises since the boundary condition of the non-heated surfaces—in the periphery of the heaters —during the actual experiments and vacuum test is not the same (h – 0 vs. h = 0); this can lead to underestimation of the heat loss [3]. A careful combination of vacuum test results and a numerical model can predict the heat loss more accurately. Since the estimated heat loss was not a significant fraction of the applied power and the RTDs were located in the center of the heater, this effect was considered very small and was added to the biased uncertainties. The heat loss was estimated based on the heaters’ powers and the temperatures of the RTDs in the vacuum experiment. The estimated heat loss ranged between 3% and 13% for the minimum and the maximum wall temperatures, respectively. It is also worth noting that the optical visualization can affect the RTD measurements due to the light source, which is a function of the light intensity and wavelength spectrum, and the magnification of the objective lens used. In the present study—in which a 2.5 objective lens was used—the effect was negligible, but could lead to temperature rise with higher magnifications (e.g., 0.2 °C for 10 at low liquid flow rates). This effect is a biased uncertainty
in the supplied heat flux, and can be eliminated by using a cooled light source similar to Chen and Garimella [20]. The measurement uncertainty in the flow rate was associated with the rotameter accuracy and ranged between ±3% and ±6% for the maximum and the minimum flow rates, respectively. The uncertainty in the temperature measurements was less than ±0.3 °C while the uncertainty in the power measurements was negligible (<0.1%). The uncertainty in the enhancement factor, E, was estimated to be between ±4% and ±12% depending on the value and the change in heat transfer coefficient. A summary of the uncertainties in heat transfer calculations is provided in Table 2.
3. Thermal boundary layer thickness To investigate the effect of bubbles on mixing and disruption of the thermal boundary layer, the thermal boundary layer thickness in the channel was estimated using a two-dimensional integral method. To apply the integral method, a fully developed velocity profile (a second-order polynomial) was considered for the crosssectional velocity distribution, and an energy balance on the thermal boundary layer (Eq. (5)) was performed. A third order polynomial was considered for the temperature distribution in the thermal boundary layer. Imposing the boundary conditions, velocity and temperature profiles were derived according to Eqs. (6) and (7).
kl
@Tðx; 0Þ d ¼ qcp @y dx
Z
dt
uðT T 0 Þdy
ð5Þ
0
y y2 u¼U 2 a a
T ¼ T0 þ
ð6Þ
" # q00w 2 1 y3 dt y þ 3 d2t kl 3
ð7Þ
where 2a = H is the channel depth, U is the liquid velocity at the centerline (y = a), and dt is the thermal boundary layer thickness. It should be noted that using a second order polynomial for the velocity profile implies flow between parallel plates, which is a valid assumption because of the large aspect ratio of the channel (W/H 7). Substituting Eqs. (6) and (7) into Eq. (5), and solving for dt, with boundary condition of dt = 0 at x = 0, the thermal boundary layer thickness was calculated according to the implicit form of Eq. (8):
a U
x¼
2 3 1 4 d d 15a t 36a2 t
ð8Þ
where a is the thermal diffusivity a = k/qcp. For a given fluid, the heater length, channel geometry, and liquid flow rate are the important parameters affecting the thermal boundary layer thickness.
Table 2 Sources of uncertainly in heat transfer measurements. Quantity
Source of uncertainty
Estimated values
RTD temperature 1-D correction for insulating layers
0.3 °C Negligible (<0.1 °C)
Total delivered power Heat loss estimation Light source effect
Negligible (<0.1%) Small (1%) Negligible
Wall temperature
Heat flux
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200
4. Results and discussion
180 160 140
x'=0.72 mm x'=1.47 mm x'=2.82 mm
(RTD #2) (RTD #3) (RTD #4) (RTD #5) (RTD #1)
120 100
Case I
δt (μm)
Three different air flow rates (2, 4, and 6 ml/min; jg = 0.1, 0.2, and 0.3 m/s) at room temperature (24 °C) were introduced into a stream of liquid water (also at room temperature) with flow rates ranging from 5 to 33.1 ml/min (corresponding to 0.25 m/s 6 jl 6 1.75 m/s, and 125 6 Re 6 825), and the effect of bubbles on the heat transfer coefficient was studied. Fig. 7 shows images of bubbles in their formation stage and downstream of the orifice for a range of flow rate combinations (a pair of images for each case). A 2.5 objective lens was used to capture the bubbles throughout the length of Heater #4. The bubble size decreased with increasing liquid flow rate and increased with increasing air flow rate; at low liquid flow rates, large bubbles formed slugs. To study the effect of the thermal boundary layer thickness on the heat transfer enhancement over Heater #4, measurements at different RTDs were carried out for two heating configurations. In Case I, all the heaters were connected in series, steady state heat transfer coefficients for single-phase and two-phase flow (with and without air bubbles) were obtained, and the enhancement factors due to the presence of bubbles were calculated for different flow rate combinations. In Case II, the first three heaters were disconnected from the power supply, and only Heater #4 was powered to provide the same wall heat flux as in Case I (31 W/ cm2); enhancement factors were calculated similar to Case I. In Case I, the thermal boundary layer had developed over a longer length along the channel and was thicker compared to Case II—for similar liquid flow rates. According to Eq. (8), as the liquid flow rate increases, the thermal boundary layer thickness decreases. The estimated thermal boundary layer thicknesses at different RTD positions for Case I and Case II are plotted in Fig. 8. The thickness at the trailing edge of Heater #4 for Case I was between 92 and 190 lm, whereas the estimated thickness for Case II was between 52 and 102 lm. The heat transfer enhancements, E, at different RTD positions for Case I are depicted in Fig. 9 for different flow rate combinations. The bubbles affect the local velocity and temperature of the liquid over the RTDs and, therefore, determine the heat transfer coefficient and the enhancement factor. At low liquid flow rates, slug flow dominated and the heat transfer coefficient changed very slightly with respect to single-phase flow. With increasing liquid
x=12.07 mm x=12.75 mm x=13.5 mm x=14.85 x=9.51 mm
80 60
Case II
730
40 20 0
0
0.5
1
1.5
2
2.5
3
jl (m/s) Fig. 8. Estimated thermal boundary layer thickness at different RTD locations for Case I and II; x0 = x 12.03 (mm).
flow rate, the flow gradually transitioned to bubbly flow and, consequently, the enhancement factor increased before peaking, and subsequently decreased. The flow rates at which the maximum was reached varied at different locations and tended toward the higher liquid flow rates for the RTDs located further downstream of the heater. Fig. 10 shows the enhancement factors for Case II. Since RTD #2 was located at the leading edge of the heater, the variation in the surface temperature was very small, independent of the flow condition. In Case II, the enhancement factors typically started with negative values at low liquid flow rates and increased up to 50% with increasing liquid flow rate. The enhancement factors were typically smaller for the upstream RTDs because the bubbles (or slugs) tended to move more slowly during the acceleration stage. In particular, the hindering effect was typically more significant for bigger bubbles, which suggests that the heat-up of the liquid layer between the heater and the bubbles/slugs (with diameter larger than the channel depth) increases the wall temperature and hinders the heat transfer process.
Fig. 7. Bubbles at different flow rates.
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90
jg = 0.1 (m/s)
80
jg = 0.2 (m/s)
70
jg = 0.3 (m/s)
120
E (%)
E (%)
jg = 0.3 (m/s)
80
50 40
60 40
30 20
20
10 0
0 0.00
0.50
1.00
1.50
90 80 70 60 50 40 30 20 10 0 -10
0.00
2.00
jl (m/s)
a jg=0.1 m/s jg=0.2 m/s jg=0.3 m/s
0.00
0.50
1.00
0.50
1.50
2.00
jl (m/s)
100 90 80 70 60 50 40 30 20 10 0
1.50
2.00
1.50
2.00
jg = 0.1 (m/s) jg = 0.2 (m/s) jg = 0.3 (m/s)
0.00
d
1.00
jl (m/s)
b
E (%)
E (%)
jg = 0.2 (m/s)
100
60
c
jg = 0.1 (m/s)
0.50
1.00
jl (m/s)
Fig. 9. Heat transfer enhancement at different RTD locations (Case I); (a) RTD #2, (b) RTD #3, (c) RTD #4, (d) RTD #5.
The velocity field measurements around the bubbles are presented in [10]. In summary, the introduction of bubbles increases the mean velocity of the liquid. Closer to the orifice, the streamlines are curved around the forming bubbles and lower velocity regions are observed in the wake of the bubbles. When the bubbles approach terminal velocity, a path with lower velocity (with approximately the same width as the bubbles) is formed in the middle of the channel surrounded by two high velocity regions on the sides. High local velocities due to the recoil of bubble tails are also observed. Comparing the enhancement factors at each RTD for Case I and Case II, it is evident that the enhancement factor was more significant in Case I, which corresponded to thicker thermal boundary layers. It is believed that deflected streamlines around the bubbles and the shear layer around them during the formation and acceleration stages promoted mixing across the channel and disrupted the thermal boundary layer. In addition, the oscillation of the bubbles caused by the initial recoil of the bubble tails could have also aided the mixing process. The net effect of the mixing, modification of the velocity field, and the formation of thin liquid layer underneath the bubbles determined the resultant heat transfer enhancement. Since all the parameters for Cases I and II, except the temperature profile of the flow right upstream of Heater #4, were kept the same, the substantial deviation in the results demonstrates the liquid mixing caused by the bubbles and their considerable effect on heat transfer enhancement. Although the main purpose of these experiments was to examine the mixing potential and boundary layer disruption of the injected bubbles, the trends observed merit further discussion. Since the RTD measurements are local, it is believed that the enhancement factors shown in Figs. 9 and 10 are related to the configuration of the bubble as they flow over the RTDs.
As shown in Fig. 8 (e.g., jg = 0.3 m/s, jl = 0.77 m/s), the bubbles undergo an oscillation period before reaching a stable (circular) shape. Elongated oval shaped bubbles (along the flow direction x) detach from the orifice; after recoiling of the tail, they turn into blunt oval bubbles (major axis in transverse direction z), before finally becoming circular. It should be noted that the oscillation phases of the bubbles are different for different flow conditions, but for a specific flow condition, all the bubbles at a specific axial location, maintain a repeatable time-independent pattern. A comparison of the results in Fig. 9 and the high speed footage of Fig. 8 suggests that the shape of the bubbles passing over the RTDs can be linked to the distinct trends observed at different RTDs. The axial dimension of the bubble defines its residence time over an RTD, so the blunt oval bubbles pass over the RTDs faster than the elongated ones for a same liquid flow rate, allowing less time for the wall temperature to rise. This blunt shape can also promote mixing more effectively in its wake. Based on the analysis of the high speed footages, it is evident that for higher liquid flow rates, the oscillation period extends a longer distance, and therefore, the blunt oval shaped bubbles form over the downstream section of the heater. RTDs #2 and #3 have the highest enhancement factors at moderate liquid flow rates while RTD #4 and RTD #5 have peak enhancement at higher liquid flow rates. This trend coincides with the location of the minimum axial dimension of the bubbles during their oscillation period. Furthermore, for the lowest gas flow rate at high liquid flow rates, the bubbles were smaller than the channel height (Fig. 8, jg = 1 m/s, jl > 0.77 m/s), which could lead to the slightly different trend observed in E. In Fig. 11, the average values of the enhancement factors calculated at different RTDs (extracted from Figs. 9 and 10) are presented. Based on the earlier discussions, and considering the heat-up of the liquid layer underneath the bubbles as a hindering
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40
jg = 0.1 (m/s)
30
jg = 0.2 (m/s)
20
jg = 0.3 (m/s)
E (%)
10 0
-10
0.00
0.50
1.00
1.50
2.00
1.50
2.00
-20 -30 -40
jl (m/s)
a 40
60
jg = 0.1 (m/s)
30
jg = 0.2 (m/s)
50
jg = 0.3 (m/s)
40
jg = 0.2 (m/s) jg = 0.3 (m/s)
30
E (%)
E (%)
20
jg = 0.1 (m/s)
10
20 10
0 0.00
0.50
1.00
1.50
2.00
0
-10
-10
-20
0.00
0.50
1.00
-20
jl (m/s)
b
jl (m/s)
c
Fig. 10. Heat transfer enhancement at different RTD locations (Case II); (a) RTD #3, (b) RTD #4, (c) RTD #5.
90 80 70 60 50 40 30 20 10 0
a
with increasing liquid flow rate, their residence time diminishes, and the enhancement factor increases. It should be noted that the effect of bubble shape, discussed above, is only one of the parameters affecting the heat transfer process, and conclusive account of the trends require a detailed transient, three-dimensional measurements of the velocity and fluid temperature fields, and the wall temperature. For instance, the significantly higher enhancement for smaller bubbles at high liquid flow rates, especially at downstream RTDs, might also be attributed to higher velocity regions in the flow closer to the RTDs in the center. The lateral mixing between the heated area—over the heaters and unheated areas on the sides—might have contributed to higher enhancement factors for moderate liquid flow rates with medium size bubbles.
40
jg = 0.1 (m/s) jg = 0.2 (m/s) jg = 0.3 (m/s)
20 10 0 -10
0
0.5
jg = 0.1 (m/s) jg = 0.2 (m/s) jg = 0.3 (m/s)
30
Eavg (%)
Eavg (%)
effect, and mixing as an enhancing effect, the dissimilar trends in Case I and Case II (bell-shaped vs. monotonic) can be explained. In Case I, the larger bubbles at lower liquid flow rates cover the RTDs for a longer period of time, and liquid layer underneath the bubbles heats up more; thus, the hindering effect is more pronounced. As the liquid flow rate increases and the bubbles become smaller, the combined effect of mixing and lower residence time of the bubbles leads to an increased enhancement. At higher liquid flow rates, because of the thinner boundary layers (and also smaller and more stretched bubbles), the effect of mixing is less significant and, therefore, the enhancement factor decreases. In Case II, because of the thin boundary layer, the effect of mixing is already small, so the main factor controlling the process is the resident time of the bubble over the RTDs. As the bubbles become smaller
1
jl (m/s)
1.5
2
0
-20
b
0.5
1
jl (m/s)
Fig. 11. Average heat transfer enhancement of the RTDs; (a) Case I, (b) Case II.
1.5
2
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5. Conclusion Immiscible air bubbles were introduced into a water stream flowing in a horizontal microchannel, and their effect on the heat transfer process was studied. The heat transfer coefficient for bubbly flow was compared to that of the single-phase flow at different locations along the heater. Experiments were carried out for nonheated flow and a thermally developing flow upstream of the test section. In particular, the effect of bubbles on liquid mixing and disruption of the thermal boundary layer was studied. Impact of bubbles on the heat transfer enhancement was more pronounced when the boundary layer was thick, and values up to 100% were observed. This demonstrates the impact of bubble injection on mixing enhancement in the mostly laminar microchannel flows. Furthermore, parameters affecting the heat transfer enhancement trends were discussed. Because of the complexity of the problem, further investigation is merited, both experimentally and numerically, to explain the parameters controlling the heat transfer processes. This should be done through a three-dimensionaltransient measurement of the heat transfer and flow field around the bubbles. It is believed that the characterization of the thermal boundary layer can provide a proper metric for comparing the results of reported studies on microscale and/or macroscale heat transfer systems. Acknowledgments This work is supported by the Office gram Manager Dr. Mark Spector). The acknowledge the staff of the Micro and Room (MNCR) at Rensselaer Polytechnic tance in fabrication of the micro devices.
of Naval Research (Proauthors would like to Nano Fabrication Clean Institute for their assis-
References [1] S.G. Kandlikar, High flux heat removal with microchannels – a roadmap of challenges and opportunities, Heat Transfer Eng. 26 (8) (2005) 5–14. [2] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, IEEE Electron Device Lett. 2 (5) (1981) 126–129.
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[3] E.A. Browne, G.J. Michna, M.K. Jensen, Y. Peles, Experimental investigation of single-phase micro-jet array heat transfer, J. Heat Transfer 132 (4) (2010). 041013. [4] F. Houshmand, Y. Peles, Convective heat transfer to shear-driven liquid film flow in a microchannel, Int. J. Heat Mass Transfer 64 (2013) 42–52. [5] A.R. Betz, D. Attinger, Can segmented flow enhance heat transfer in microchannel heat sinks?, Int J. Heat Mass Transfer 53 (2010) 3683–3691. [6] A. Asthana, I. Zinovik, C. Weinmueller, D. Poulikakos, Significant Nusselt number increase in microchannels with a segmented flow of two immiscible liquids: an experimental study, Int. J. Heat Mass Transfer 54 (2011) 1456– 1464. [7] J.F. Tullius, T.K. Tullius, Y. Bayazitoglu, Optimization of short micro pin fins in minichannels, Int. J. Heat Mass Transfer 55 (15–16) (2012) 3921–3932. [8] W. Qu, A.M. Siu-Ho, Liquid single-phase flow in an array of micro-pin-fins – Part I: heat transfer characteristics, J. Heat Transfer 130 (12) (2008) 122402. [9] R. Prasher, J.Y. Chang, Cooling of electronic chips using microchannel and micro-pin fin heat exchangers, ASME 6th International Conference on Nanochannels, Microchannels, and Minichannels, Darmstadt, Germany, 2008, pp. 1881–1887. [10] A. Kosßar, Y. Peles, Thermal-hydraulic performance of MEMS-based pin fin heat sink, J. Heat Transfer 128 (2) (2006) 121–131. [11] Y. Wang, F. Houshmand, D. Elcock, Y. Peles, Convective heat transfer and mixing enhancement in a microchannel with a pillar, Int. J. Heat Mass Transfer 62 (2013) 553–561. [12] G. Hetsroni, A. Mosyak, E. Pogrebnyak, Z. Segal, Heat transfer of gas–liquid mixture in micro-channel heat sink, Int. J. Heat Mass Transfer 52 (2009) 3963– 3971. [13] J.A. Howard, P.A. Walsh, E.J. Walsh, Prandtl and capillary effects on heat transfer performance within laminar liquid–gas slug flows, Int. J. Heat Mass Transfer 54 (2011) 4752–4761. [14] F. Houshmand, Y. Peles, Impact of flow dynamics on the heat transfer of bubbly flow in a microchannel, J. Heat Transfer 136 (2) (2013). 022902. [15] P.-S. Lee, S. Garimella, Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios, Int. J. Heat Mass Transfer 49 (2006) 3060–3067. [16] Y. Mishan, A. Mosyak, E. Pogrebnyak, G. Hetsroni, Effect of developing flow and thermal regime on momentum and heat transfer in microscale heat sink, Int. J. Heat Mass Transfer 50 (2007) 3100–3114. [17] J.L. Xu, Y.H. Gan, D.C. Zhang, X.H. Li, Microscale heat transfer enhancement using thermal boundary layer redeveloping concept, Int. J. Heat Mass Transfer 48 (2005) 1662–1674. [18] L. Chai, G. Xia, L. Wang, M. Zhou, Z. Cui, Heat transfer enhancement in microchannel heat sinks with periodic expansion–constriction cross-sections, Int. J. Heat Mass Transfer 62 (2013) 741–751. [19] Y.J. Lee, P.S. Lee, S.K. Chou, Enhanced thermal transport in microchannel using oblique fins, J. Heat transfer 134 (10) (2012) 101901. [20] T. Chen, S.V. Garimella, Measurements and high-speed visualizations of flow boiling of a dielectric fluid in a silicon microchannel heat sink, Int. J. Multiphase flow 32 (2006) 957–971.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer enhancement with liquid–gas flow in microchannels and the effect of thermal boundary layer Farzad Houshmand, Yoav Peles ⇑ Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110, 8th street, Troy, New York 12180, USA
a r t i c l e
i n f o
Article history: Received 5 September 2013 Received in revised form 15 November 2013 Accepted 15 November 2013 Available online 12 December 2013 Keywords: Bubbles Microchannel Convective heat transfer Two-phase flow Heat transfer enhancement Thermal boundary layer
a b s t r a c t Heat transfer coefficient of air–water two-phase flow in a microchannel was experimentally studied and the effect of the thermal boundary layer on the heat transfer process was elucidated. Air stream was injected into liquid water flow in a 210 lm deep and 1.5 mm wide horizontal microchannel, and the heat transfer coefficients due to the presence of bubbles were measured through an array of heaters and resistance temperature detectors (RTDs) inside the channel. Using different configurations of heated areas in the channel, the mixing effect of the bubbles and the interaction with the thermal boundary layer were studied for a range of liquid and gas flow rates. With two-phase flow, enhancement of up to 100% in the heat transfer coefficient was observed compared to single-phase flow. The enhancement was observed to be more significant for thermally developing flow with thicker thermal boundary layers. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Convective heat transfer in microchannels, especially for electronic cooling applications, has been a topic of much interest (e.g., [1]) ever since the early work of Tuckerman and Pease [2]. Over the years, various methods were developed to enhance heat transfer at the microscale, such as impinging jets [3], shear-driven flow [4], segmented flow [5,6], and extended surfaces [7–11]. Injection of gas bubbles into liquid flow (i.e., non-boiling gas–liquid two-phase flow) is a technique that can be triggered upon demand locally or at the system level, and similar to other active techniques, holds key advantages compared to passive approaches. In addition, knowledge about the processes controlling such flow can assist revealing the interaction of vapor bubbles with liquid flow during flow boiling. Although gas–liquid two-phase flow heat transfer is common (especially in chemical engineering applications), studies at the microscale are scarce (e.g., [12,13]). In a previous study by Houshmand and Peles [14], the effect of injected immiscible air bubbles on heat transfer and flow field in a microchannel was experimentally studied. A notable difference in the heat transfer enhancement was observed relative to other gas–liquid studies, such as the study of Betz and Attinger [5]. Comparison of the micro devices and the experimental conditions suggested that the thermal boundary layer thickness in the chan⇑ Corresponding author. Tel.: +1 (518) 276 2886; fax: +1 (518) 276 2623. E-mail addresses: [email protected] (F. Houshmand), [email protected] (Y. Peles). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.053
nel was a key difference between the experiments, requiring further investigation. Independently, the effect of developing flow on heat transfer in microchannels has been discussed in previous studies [15,16], and other studies, such as [17–19], have leveraged this concept to design more efficient micro devices. In this study, a new set of micro devices was designed and fabricated to study the interaction of injected bubbles with the thermal boundary layer; its effect on the heat transfer process was carefully examined. Disruption of the thermal boundary layer brings colder liquid closer to the heated surface and, as a result, enhances heat transfer. It is believed that characterization of the thermal boundary layer in the test section and careful analysis of the associated conjugate effects help assess and compare the heat transfer measurements in different studies. 2. Experimental setup and method 2.1. Microdevice To study the interaction of the injected bubbles and the thermal boundary layer, a microchannel with multiple heaters and wall temperature sensors was designed and fabricated. With multipleheater configuration, the length of the heated area was varied, and consequently, the thickness of the thermal boundary layer was controlled. A schematic of the microdevice is shown in Fig. 1. Distilled water flowed into a 210 lm deep, 1.5 mm wide, and 22 mm long microchannel; air bubbles were injected into the microchannel
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Nomenclature a Ac AH cp Dh E h H ji keq kl Nu q00 Q_ loss Q_ net Q_ tot
half-depth of the channel (m) cross sectional area (m2) heater area (m2) specific heat (J/kgK) hydraulic diameter (m) enhancement factor (–) heat transfer coefficient (W/mK) channel depth (m) superficial velocity of fluid i (m/s) equivalent thermal conductivity (W/mK) liquid thermal conductivity (W/mk) Nusselt number (–) heat flux (W/m2) power loss (W) net power (W) total power (W)
through a 250 lm diameter orifice located 13.9 mm (x = 10.4 mm) downstream of the inlet manifold. Titanium heaters and resistance temperature detectors (RTDs) were embedded in the channel to dissipate heat to the flow and directly measure the wall temperature, respectively. Heater #1 (located 3.5 mm downstream of the inlet manifold) served as a pre-heater; it allowed the thermal boundary layer, upstream of the bubble injection orifice, to grow. The flow temperature upstream of the bubbles was also controlled through the power delivered to Heater #1, and the corresponding wall temperature was measured by RTD #1. Heater #4 was the main test section of the channel, where the other four RTDs were located. The micro device consisted of two processed Pyrex substrates and a patterned double-side adhesive-coated vinyl layer that bonded them together (Fig. 2). Four 120 nm thick and 1 mm wide heaters, and five 70 nm thick RTDs (Table 1) were formed on the bottom Pyrex substrate through a sequence of deposition and wet etching steps in a cleanroom environment. Initially, the four heaters were formed on the substrate, and after depositing a 1 lm thick layer of silicon dioxide—to electrically insulate the RTDs from the heaters beneath—the five RTDs were planted on top of the heaters. A 250 nm thick layer of silicon dioxide as well as a 150 nm thick layer of silicon nitride were also deposited on the top to electrically insulate the RTDs from the water. Subsequently, insulating layers on top of the contact pads were etched away to provide contact between the device and the electrical loop through spring loaded probe pins. Finally, the inlet and outlet
Fig. 1. A schematic of the microdevice (top Pyrex layer removed).
Re teq T0 TRTD Tw U u W x y
a Ci dt
li t q
Reynolds number (–) equivalent thickness (m) inlet temperature (C) RTD temperature (C) wall temperature (C) mid-plane (maximum) velocity (m/s) average velocity (m/s) channel width (m) axial length (m) vertical distance from wall (m) thermal diffusivity (m2/s) volumetric flow rate of fluid i (m3/s) thermal boundary layer thickness (m) viscosity of fluid i (kg/ms) kinematic viscosity (m2/s) density (kg/m3)
manifolds (D = 1 mm), as well as the bubble injection orifice, were drilled through the bottom substrate. To form the heaters and the RTDs, a layer of titanium followed by a layer of aluminum were sputtered on the surface. The electric vias and pads were covered with patterned photoresist and the remaining aluminum was removed. After rinsing the photoresist, the heater area and the aluminum patches were covered and the rest of the titanium was etched away. As a result, the exposed titanium area formed the heaters and RTDs and the low-resistance layer of aluminum composed the electric pads and vias. The final cross-section of the bottom Pyrex substrate is shown in Fig. 3 for the heaters (left) and the RTDs (right). The vinyl layer was patterned with a laser-cutting machine (Hurricane 80 W) to form the microchannel and the access holes for the probe pins over the contact pads. Similar holes were also drilled in the Pyrex substrate that formed the top wall of the microchannel. The transparent Pyrex layer on the top enables flow visualization during experiments. After aligning and bonding the three substrates, individual devices were cut out using a diesaw.
2.2. Device packaging To connect the micro device to the fluid lines and the measurement apparatus, a two-piece packaging system was designed and Ò built (Fig. 4). The micro device sits in the groove on the Delrin block, which connects the inlet and outlet ports of the microchannel to the supply connector and the drain pipe; it also connects the bubble injection orifice to the syringe pump. A set of miniature Orings were used in the grooves beneath the fluidic ports to seal the connections between the device and the package. A set of similar O-rings was placed beneath the device to provide a uniform and elastic support and to provide an air gap between the device and the package to minimize heat loss. The cover plate (Fig. 4(b) and (c)) consisted of a printed circuit board (PCB) substrate with soldered gold-plated probe pins and a male insulation-displacement connector (IDC) supported by a reinÒ forcing Delrin piece. The cover plate provided the electrical connections between the contact pads on the micro device, power supplies, and data acquisition system (DAQ) through the IDC ribbon cables. It also supported the micro device and compressed the O-rings to ensure proper sealing of the device. A window was machined in the center of the cover plate to enable flow visualization during the experiments. It should be noted that the overall
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Table 1 Dimensions and locations of the heaters and RTDs; (center point is used for RTD locations).
Heater #1 Heater #2 Heater #3 Heater #4 RTD #1 RTD #2 RTD #3 RTD #4 RTD #5
Dimension
location
10 mm 1 mm 0.94 mm 1 mm 1 mm 1 mm 3 mm 1 mm 600 lm 20 lm 200 lm 15 lm 200 lm 15 lm 200 lm 15 lm 200 lm 15 lm
x = 0 to 3 mm x = 10.03 to 10.97 mm x = 11 to 12 mm x = 12.03 to 15.03 mm x = 9.51 mm x = 12.07 mm x = 12.75 mm x = 13.50 mm x = 14.85 mm
RTDs’ wires to measure the resistance of the RTDs. All the measurements were recorded in a personal computer (PC) through National Instrument (NI) LabView interface. The package was held horizontally over an inverted microscope (Zeiss Observer Z1m) to visualize the flow. The test section was illuminated by a halogen lamp, and the images were recorded by a high speed Complementary Metal-Oxide-Semiconductor (CMOS) camera (Phantom V4.2). 2.4. Experimental procedure and data reduction
Fig. 2. Microdevice details.
thickness of the cover plate was constrained by the minimum working distance of the objective lenses (9 mm). 2.3. Experimental apparatus The schematic of the experimental setup is shown in Fig. 5. A pressurized tank propelled distilled water in the main line and a Ò FL-3600 series rotameter from Omega was used to measure the flow rate, which was controlled by a metering valve upstream of the package. The bubbles were generated by a gas stream injected through a controllable syringe pump made by Harvard apparatus. The heaters and RTDs in the micro device were connected to a terminal block through the cover plate and the ribbon cables. The terminal block connected electrical wires to a series of DC power supplies while the voltage and current were measured by two digital multimeters (HP 3457A and Agilent 34401A) to calculate the power delivered to the heaters. A current excitation module and an isolated analog input module were connected to the
In order to use the RTDs to measure local temperatures, the resistance of the RTDs was determined at different temperatures. The calibration process was carried out in a controllable oven and the resistances of the RTDs were recorded at different temperatures. A 6 mm thick copper block was machined to seat the devices and to fasten the cover plate on the device. Two calibrated thermocouples were also attached to the bottom of the device through the copper block to measure the temperature of the device. The entire assembly was placed in the oven, and the ribbon cables and the thermocouples were connected to the terminal block and the DAQ through the insulated opening of the oven. The oven temperature was set, and after reaching steady state temperature in the device (variations less than 0.1 °C), resistances and temperatures were recorded and a calibration curve was plotted for each RTD (e.g., Fig. 6). To estimate the heat loss to the substrate, the device was vacuumed and the temperatures of the RTDs were measured for a range of heaters’ powers. Assuming negligible natural convection and radiation in the channel, the recorded power was used to estimate the heat loss during the experiments based on the temperature of the RTDs. The procedure was performed for the two combinations of powered heaters during experiments (Cases I and II) to minimize the effect of discrepancy in the axial conduction pattern on the heat loss estimate between the two cases. Once the RTD calibration curves and heat loss estimations were obtained, time-averaged steady state heat transfer coefficient for single-phase flow and bubbly flow was calculated for various liquid and gas flow rates at different RTD locations on Heater #4. The experiments were performed and compared for two cases of thermally developing flow: (1) only Heater #4 turned on, and (2)
Fig. 3. Cross-section of the deposited layers; heaters (left), RTDs (right).
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a
b Cover plate
c Delrin block
Fig. 4. Device packaging; (a) exploded view, (b) cover plate (top), (c) cover plate (bottom).
Fig. 5. A Schematic of the experimental setup.
all heaters turned on. To prevent cavitation of the dissolved gas in the microchannel, the tank containing distilled water was degassed using a vacuum pump, and subsequently pressurized helium— which is insoluble gas in water (15 mg/kg)— was introduced into the tank. The bubble formation and trajectory over Heaters #3 and #4 were captured by the high speed camera through a 2.5 objective lens while the test section was illuminated by a halogen lamp. To quantify the flow rates in the two-phase regime, superficial velocities of liquid and gas phases were used:
100.0 90.0 80.0 T ( C)
70.0 60.0 50.0
ji ¼
40.0 30.0 20.0 285
290
295
300
305
310
315
320
R (Ω) Fig. 6. An example of RTD calibration curve; (RTD #2).
325
Ci Ac
ð1Þ
where i specifies the phase (i.e., liquid or gas), Ci (m3/s) is the volumetric flow rate of fluid i, and Ac (m2) is the cross-sectional area of the microchannel. Reynolds number was defined as:
Re ¼
quDh l
ð2Þ
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where q (kg/m3) is the density, l (kg/m s) is the dynamic viscosity, (m/s) is the average liquid velocity, and Dh (m) is the hydraulic u diameter of the channel. The thermophysical properties were calculated at the inlet temperature. The local heat transfer coefficient at each RTD was calculated based on the convective heat transfer equation:
q00net ¼ hðT w T 0 Þ
ð3Þ
where Tw is the calculated wall temperature at the RTD, T0 is the inlet channel temperature and q00net is the effective heat flux of the hea ter: Q_ tot Q_ loss =AH . Because of the insulating layers on the RTDs, the wall temperature is slightly lower than the RTD temperature, which was corrected through a one-dimensional conduction analysis: T w ¼ T RTD q00 t eq =keq where teq and keq are the equivalent thickness and thermal conductivity of the composite insulation layer, respectively. However, this estimated temperature difference in the present study was calculated and found to be very small (<0.1 °C). The effect of bubbles on the heat transfer coefficient was quantified by introducing enhancement factor, E, which compares the heat transfer coefficient of the bubbly flow to that of the singlephase liquid flow at the same liquid flow rate:
E¼
hb hsp hsp
ð4Þ
hb and hsp denote bubbly flow and single-phase heat transfer coefficients at a same RTD, respectively. 2.5. Heat loss and uncertainties The conjugate conduction/convection effect, which is a result of a non-ideal insulating substrate, is an important factor that should be considered in microscale convective heat transfer experiments. The conduction is a three-dimensional process, which can be divided into depth-wise direction (y) and planar direction (z, x; transverse and axial). Depth-wise conduction is mainly through the Pyrex, and the planar conduction mainly occurs near the heater edges through the composite structure made of Al, Ti, and Pyrex layers. In the present study, the method used to estimate the heat loss—through conduction—at each RTD location is based on the temperature of the RTD. The surface temperature corresponding to conduction heat transfer to the substrate (assuming no convection and radiation and uniform heat generation in the heater) was obtained through the vacuum test. Therefore, if the temperature of the RTD is known during the experiments, the combined value of the heat loss can be estimated. A concern arises since the boundary condition of the non-heated surfaces—in the periphery of the heaters —during the actual experiments and vacuum test is not the same (h – 0 vs. h = 0); this can lead to underestimation of the heat loss [3]. A careful combination of vacuum test results and a numerical model can predict the heat loss more accurately. Since the estimated heat loss was not a significant fraction of the applied power and the RTDs were located in the center of the heater, this effect was considered very small and was added to the biased uncertainties. The heat loss was estimated based on the heaters’ powers and the temperatures of the RTDs in the vacuum experiment. The estimated heat loss ranged between 3% and 13% for the minimum and the maximum wall temperatures, respectively. It is also worth noting that the optical visualization can affect the RTD measurements due to the light source, which is a function of the light intensity and wavelength spectrum, and the magnification of the objective lens used. In the present study—in which a 2.5 objective lens was used—the effect was negligible, but could lead to temperature rise with higher magnifications (e.g., 0.2 °C for 10 at low liquid flow rates). This effect is a biased uncertainty
in the supplied heat flux, and can be eliminated by using a cooled light source similar to Chen and Garimella [20]. The measurement uncertainty in the flow rate was associated with the rotameter accuracy and ranged between ±3% and ±6% for the maximum and the minimum flow rates, respectively. The uncertainty in the temperature measurements was less than ±0.3 °C while the uncertainty in the power measurements was negligible (<0.1%). The uncertainty in the enhancement factor, E, was estimated to be between ±4% and ±12% depending on the value and the change in heat transfer coefficient. A summary of the uncertainties in heat transfer calculations is provided in Table 2.
3. Thermal boundary layer thickness To investigate the effect of bubbles on mixing and disruption of the thermal boundary layer, the thermal boundary layer thickness in the channel was estimated using a two-dimensional integral method. To apply the integral method, a fully developed velocity profile (a second-order polynomial) was considered for the crosssectional velocity distribution, and an energy balance on the thermal boundary layer (Eq. (5)) was performed. A third order polynomial was considered for the temperature distribution in the thermal boundary layer. Imposing the boundary conditions, velocity and temperature profiles were derived according to Eqs. (6) and (7).
kl
@Tðx; 0Þ d ¼ qcp @y dx
Z
dt
uðT T 0 Þdy
ð5Þ
0
y y2 u¼U 2 a a
T ¼ T0 þ
ð6Þ
" # q00w 2 1 y3 dt y þ 3 d2t kl 3
ð7Þ
where 2a = H is the channel depth, U is the liquid velocity at the centerline (y = a), and dt is the thermal boundary layer thickness. It should be noted that using a second order polynomial for the velocity profile implies flow between parallel plates, which is a valid assumption because of the large aspect ratio of the channel (W/H 7). Substituting Eqs. (6) and (7) into Eq. (5), and solving for dt, with boundary condition of dt = 0 at x = 0, the thermal boundary layer thickness was calculated according to the implicit form of Eq. (8):
a U
x¼
2 3 1 4 d d 15a t 36a2 t
ð8Þ
where a is the thermal diffusivity a = k/qcp. For a given fluid, the heater length, channel geometry, and liquid flow rate are the important parameters affecting the thermal boundary layer thickness.
Table 2 Sources of uncertainly in heat transfer measurements. Quantity
Source of uncertainty
Estimated values
RTD temperature 1-D correction for insulating layers
0.3 °C Negligible (<0.1 °C)
Total delivered power Heat loss estimation Light source effect
Negligible (<0.1%) Small (1%) Negligible
Wall temperature
Heat flux
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200
4. Results and discussion
180 160 140
x'=0.72 mm x'=1.47 mm x'=2.82 mm
(RTD #2) (RTD #3) (RTD #4) (RTD #5) (RTD #1)
120 100
Case I
δt (μm)
Three different air flow rates (2, 4, and 6 ml/min; jg = 0.1, 0.2, and 0.3 m/s) at room temperature (24 °C) were introduced into a stream of liquid water (also at room temperature) with flow rates ranging from 5 to 33.1 ml/min (corresponding to 0.25 m/s 6 jl 6 1.75 m/s, and 125 6 Re 6 825), and the effect of bubbles on the heat transfer coefficient was studied. Fig. 7 shows images of bubbles in their formation stage and downstream of the orifice for a range of flow rate combinations (a pair of images for each case). A 2.5 objective lens was used to capture the bubbles throughout the length of Heater #4. The bubble size decreased with increasing liquid flow rate and increased with increasing air flow rate; at low liquid flow rates, large bubbles formed slugs. To study the effect of the thermal boundary layer thickness on the heat transfer enhancement over Heater #4, measurements at different RTDs were carried out for two heating configurations. In Case I, all the heaters were connected in series, steady state heat transfer coefficients for single-phase and two-phase flow (with and without air bubbles) were obtained, and the enhancement factors due to the presence of bubbles were calculated for different flow rate combinations. In Case II, the first three heaters were disconnected from the power supply, and only Heater #4 was powered to provide the same wall heat flux as in Case I (31 W/ cm2); enhancement factors were calculated similar to Case I. In Case I, the thermal boundary layer had developed over a longer length along the channel and was thicker compared to Case II—for similar liquid flow rates. According to Eq. (8), as the liquid flow rate increases, the thermal boundary layer thickness decreases. The estimated thermal boundary layer thicknesses at different RTD positions for Case I and Case II are plotted in Fig. 8. The thickness at the trailing edge of Heater #4 for Case I was between 92 and 190 lm, whereas the estimated thickness for Case II was between 52 and 102 lm. The heat transfer enhancements, E, at different RTD positions for Case I are depicted in Fig. 9 for different flow rate combinations. The bubbles affect the local velocity and temperature of the liquid over the RTDs and, therefore, determine the heat transfer coefficient and the enhancement factor. At low liquid flow rates, slug flow dominated and the heat transfer coefficient changed very slightly with respect to single-phase flow. With increasing liquid
x=12.07 mm x=12.75 mm x=13.5 mm x=14.85 x=9.51 mm
80 60
Case II
730
40 20 0
0
0.5
1
1.5
2
2.5
3
jl (m/s) Fig. 8. Estimated thermal boundary layer thickness at different RTD locations for Case I and II; x0 = x 12.03 (mm).
flow rate, the flow gradually transitioned to bubbly flow and, consequently, the enhancement factor increased before peaking, and subsequently decreased. The flow rates at which the maximum was reached varied at different locations and tended toward the higher liquid flow rates for the RTDs located further downstream of the heater. Fig. 10 shows the enhancement factors for Case II. Since RTD #2 was located at the leading edge of the heater, the variation in the surface temperature was very small, independent of the flow condition. In Case II, the enhancement factors typically started with negative values at low liquid flow rates and increased up to 50% with increasing liquid flow rate. The enhancement factors were typically smaller for the upstream RTDs because the bubbles (or slugs) tended to move more slowly during the acceleration stage. In particular, the hindering effect was typically more significant for bigger bubbles, which suggests that the heat-up of the liquid layer between the heater and the bubbles/slugs (with diameter larger than the channel depth) increases the wall temperature and hinders the heat transfer process.
Fig. 7. Bubbles at different flow rates.
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90
jg = 0.1 (m/s)
80
jg = 0.2 (m/s)
70
jg = 0.3 (m/s)
120
E (%)
E (%)
jg = 0.3 (m/s)
80
50 40
60 40
30 20
20
10 0
0 0.00
0.50
1.00
1.50
90 80 70 60 50 40 30 20 10 0 -10
0.00
2.00
jl (m/s)
a jg=0.1 m/s jg=0.2 m/s jg=0.3 m/s
0.00
0.50
1.00
0.50
1.50
2.00
jl (m/s)
100 90 80 70 60 50 40 30 20 10 0
1.50
2.00
1.50
2.00
jg = 0.1 (m/s) jg = 0.2 (m/s) jg = 0.3 (m/s)
0.00
d
1.00
jl (m/s)
b
E (%)
E (%)
jg = 0.2 (m/s)
100
60
c
jg = 0.1 (m/s)
0.50
1.00
jl (m/s)
Fig. 9. Heat transfer enhancement at different RTD locations (Case I); (a) RTD #2, (b) RTD #3, (c) RTD #4, (d) RTD #5.
The velocity field measurements around the bubbles are presented in [10]. In summary, the introduction of bubbles increases the mean velocity of the liquid. Closer to the orifice, the streamlines are curved around the forming bubbles and lower velocity regions are observed in the wake of the bubbles. When the bubbles approach terminal velocity, a path with lower velocity (with approximately the same width as the bubbles) is formed in the middle of the channel surrounded by two high velocity regions on the sides. High local velocities due to the recoil of bubble tails are also observed. Comparing the enhancement factors at each RTD for Case I and Case II, it is evident that the enhancement factor was more significant in Case I, which corresponded to thicker thermal boundary layers. It is believed that deflected streamlines around the bubbles and the shear layer around them during the formation and acceleration stages promoted mixing across the channel and disrupted the thermal boundary layer. In addition, the oscillation of the bubbles caused by the initial recoil of the bubble tails could have also aided the mixing process. The net effect of the mixing, modification of the velocity field, and the formation of thin liquid layer underneath the bubbles determined the resultant heat transfer enhancement. Since all the parameters for Cases I and II, except the temperature profile of the flow right upstream of Heater #4, were kept the same, the substantial deviation in the results demonstrates the liquid mixing caused by the bubbles and their considerable effect on heat transfer enhancement. Although the main purpose of these experiments was to examine the mixing potential and boundary layer disruption of the injected bubbles, the trends observed merit further discussion. Since the RTD measurements are local, it is believed that the enhancement factors shown in Figs. 9 and 10 are related to the configuration of the bubble as they flow over the RTDs.
As shown in Fig. 8 (e.g., jg = 0.3 m/s, jl = 0.77 m/s), the bubbles undergo an oscillation period before reaching a stable (circular) shape. Elongated oval shaped bubbles (along the flow direction x) detach from the orifice; after recoiling of the tail, they turn into blunt oval bubbles (major axis in transverse direction z), before finally becoming circular. It should be noted that the oscillation phases of the bubbles are different for different flow conditions, but for a specific flow condition, all the bubbles at a specific axial location, maintain a repeatable time-independent pattern. A comparison of the results in Fig. 9 and the high speed footage of Fig. 8 suggests that the shape of the bubbles passing over the RTDs can be linked to the distinct trends observed at different RTDs. The axial dimension of the bubble defines its residence time over an RTD, so the blunt oval bubbles pass over the RTDs faster than the elongated ones for a same liquid flow rate, allowing less time for the wall temperature to rise. This blunt shape can also promote mixing more effectively in its wake. Based on the analysis of the high speed footages, it is evident that for higher liquid flow rates, the oscillation period extends a longer distance, and therefore, the blunt oval shaped bubbles form over the downstream section of the heater. RTDs #2 and #3 have the highest enhancement factors at moderate liquid flow rates while RTD #4 and RTD #5 have peak enhancement at higher liquid flow rates. This trend coincides with the location of the minimum axial dimension of the bubbles during their oscillation period. Furthermore, for the lowest gas flow rate at high liquid flow rates, the bubbles were smaller than the channel height (Fig. 8, jg = 1 m/s, jl > 0.77 m/s), which could lead to the slightly different trend observed in E. In Fig. 11, the average values of the enhancement factors calculated at different RTDs (extracted from Figs. 9 and 10) are presented. Based on the earlier discussions, and considering the heat-up of the liquid layer underneath the bubbles as a hindering
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Fig. 10. Heat transfer enhancement at different RTD locations (Case II); (a) RTD #3, (b) RTD #4, (c) RTD #5.
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with increasing liquid flow rate, their residence time diminishes, and the enhancement factor increases. It should be noted that the effect of bubble shape, discussed above, is only one of the parameters affecting the heat transfer process, and conclusive account of the trends require a detailed transient, three-dimensional measurements of the velocity and fluid temperature fields, and the wall temperature. For instance, the significantly higher enhancement for smaller bubbles at high liquid flow rates, especially at downstream RTDs, might also be attributed to higher velocity regions in the flow closer to the RTDs in the center. The lateral mixing between the heated area—over the heaters and unheated areas on the sides—might have contributed to higher enhancement factors for moderate liquid flow rates with medium size bubbles.
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effect, and mixing as an enhancing effect, the dissimilar trends in Case I and Case II (bell-shaped vs. monotonic) can be explained. In Case I, the larger bubbles at lower liquid flow rates cover the RTDs for a longer period of time, and liquid layer underneath the bubbles heats up more; thus, the hindering effect is more pronounced. As the liquid flow rate increases and the bubbles become smaller, the combined effect of mixing and lower residence time of the bubbles leads to an increased enhancement. At higher liquid flow rates, because of the thinner boundary layers (and also smaller and more stretched bubbles), the effect of mixing is less significant and, therefore, the enhancement factor decreases. In Case II, because of the thin boundary layer, the effect of mixing is already small, so the main factor controlling the process is the resident time of the bubble over the RTDs. As the bubbles become smaller
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Fig. 11. Average heat transfer enhancement of the RTDs; (a) Case I, (b) Case II.
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5. Conclusion Immiscible air bubbles were introduced into a water stream flowing in a horizontal microchannel, and their effect on the heat transfer process was studied. The heat transfer coefficient for bubbly flow was compared to that of the single-phase flow at different locations along the heater. Experiments were carried out for nonheated flow and a thermally developing flow upstream of the test section. In particular, the effect of bubbles on liquid mixing and disruption of the thermal boundary layer was studied. Impact of bubbles on the heat transfer enhancement was more pronounced when the boundary layer was thick, and values up to 100% were observed. This demonstrates the impact of bubble injection on mixing enhancement in the mostly laminar microchannel flows. Furthermore, parameters affecting the heat transfer enhancement trends were discussed. Because of the complexity of the problem, further investigation is merited, both experimentally and numerically, to explain the parameters controlling the heat transfer processes. This should be done through a three-dimensionaltransient measurement of the heat transfer and flow field around the bubbles. It is believed that the characterization of the thermal boundary layer can provide a proper metric for comparing the results of reported studies on microscale and/or macroscale heat transfer systems. Acknowledgments This work is supported by the Office gram Manager Dr. Mark Spector). The acknowledge the staff of the Micro and Room (MNCR) at Rensselaer Polytechnic tance in fabrication of the micro devices.
of Naval Research (Proauthors would like to Nano Fabrication Clean Institute for their assis-
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