- Email: [email protected]
Experimental investigation of the heat transfer and flow characteristics of microchannels with microribs
International Journal of Heat and Mass Transfer 143 (2019) 118482
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation of the heat transfer and flow characteristics of microchannels with microribs Juan Li a,⇑, Zhangyu Zhu a, Liang Zhao b, Hao Peng c,⇑ a
School of Mechanical and Electrical Engineering, Nanjing Forestry University, 159 Long Pan Road, Nanjing 210037, PR China School of Materials Science and Engineering, Nanjing Forestry University, 159 Long Pan Road, Nanjing 210037, PR China c School of Mechanical and Power Engineering, Nanjing Tech University, 30 South Pu Zhu Road, Nanjing 211816, PR China b
a r t i c l e
i n f o
Article history: Received 24 April 2019 Received in revised form 7 July 2019 Accepted 25 July 2019 Available online 7 August 2019 Keywords: Microchannel Microrib Heat transfer Friction factor
a b s t r a c t The single-phase heat transfer and flow characteristics of microchannels with microribs were investigated experimentally in this paper. Based on a smooth rectangular microchannel (MC-S), rectangular microchannels with rectangular ribs on one side (MC-OSR) and both sides (MC-BSR) were proposed. The effects of the volumetric flow rate and inlet temperature on the Nusselt number and friction factor were analyzed. Five positions were assigned evenly in the flow direction at the wall to measure the temperature and determine the wall temperature distribution. The results showed that the Nusselt number increased as the volumetric flow rate and inlet temperature increase. The friction factor decreased with increasing inlet temperature. The thermal performance index of the MC-OSR was higher than those of the MC-BSR and MC-S, which reflected the superior heat transfer performance of the MC-OSR. The wall temperature was nonlinearly distributed in the flow direction. The amplitude of the temperature difference gradually decreased. Compared to the MC-S, the entrance effects of the MC-OSR and MC-BSR were more obvious mainly due to the presence of ribs. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction With the miniaturization and integration of equipment in aerospace, microelectronics, nuclear energy and other advanced engineering fields, efficient heat transfer device is becoming more and more significant. The heat transfer efficiency of microchannels can be increased by two to three orders of magnitude above the conventional size channels. Specifically, for compact equipment, micro/mini-channels not only meet the relevant small size requirements but also provide a high heat transfer efficiency. With the improvements in microfabrication process, optimizing the microchannel structure has become an efficient method of enhancing microscale heat transfer. This process increases the heat transfer area of microchannels. Furthermore, the heat transfer performance of microchannels can be enhanced by improving the mixed flow regime and breaking the thermal and hydraulic boundary layers typically related to the conventional size channels [1–5]. Recently, various microchannels with novel structures, such as rough channels, ribs, cavities and grooves, have been developed. Rawool et al. [6] numerically studied flow through serpentine microchannels with a designed roughness placed along the chan⇑ Corresponding authors. E-mail addresses: [email protected] (J. Li), [email protected] (H. Peng). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118482 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
nel walls and found that the friction factor increases with increasing obstruction height. Masoud et al. [7] conducted a numerical study to investigate the effects of aligned and offset roughness patterns on the fluid flow and heat transfer phenomena within rectangular cross sections of microchannels. The study found that the offset arrangement provided lower pressure loss for the considered fluids and a lower heat transfer rate for water than the aligned pattern at high roughness heights and low channel heights. Some scholars [8–10] have found that the Poiseuille and Nusselt numbers were higher when the relative surface roughness was larger by investigating the effect of surface roughness on the flow and heat transfer characteristics in different microchannels. Kang et al. [11] used deionized water as the working fluid to experimentally investigate the flow and heat transfer characteristics in four types of silicon-based microchannels with different cylindrical pin-fin arrangements. The results showed that pin-fin arrays enhanced the heat transfer coefficients and simultaneously increased flow resistances. Under the same conditions, larger friction factors and heat transfer coefficients were obtained in staggered pin-fin microchannels than in in-line pin-fin microchannels. By combining numerical studies with experimental studies, Zhang et al. [12] investigated the characteristics of flow and heat transfer in microchannel heat sinks with circular, triangular and square cross-section pin-fin arrays. The results showed that
2
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Nomenclature A B b Cp Dh di f H h have hf L R le R li Nu P DP DPin DPout Q R Re T
heat transfer area, m2 microchannel width, m rib width, m constant pressure specific heat, J/(kg∙K) hydraulic diameter, m inner diameter of the pipe, m friction factor microchannel height, m rib height, m average heat transfer coefficient, W/(m2∙K) energy loss of the pipeline system, J/kg microchannel length, m total length of the straight pipe, m total equivalent length of valves, m Nusselt number pressure, kPa pressure drop, kPa inlet pressure loss, kPa outlet pressure loss, kPa heat transfer rate, W relative uncertainty Reynolds number temperature of microchannel, K
the friction coefficient decreased and Nu increased with increasing Re. These assessments of comprehensive flow and heat transfer performance indicate that the circular pin-fin structure performs better than others arrangements. In contrast to the corresponding conventional rectangular microchannel, Chai et al. [13–17] performed investigations on the fluid flow and heat transfer characteristics of microchannel heat sinks with ribs or cavities. The results showed that these microchannels exhibited superior heat transfer enhancement characteristics. As a consequence of the significant pressure drop, the microchannel heat sink with offset ribs gradually lost its advantage as an effective heat transfer enhancement method at high Reynolds numbers. Furthermore, ribs can significantly reduce the temperature increase of the heat sink base and efficiently prevent the drop of the local heat transfer coefficient along the flow direction but also result in a higher local friction factor than that for straight microchannels in some cases. Wang et al. [18] studied the thermo-hydraulic performance of the microchannel heat sink (MCHS) with bidirectional ribs (BRs) experimentally. It indicates that bidirectional ribs could strengthen the heat transfer by interrupting the thermal boundary layer and inducing recirculation in both vertical and spanwise directions. Zeng et al. [19] numerically studied the effects of isosceles triangle grooves on fluid flow and heat transfer in microchannels. Compared to a smooth microchannel, the isosceles triangle groove structure increased the Nusselt number and pressure drop. Ahmed et al. [20] numerically investigated the effects of geometrical parameters on the laminar water flow and forced convective heat transfer characteristics in a grooved microchannel heat sink (GMCHS). The results showed that trapezoidal grooves with a groove tip length ratio of d = 0.5, groove depth ratio of b = 0.4, groove pitch ratio of w = 3.334, groove orientation ratio of n = 0.00 and Re = 100 provided the optimum thermal design for the GMCHS, with a Nusselt number enhancement of 51.59% and friction factor improvement of 2.35%. Deng et al. [21] studied a
t Dtm u V w Y
temperature of cooler, K Logarithmic mean temperature difference, K velocity of deionized water, m/s volumetric flow rate, ml/min mass flux, kg/s independent variable
Greek symbols e actual effectiveness q density, kg/m3 k thermal conductivity, W/(m∙K) kl friction factor of the pipeline, l dynamic viscosity, kg/(m·s) Rni total local drag coefficients g Thermal performance index Subscripts ave average cool cooler hot microchannel in inlet out outlet
novel type of periodic expanded-constrained microchannels (PECM) heat sink by experimental tests and numerical simulations. It was obtained that the heat transfer enhancement of PECM was not accompanied with the expense of pressure drop penalty compared to the rectangular counterpart. According to some other studies [22–26], the heat transfer enhancement mechanism of cavities could be attributed to the interactions associated with the redevelopment of the hydraulic and thermal boundary layers, the effect of jetting and throttling and the stagnation zone in laminar flow. A hybrid strategy involving ribs and either grooves or cavities has also been adopted as an effective technique for enhancing heat transfer. By referring mainly to Li et al. [27], Ghani et al. [28] numerically studied the characteristics of fluid flow and heat transfer for newly designed microchannel heat sinks with sinusoidal cavities and rectangular ribs (MC-SCRR) based on Reynolds numbers ranging from 100 to 800. By comparing the performance of the proposed microchannel to that of a microchannel with rectangular ribs (MC-RR) and that of a microchannel with sinusoidal cavities (MC-SC), the study found that the thermal performance of the MC-SCRR was superior to that of the MC-RR and MC-SC. The new design of the MC-SCRR effectively combined two important features: a large flow area that significantly reduces the pressure drop and high flow disturbances caused by the existence of ribs in the central portion of the channel. As mentioned above, the lack of data and limited availability of microchannels are major difficulties that limit practical applications. In particular, the heat transfer and flow performance of novel microchannel structures should be evaluated through extensive test results. It is necessary to conduct experimental studies and provide design references. In this paper, rectangular microchannels with rectangular ribs on one side (MC-OSR) and both sides (MC-BSR) were proposed. The single-phase heat transfer and flow characteristics were experimentally investigated. The effects of the volumetric flow rate and inlet temperature on the Nusselt
3
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
number and friction factor were analyzed. The wall temperature distribution was examined to explore the heat transfer enhancement effect and mechanism of the ribs. 2. Experimental investigations
Microchannel
Cooling water outlet
2.1. Experimental apparatus A schematic diagram of the experimental apparatus is shown in Fig. 1. The apparatus consists of a test section, a heating system, a cooling cycle system and a data collection system. Deionized water was used as the working fluid. The temperature of deionized water is adjusted with a heater which could be regulated in the ranges of 0–3 kW. The volumetric flow rate of the working fluid was controlled by a peristaltic pump which worked in a range of 0–300 ml/min with an accuracy of ±0.5 ml/min. The working fluid was cooled in the test section and then flows into a container. The circulation cooling fluid was supplied by a thermostatic water bath which worked in a range of 243 to 373 K with an accuracy of ±0.1 K. All the signals from the pressure transducer in a range of 0–25 kPa with an accuracy of 0.25% and thermocouples in a range of 73 to 633 K with precision of ±0.1 K were collected by a data acquisition system. All equipment was calibrated before test. To minimize heat loss, the pipeline system was designed to be as short as possible and covered with adiabatic material made of nitrile butadiene rubber and polyvinyl chloride. To evaluate the effects of Re and the inlet temperature on the heat transfer performance of the microchannel, two test cases were conducted in this study. The first test was conducted to increase the inlet flow rate from 30 ml/min to 90 ml/min with a fixed inlet temperature of 343.15 K. The second test was conducted to increase the inlet temperature from 298.15 K to 358.15 K with a fixed inlet flow rate of 75 ml/min. The inlet flow rate and temperature of the cooling fluid were 180 ml/min and 278.15 K, respectively. 2.2. Test section The test section mainly contains the cover plate, the experimental microchannel plate and the cooler plate. A detailed introduction to the test module is given in Fig. 2. Based on the thermal conductivity, sealing performance, processing degree and other factors,
T
Thermocouple holes
Cooling water inlet Heang water outlet
Cooler plate
Fig. 2. Test section example.
the test section was completely manufactured using aluminum alloy. To prevent the leakage of the working fluid, the test section was assembled with bolted connections and high-temperature resistant metal gaskets and sealants. To reduce heat loss, adiabatic material was wrapped around the test section. The smooth rectangular microchannel (MC-S), MC-OSR and MC-BSR were tested in this paper. All the three different types of microchannels are manufactured by precise carving mechanism. These channels have the same hydraulic diameter of 1 mm. The plane structure and main dimensions of the microchannels, such as the total length (L), total width (B), total height (H), rib height (h) and rib width (b), are illustrated in Fig. 3. The detailed dimensional parameters of the experimental microchannels are shown in Table 1. The distance between adjacent ribs is 3.5 mm. The pressure transducers and T-type thermocouples were installed 60 mm away from the inlet and outlet of microchannels to measure the inlet and outlet pressure and temperature. Another five thermocouples were inserted at the bottom of the tested microchannels with a horizontal spacing of 16 mm for wall temperature measurements. The distance between the microchannel base and the thermocouples is 1 mm. The designed positions are shown in Fig. 4. 2.3. Data reduction This section presents the relevant formulas used to calculate the characteristics of heat transfer and fluid flow in microchannels. The energy balance equation for a counter-flow microchannel heat sink is expressed by
Data acquision P
Cover plate Heang water inlet
Q cool ¼ e Q hot
ð1Þ
P
PC
Test secon Peristalc pump
Volume flow meter
MC-OSR MC-BSR MC-S
Heater
Thermostac water bath Fig. 1. Experimental apparatus.
Container Fig. 3. Tested microchannels.
4
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Table 1 Structural parameters of the experimental microchannels. Microchannel
MC-S
MC-OSR
MC-BSR
Microchannel width (B) Microchannel height (H) Microchannel length (L) Rib width (b) Rib height (h) Hydraulic diameter (Dh)
1 mm 1 mm 100 mm – – 1 mm
1 mm 1 mm 100 mm 0.5 mm 0.5 mm 1 mm
1 mm 1 mm 100 mm 0.5 mm 0.5 mm 1 mm
where q is the mean density of deionized water, u is the velocity and l is the mean viscosity. The pressure drop is obtained from experimental observations, and the theoretical formulas is as follows [29]:
DP ¼ Pin Pout DPin DPout
ð11Þ
where DP in is the inlet pressure loss of the microchannel and DPout is the outlet pressure loss.
DPin ¼ q hf
ð12Þ
DPout ¼ q hf
ð13Þ
P P 2 li þ le X u þ ni hf ¼ kl di 2
ð14Þ
where hf is the energy loss of the pipeline system, kl is the friction P factor of the pipeline, li is the total length of the straight pipe, P le is the total equivalent length of valves, di is the inner diameter P of the pipe, and ni is sum of local drag coefficients. The friction factor is defined as:
f ¼
2DPDh qu2 L
ð15Þ
The thermal performance index, which was used to evaluate the heat transfer changes at a constant pumping power, was introduced by Webb [30–32]: Fig. 4. Measurement points.
g¼
13 Nu f Nu0 f0
ð16Þ
where Q cool denotes the heat transfer rate of the cooler, Q hot denotes the heat transfer rate of the microchannel and e denotes actual effectiveness.
where Nu0 and Nu are the Nusselt numbers of a smooth microchannel and a microchannel with ribs respectively, and f 0 and f are the corresponding friction factor.
Q cool ¼ Cpcool wcool ðt out tin Þ
ð2Þ
2.4. Uncertainty analysis
Q cool ¼ Cphot whot ðT out T in Þ
ð3Þ
where Cpcool and Cphot are the specific heat values of the corresponding fluid, wcool and whot are the mass fluxes, t out and T out are the outlet temperatures and t in and T in are the inlet temperatures.
w¼V q
ð4Þ
where V is the volumetric flow rate and q is the density. The average heat transfer coefficient is calculated by
hav e ¼
Q cool A Dt m
ð5Þ
where A is the heat transfer area. In this case, Dt m is the logarithmic mean temperature difference, which is calculated as follows.
Dt m ¼
DT 1 DT 2 ln DDTT 12
3.1. Validation of the experimental results
DT 2 ¼ T out tin
ð8Þ
ð9Þ
where Dh is the hydraulic diameter of the microchannel and k is the thermal conductivity of deionized water. The Reynolds number is defined as
q u Dh l
The variation of the Nusselt number against Reynolds number for the MC-S is described in Fig. 5. The result of Ref. [33] is adopted Table 2 Maximum uncertainties.
The average Nusselt number is calculated by
Re ¼
ð17Þ
3. Results and discussion
ð7Þ
hav e Dh k
" #12 n X DR DY i 2 ¼ R Yi i¼1
ð6Þ
DT 1 ¼ T in t out
Nu ¼
All temperatures were measured with T-type thermocouples, and all pressures were measured with pressure transducers. All data except the volumetric flow rate were collected using a data acquisition system. The inlet volumetric flow rates of the microchannel and the cooler were controlled by a peristaltic pump and a volumetric flow meter, respectively. The maximum uncertainty of each experimental parameter is given in Table 2 based on the following equation.
ð10Þ
Parameters
Maximum uncertainty
Temperature Volumetric flow rate Pressure Reynolds number Heat transfer coefficient Nusselt number Friction factor Thermal performance index
±0.1 K ±0.35% ±0.5% ±2.15% ±2.17% ±2.68% ±2.41% ±3.92%
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Fig. 5. Variation of the Nusselt number with Re for the MC-S.
5
Fig. 7. Variations in the Nusselt number with the inlet temperature for the MC-S, MC-OSR and MC-BSR.
to validate. The results show the same trend. Furthermore, the Nusselt number of reference is lower than that of present work. It could be due to the uneven temperature distribution in multiple microchannels. The variation of calculated friction factor in MC-S with Reynolds number is compared with theoretical correlation of Shah and London [34] as shown in Fig. 6. The friction factor obtained by the experiment presents the same trend with the theoretical calculation curve. There is some discrepancy between them which can be referred to the multiple vertical bending at inlet and outlet of the microchannel. 3.2. The effect of the inlet temperature Fig. 7 shows the variations in the Nusselt numbers of the tested microchannels with the inlet temperature when the volumetric flow rate is 90 ml/min. The Nusselt number increases with increasing inlet temperature because the viscosity of the fluid decreases with increasing inlet temperature, which causes the thermal and hydraulic boundary layers to easily break up. At different inlet temperatures, MC-OSR displays the highest Nusselt number. Fig. 8 displays the variations in the friction factor with the inlet temperature for the MC-S, MC-OSR and MC-BSR. With increasing temperature, the friction factor in the microchannels decreases
Fig. 8. Variations in the friction factor with the inlet temperature for the MC-S, MCOSR and MC-BSR.
slightly, which is attributed to the decrease in the viscosity of the fluid. 3.3. The effect of the volumetric flow rate
Fig. 6. Variation of the friction factor with Re for the MC-S.
The variations in the Nusselt number with the volumetric flow rate for the three microchannels are illustrated in Fig. 9. The Nusselt number increases with increasing volumetric flow rate, and the slopes of the Nusselt number curves decrease with increasing volumetric flow rate. The Nusselt numbers of the three microchannels are relatively similar at low volumetric flow rates. By comparison, the Nusselt numbers of the MC-OSR and MC-BSR are higher than that of the MC-S. This finding indicates that the ribs enhance heat transfer by increasing the heat transfer area, the jetting and throttling effects and the chaotic advection caused by ribs. Simultaneously, the MC-OSR displays the best thermal performance. When the ribs are placed on one side, the fluid flow on both sides is asymmetrical, which causes an obvious heat transfer enhancement due to boundary layer breakup and intensified chaotic mixing.
6
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Fig. 9. Variations in the Nusselt number with the volumetric flow rate for the MC-S, MC-OSR and MC-BSR.
Fig. 10. Variations in the friction factor with the volumetric flow rate for the MC-S, MC-OSR and MC-BSR.
Fig. 11. Variations in the thermal performance index with the inlet temperature for the MC-S, MC-OSR and MC-BSR.
Fig. 12. Variations in the thermal performance index with the volumetric flow rate for the MC-S, MC-OSR and MC-BSR.
3.4. Thermal performance index As illustrated in Fig. 10, the trend of the friction factor curves is downward when the volumetric flow rate is less than 60 ml/min. And then there is a mutation in the friction factor curve which indicates the transition of flow state. The friction factor for the MC-OSR and MC-BSR are lower than that for the MC-S. This result suggests that the flow area enlargement caused by the ribs can reduce the pressure loss. At low volumetric flow rate, the velocity of recirculation is small which cause the formation of flow stagnation regions [27,28]. The main stream slips over the ribs and the friction coefficient between the fluid and the microchannel walls is partly replaced by that between the fluid and the fluid in the MC-OSR or MC-BSR. Obviously, friction resistance between the fluids is smaller than that between the fluid and the microchannel walls. When the volumetric flow rate is greater than 60 ml/min, the recirculation and the jetting and throttling effects [14,21,27,28] enhance by the ribs. The difference of friction factor for the microchannel with or without ribs is smaller. Additionally, the MC-OSR has a slightly larger friction factor than the MC-BSR because of the asymmetrical flow.
The purpose of the proposed novel structure is to develop a microchannel heat exchanger with high thermal performance and a low pressure drop. The thermal performance index, which represents the Nusselt number ratio divided by the friction factor ratio to the power of one-third, is used to evaluate the overall performance of each microchannel in this study. The value of the performance index indicates the thermal effectiveness relative to the pressure drop. Therefore, the higher the performance index value is (greater than 1), the better the performance of the microchannel. The variations in the performance index with the inlet temperature and volumetric flow rate are presented in Figs. 11 and 12 respectively. The performance index exhibits a slight decrease with increasing inlet temperature. This result clearly shows that the viscosity of the fluid has a certain effect on the heat transfer enhancement as demonstrated by the small negative trend. The performance index values of the MC-OSR and MC-BSR are directly proportional to the flow rate, except at high
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
flow rates, when the performance index slightly decreases. This finding indicates that increasing the flow rate is not an effective method of improving performance when the flow rate reaches a certain value. The performance index of the MC-OSR is superior compared with that of the MC-BSR. When the main flow with a constant volumetric flow rate crosses the expanded flow area, the ribs placed on one side of domain disrupt the flow and lead to the breakup of the hydraulic and thermal boundary layers due to asymmetry more obviously. The superiority of the thermal performance of the microchannels with ribs can be attributed to many reasons: (1) the increase in the heat transfer area due to the presence of ribs leads to increased heat transfer and a slight reduction in the pressure loss; (2) the jetting and throttling effects caused by the ribs lead to flow disruption, which promotes flow instabilities and flow mixing; and (3) although the fluid entering the rib region is partially trapped, which leads to the formation of flow stagnation regions, the ribs are able to enhance heat transfer due to the transverse convection [28] between the partial fluid in the ribs region and the main flow in the central region.
7
3.5. Wall temperature distribution and temperature difference analysis Figs. 13–15 illustrate the wall temperature distributions and temperature differences at different inlet temperatures for the MC-OSR, MC-BSR and MC-S, respectively. Figs. 13(a), 14(a) and 15(a) indicate that the trend of the wall temperature distribution is nonlinear in the flow direction for different inlet temperatures. For five temperature measurement points at x ¼ 18; 34; 50; 66; and 82 mm along the length of the microchannel, the wall temperature increases with increasing inlet temperature. The wall temperatures of the MC-OSR and MC-BSR are higher than that of the MC-S. For the MC-OCR, MC-BSR and MC-S, the wall temperature differences in the flow direction are displayed in Figs. 13(a), 14(a) and 15(a), respectively. The height of the first column represents the temperature difference between the first and second temperature measurement points, and the subsequent corresponding differences are shown in the next three columns. At a fixed inlet temperature, the wall temperature difference gradually decreases in the flow direction, as shown by the blue arrow. The temperature
Fig. 13. (a) Wall temperature distribution for the MC-OSR at different inlet temperatures; (b) Wall temperature differences for the MC-OSR at different inlet temperatures.
Fig. 14. (a) Wall temperature distribution for the MC-BSR at different inlet temperatures; (b) Wall temperature differences for the MC-BSR at different inlet temperatures.
8
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Fig. 15. (a) Wall temperature distribution for the MC-S at different inlet temperatures; (b) Wall temperature differences for the MC-S at different inlet temperatures.
Fig. 16. (a) Wall temperature distribution for the MC-OSR at different volumetric flow rates; (b) Wall temperature differences for the MC-OSR at different volumetric flow rates.
Fig. 17. (a) Wall temperature distribution for the MC-BSR at different volumetric flow rates; (b) Wall temperature differences for the MC-BSR at different volumetric flow rates.
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
9
Fig. 18. (a) Wall temperature distribution for the MC-S at different volumetric flow rates; (b) Wall temperature differences for the MC-S at different volumetric flow rates.
of the partial fluid in the ribs and the main stream in the central region both decrease along the length of microchannels. For low temperature, the dynamic viscosity of fluid is large and the thermal conductivity coefficient of the fluid is low which lead to the formation of local flow stagnation regions and weaken the heat transfer. This condition is dominant in the MC-OSR and MC-BSR. As the inlet temperature increases, the heights of the four columns decrease. The four columns are highest at T in ¼ 358K. It indicate that the thermal boundary layer is thinner at the entrance and the extent of the interruption and redevelopment of thermal boundary layer caused by reflux is wider which can be referred to the physical properties of fluids at high inlet temperature. The wall temperature distribution and temperature differences at different volumetric flow rates are depicted in Figs. 16–18. As shown in Figs. 16(a), 17(a) and 18(a), the wall temperature displays nonlinear growth in the flow direction for different volumetric flow rates. The wall temperature of the MC-OSR is the highest, and that of the MC-S is the lowest. According to Figs. 16(a), 17(a) and 18(a), the heights of the columns gradually decrease, as shown by the blue arrow for a fixed flow rate. With increasing flow rate, the height of the first column decreases. At low flow rates, the thermal boundary layer is thinner at the entrance of the microchannel which causes the smaller thermal resistance. The heat transfer enhancement caused by the entrance effect is more obvious than the effect of the interruption and redevelopment of thermal boundary layer caused by reflux. In contrast, the height of the remaining three columns increases with the flow rate. This result indicates that the interruption and redevelopment of thermal boundary layer is severer. The rate of thermal boundary layer development is slower due to the lower thermal resistance, which enhance the heat transfer at higher flow rates. The height of the first column for the MC-OSR and MC-BSR is larger than that for the MC-S, mainly because of the more obvious entrance effect for the MC-OSR and MC-BSR due to the ribs. In addition, the asymmetric ribs have a significant effect on the temperature difference compared with the symmetric ribs due to the intensification of flow instabilities and flow mixing. 4. Conclusions In this paper, the heat transfer and flow performance of the MC-OSR and MC-BSR are compared with that of the MC-S based on experimental studies. The heat transfer enhancement effect and mechanism of the ribs were explored by analyzing the effects
of the volumetric flow rate and the inlet temperature on the Nusselt number and friction factor considering the wall temperature distribution. The following conclusions can be extracted from the results. (1) The Nusselt number increases and friction factor decreases with increasing inlet temperature. Considering the Nusselt number difference, the inlet temperature has a smaller effect on the increased heat transfer than does the volumetric flow rate. (2) As the volumetric flow rate increases, the Nusselt number increases, the friction factor decreases and the slopes of the Nusselt number curves decrease. At a low flow rate, the use of ribs has a notable influence on the enhanced heat transfer. When the volume flow rate is around 60 ml/min, there is a transition of flow state. (3) Under the given working conditions, the MC-OSR has the highest Nu, and the MC-BSR has the lowest friction factor. The performance index exhibits a slight decrease with increasing inlet temperature. The MC-OSR displays the best overall performance. Specifically, when the volume flow rate is around 75 ml/min, the MC-OSR has the highest thermal performance index value. (4) The wall temperature is distributed nonlinearly in the flow direction. The wall temperature increases with the flow rate or inlet temperature. As the flow rate increases, the first temperature difference decreases, but the remaining three temperature differences increase. Compared to those for the MC-S, the entrance effects for the MC-OSR and MC-BSR are more obvious. (5) The heat transfer enhancement of the ribbed channels can be referred to the recirculation and the jetting and throttling effects caused by ribs. The formation of local flow stagnation regions can decrease frictional pressure loss at low flow rate.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors acknowledge the financial support provided by the National Natural Science Foundation of China (Nos. 51776095 and
10
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
51606103) and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (No. 15KJB470007). References [1] A. Dewan, P. Srivastava, A review of heat transfer enhancement through flow disruption in microchannel, J. Therm. Sci. 24 (3) (2015) 203–214. [2] A. Bergels, Enhanced heat transfer: endless frontier, or mature and routine?, Enhanc Heat Transf. 6 (1999) 79–88. [3] R. Webb, N. Kim, Principle of enhanced heat transfer, second ed., Taylor & Francis, Boca Ration, 2005, p. 28. [4] M.E. Steinke, S.G. Kandlikar, Review of single-phase heat transfer enhancement techniques for application in microchannels, microchannels and microdevices, Int. J. Heat Technol. 22 (2) (2004) 3–11. [5] N. Zhao, C. Qi, T.T. Chen, et al., Experimental study on influences of cylindrical grooves on thermal efficiency, exergy efficiency and entropy generation of CPU cooled by nanofluids, Int. J. Heat Mass Transf. 135 (2019) 16–32. [6] A. Rawool, S. Mitra, S. Kandlikar, Numerical simulation of flow through microchannels with designed roughness, Microfluid. Nanofluid. 2 (3) (2006) 215–221. [7] M. Kharati-Koopaee, M. Zare, Effect of aligned and offset roughness patterns on the fluid flow and heat transfer within microchannels consist of sinusoidal structured roughness, Int. J. Therm. Sci. 90 (2015) 9–23. [8] X. Yuan, Z. Tao, H.W. Li, et al., Experimental investigation of surface roughness effects on flow behavior and heat transfer characteristics for circular microchannels, Chin. J. Aeronaut. 29 (6) (2016) 1575–1581. [9] Y.P. Liu, G.Q. Xu, J.N. Sun, et al., Investigation of the roughness effect on flow behavior and heat transfer characteristics in microchannels, Int. J. Heat Mass Transf. 83 (2015) 11–20. [10] H. Miao, Y. Huang, H.G. Chen, Flow and heat transfer characteristics in laminar flow through random rough microchannels, J. Beijing Univ. Aeronaut. Astronaut. 37 (6) (2011) 738–742. [11] N. Kang, H.Y. Wu, F.Y. Xu, et al., Flow and heat transfer characteristics in silicon-based pin-fin microchannels, J. Eng. Thermophys. 36 (7) (2015) 1572– 1577. [12] X.Q. Zhang, J.Y. Hua, X.B. Zhao, et al., Study on the flow and heat-transfer properties of microchannel heat sink with different pin-fin shapes, J. Nanjing Normal Univ. (Eng. Technol. Ed.) 18 (1) (2018) 47–55. [13] L. Chai, G.D. Xia, M.Z. Zhou, et al., Numerical simulation of fluid flow and heat transfer in a microchannel with fan-shaped reentrant cavities, J. Harbin Inst. Technol. 43 (6) (2011) 2725–2730. [14] L. Chai, G.D. Xia, M.Z. Zhou, et al., Heat transfer enhancement characteristics of parallel-microchannel silicon heat sink with expansion-constriction cross section, J. Aerosp. Power 28 (12) (2013) 2725–2730. [15] L. Chai, G.D. Xia, H.S. Wang, Numerical study of laminar flow and heat transfer in microchannel heat sink with offset ribs on sidewalls, Appl. Therm. Eng. 92 (2016) 32–41. [16] L. Chai, L. Wang, X. Bai, Thermohydraulic performance of microchannel heat sinks with triangular ribs on sidewalls – Part 1: Local fluid flow and heat transfer characteristics, Int. J. Heat Mass Transf. 127 (2018) 1124–1137.
[17] L. Chai, L. Wang, X. Bai, Thermohydraulic performance of microchannel heat sinks with triangular ribs on sidewalls – Part 2: Average fluid flow and heat transfer characteristics, Int. J. Heat Mass Transf. 128 (2019) 634–648. [18] G.L. Wang, N. Qian, G.F. Ding, Heat transfer enhancement in microchannel heat sink with bidirectional rib, Int. J. Heat Mass Transf. 136 (2019) 597–609. [19] S.J. Zeng, B.D. Shao, L.F. Wang, et al., Numerical analysis of micro-channel with an isosceles triangle grooves, Int. Commun. Heat Mass Transf. 66 (2015) 47– 57. [20] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal and rectangular grooved microchannel heat sinks, J. Liaoning Tech. Univ. (Nat. Sci.) 36 (12) (2017) 47–57. [21] D.X. Deng, L. Chen, X.L. Chen, et al., Heat transfer and pressure drop of a periodic expanded-constrained microchannels heat sink, Int. J. Heat Mass Transf. 140 (2019) 678–690. [22] D.D. Ma, G.D. Xia, W. Wang, et al., Study on thermal performance of microchannel heat sinks with periodic jetting and throttling structures in sidewalls, Appl. Therm. Eng. 158 (2019). [23] M.Q. Pan, H.W. Wang, Y.J. Zhou, Experimental investigation of the heat transfer performance of microchannel heat exchangers with fan-shaped cavities, Int. J. Heat Mass Transf. 134 (2019) 1199–1208. [24] E. Bayrak, A.B. Olcay, M.F. Serincan, Numerical investigation of the effects of geometric structure of microchannel heat sink on flow characteristics and heat transfer performance, Int. J. Therm. Sci. 135 (2019) 589–600. [25] H. Ghaedamini, P.S. Lee, C.J. Teo, Developing forced convection in converging– diverging microchannels, Int. J. Heat Mass Transf. 65 (2013) 491–499. [26] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal and rectangular grooved microchannel heat sinks, Int. Commun. Heat Mass Transf. 66 (2015) 47–57. [27] Y.F. Li, G.D. Xia, D.D. Ma, Characteristics of laminar flow and heat transfer in microchannel heat sink with triangular cavities and rectangular ribs, Int. J. Heat Mass Transf. 98 (2016) 17–28. [28] I. Ghani, N. Kamaruzaman, N. Sidik, Heat transfer augmentation in a microchannel heat sink with sinusoidal cavities and rectangular ribs, Int. J. Heat Mass Transf. 108 (2017) 1969–1981. [29] Q. Xia, S.Y. Jia, Unit operations of chemical engineering (I), Tianjin University Press, 2012. [30] R. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transf. 24 (4) (1981) 715– 726. [31] R. Webb, M. Scott, A parametric analysis of the performance of internally finned tubes for heat exchanger application, J. Heat Transf. 102 (1) (1980) 38– 43. [32] D.L. Gee, R. Webb, Forced convection heat transfer in helically rib-roughened tubes, Int. J. Heat Mass Transf. 23 (8) (1980) 1127–1136. [33] Q. Esmaili, A.A. Ranjbar, S. Porkhial, Experimental analysis of heat transfer in ribbed microchannel, Int. J. Therm. Sci. 130 (2018) 140–147. [34] R.K. Shah, A.L. London, Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data, Academic Press, New York, USA, 1978.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation of the heat transfer and flow characteristics of microchannels with microribs Juan Li a,⇑, Zhangyu Zhu a, Liang Zhao b, Hao Peng c,⇑ a
School of Mechanical and Electrical Engineering, Nanjing Forestry University, 159 Long Pan Road, Nanjing 210037, PR China School of Materials Science and Engineering, Nanjing Forestry University, 159 Long Pan Road, Nanjing 210037, PR China c School of Mechanical and Power Engineering, Nanjing Tech University, 30 South Pu Zhu Road, Nanjing 211816, PR China b
a r t i c l e
i n f o
Article history: Received 24 April 2019 Received in revised form 7 July 2019 Accepted 25 July 2019 Available online 7 August 2019 Keywords: Microchannel Microrib Heat transfer Friction factor
a b s t r a c t The single-phase heat transfer and flow characteristics of microchannels with microribs were investigated experimentally in this paper. Based on a smooth rectangular microchannel (MC-S), rectangular microchannels with rectangular ribs on one side (MC-OSR) and both sides (MC-BSR) were proposed. The effects of the volumetric flow rate and inlet temperature on the Nusselt number and friction factor were analyzed. Five positions were assigned evenly in the flow direction at the wall to measure the temperature and determine the wall temperature distribution. The results showed that the Nusselt number increased as the volumetric flow rate and inlet temperature increase. The friction factor decreased with increasing inlet temperature. The thermal performance index of the MC-OSR was higher than those of the MC-BSR and MC-S, which reflected the superior heat transfer performance of the MC-OSR. The wall temperature was nonlinearly distributed in the flow direction. The amplitude of the temperature difference gradually decreased. Compared to the MC-S, the entrance effects of the MC-OSR and MC-BSR were more obvious mainly due to the presence of ribs. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction With the miniaturization and integration of equipment in aerospace, microelectronics, nuclear energy and other advanced engineering fields, efficient heat transfer device is becoming more and more significant. The heat transfer efficiency of microchannels can be increased by two to three orders of magnitude above the conventional size channels. Specifically, for compact equipment, micro/mini-channels not only meet the relevant small size requirements but also provide a high heat transfer efficiency. With the improvements in microfabrication process, optimizing the microchannel structure has become an efficient method of enhancing microscale heat transfer. This process increases the heat transfer area of microchannels. Furthermore, the heat transfer performance of microchannels can be enhanced by improving the mixed flow regime and breaking the thermal and hydraulic boundary layers typically related to the conventional size channels [1–5]. Recently, various microchannels with novel structures, such as rough channels, ribs, cavities and grooves, have been developed. Rawool et al. [6] numerically studied flow through serpentine microchannels with a designed roughness placed along the chan⇑ Corresponding authors. E-mail addresses: [email protected] (J. Li), [email protected] (H. Peng). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118482 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
nel walls and found that the friction factor increases with increasing obstruction height. Masoud et al. [7] conducted a numerical study to investigate the effects of aligned and offset roughness patterns on the fluid flow and heat transfer phenomena within rectangular cross sections of microchannels. The study found that the offset arrangement provided lower pressure loss for the considered fluids and a lower heat transfer rate for water than the aligned pattern at high roughness heights and low channel heights. Some scholars [8–10] have found that the Poiseuille and Nusselt numbers were higher when the relative surface roughness was larger by investigating the effect of surface roughness on the flow and heat transfer characteristics in different microchannels. Kang et al. [11] used deionized water as the working fluid to experimentally investigate the flow and heat transfer characteristics in four types of silicon-based microchannels with different cylindrical pin-fin arrangements. The results showed that pin-fin arrays enhanced the heat transfer coefficients and simultaneously increased flow resistances. Under the same conditions, larger friction factors and heat transfer coefficients were obtained in staggered pin-fin microchannels than in in-line pin-fin microchannels. By combining numerical studies with experimental studies, Zhang et al. [12] investigated the characteristics of flow and heat transfer in microchannel heat sinks with circular, triangular and square cross-section pin-fin arrays. The results showed that
2
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Nomenclature A B b Cp Dh di f H h have hf L R le R li Nu P DP DPin DPout Q R Re T
heat transfer area, m2 microchannel width, m rib width, m constant pressure specific heat, J/(kg∙K) hydraulic diameter, m inner diameter of the pipe, m friction factor microchannel height, m rib height, m average heat transfer coefficient, W/(m2∙K) energy loss of the pipeline system, J/kg microchannel length, m total length of the straight pipe, m total equivalent length of valves, m Nusselt number pressure, kPa pressure drop, kPa inlet pressure loss, kPa outlet pressure loss, kPa heat transfer rate, W relative uncertainty Reynolds number temperature of microchannel, K
the friction coefficient decreased and Nu increased with increasing Re. These assessments of comprehensive flow and heat transfer performance indicate that the circular pin-fin structure performs better than others arrangements. In contrast to the corresponding conventional rectangular microchannel, Chai et al. [13–17] performed investigations on the fluid flow and heat transfer characteristics of microchannel heat sinks with ribs or cavities. The results showed that these microchannels exhibited superior heat transfer enhancement characteristics. As a consequence of the significant pressure drop, the microchannel heat sink with offset ribs gradually lost its advantage as an effective heat transfer enhancement method at high Reynolds numbers. Furthermore, ribs can significantly reduce the temperature increase of the heat sink base and efficiently prevent the drop of the local heat transfer coefficient along the flow direction but also result in a higher local friction factor than that for straight microchannels in some cases. Wang et al. [18] studied the thermo-hydraulic performance of the microchannel heat sink (MCHS) with bidirectional ribs (BRs) experimentally. It indicates that bidirectional ribs could strengthen the heat transfer by interrupting the thermal boundary layer and inducing recirculation in both vertical and spanwise directions. Zeng et al. [19] numerically studied the effects of isosceles triangle grooves on fluid flow and heat transfer in microchannels. Compared to a smooth microchannel, the isosceles triangle groove structure increased the Nusselt number and pressure drop. Ahmed et al. [20] numerically investigated the effects of geometrical parameters on the laminar water flow and forced convective heat transfer characteristics in a grooved microchannel heat sink (GMCHS). The results showed that trapezoidal grooves with a groove tip length ratio of d = 0.5, groove depth ratio of b = 0.4, groove pitch ratio of w = 3.334, groove orientation ratio of n = 0.00 and Re = 100 provided the optimum thermal design for the GMCHS, with a Nusselt number enhancement of 51.59% and friction factor improvement of 2.35%. Deng et al. [21] studied a
t Dtm u V w Y
temperature of cooler, K Logarithmic mean temperature difference, K velocity of deionized water, m/s volumetric flow rate, ml/min mass flux, kg/s independent variable
Greek symbols e actual effectiveness q density, kg/m3 k thermal conductivity, W/(m∙K) kl friction factor of the pipeline, l dynamic viscosity, kg/(m·s) Rni total local drag coefficients g Thermal performance index Subscripts ave average cool cooler hot microchannel in inlet out outlet
novel type of periodic expanded-constrained microchannels (PECM) heat sink by experimental tests and numerical simulations. It was obtained that the heat transfer enhancement of PECM was not accompanied with the expense of pressure drop penalty compared to the rectangular counterpart. According to some other studies [22–26], the heat transfer enhancement mechanism of cavities could be attributed to the interactions associated with the redevelopment of the hydraulic and thermal boundary layers, the effect of jetting and throttling and the stagnation zone in laminar flow. A hybrid strategy involving ribs and either grooves or cavities has also been adopted as an effective technique for enhancing heat transfer. By referring mainly to Li et al. [27], Ghani et al. [28] numerically studied the characteristics of fluid flow and heat transfer for newly designed microchannel heat sinks with sinusoidal cavities and rectangular ribs (MC-SCRR) based on Reynolds numbers ranging from 100 to 800. By comparing the performance of the proposed microchannel to that of a microchannel with rectangular ribs (MC-RR) and that of a microchannel with sinusoidal cavities (MC-SC), the study found that the thermal performance of the MC-SCRR was superior to that of the MC-RR and MC-SC. The new design of the MC-SCRR effectively combined two important features: a large flow area that significantly reduces the pressure drop and high flow disturbances caused by the existence of ribs in the central portion of the channel. As mentioned above, the lack of data and limited availability of microchannels are major difficulties that limit practical applications. In particular, the heat transfer and flow performance of novel microchannel structures should be evaluated through extensive test results. It is necessary to conduct experimental studies and provide design references. In this paper, rectangular microchannels with rectangular ribs on one side (MC-OSR) and both sides (MC-BSR) were proposed. The single-phase heat transfer and flow characteristics were experimentally investigated. The effects of the volumetric flow rate and inlet temperature on the Nusselt
3
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
number and friction factor were analyzed. The wall temperature distribution was examined to explore the heat transfer enhancement effect and mechanism of the ribs. 2. Experimental investigations
Microchannel
Cooling water outlet
2.1. Experimental apparatus A schematic diagram of the experimental apparatus is shown in Fig. 1. The apparatus consists of a test section, a heating system, a cooling cycle system and a data collection system. Deionized water was used as the working fluid. The temperature of deionized water is adjusted with a heater which could be regulated in the ranges of 0–3 kW. The volumetric flow rate of the working fluid was controlled by a peristaltic pump which worked in a range of 0–300 ml/min with an accuracy of ±0.5 ml/min. The working fluid was cooled in the test section and then flows into a container. The circulation cooling fluid was supplied by a thermostatic water bath which worked in a range of 243 to 373 K with an accuracy of ±0.1 K. All the signals from the pressure transducer in a range of 0–25 kPa with an accuracy of 0.25% and thermocouples in a range of 73 to 633 K with precision of ±0.1 K were collected by a data acquisition system. All equipment was calibrated before test. To minimize heat loss, the pipeline system was designed to be as short as possible and covered with adiabatic material made of nitrile butadiene rubber and polyvinyl chloride. To evaluate the effects of Re and the inlet temperature on the heat transfer performance of the microchannel, two test cases were conducted in this study. The first test was conducted to increase the inlet flow rate from 30 ml/min to 90 ml/min with a fixed inlet temperature of 343.15 K. The second test was conducted to increase the inlet temperature from 298.15 K to 358.15 K with a fixed inlet flow rate of 75 ml/min. The inlet flow rate and temperature of the cooling fluid were 180 ml/min and 278.15 K, respectively. 2.2. Test section The test section mainly contains the cover plate, the experimental microchannel plate and the cooler plate. A detailed introduction to the test module is given in Fig. 2. Based on the thermal conductivity, sealing performance, processing degree and other factors,
T
Thermocouple holes
Cooling water inlet Heang water outlet
Cooler plate
Fig. 2. Test section example.
the test section was completely manufactured using aluminum alloy. To prevent the leakage of the working fluid, the test section was assembled with bolted connections and high-temperature resistant metal gaskets and sealants. To reduce heat loss, adiabatic material was wrapped around the test section. The smooth rectangular microchannel (MC-S), MC-OSR and MC-BSR were tested in this paper. All the three different types of microchannels are manufactured by precise carving mechanism. These channels have the same hydraulic diameter of 1 mm. The plane structure and main dimensions of the microchannels, such as the total length (L), total width (B), total height (H), rib height (h) and rib width (b), are illustrated in Fig. 3. The detailed dimensional parameters of the experimental microchannels are shown in Table 1. The distance between adjacent ribs is 3.5 mm. The pressure transducers and T-type thermocouples were installed 60 mm away from the inlet and outlet of microchannels to measure the inlet and outlet pressure and temperature. Another five thermocouples were inserted at the bottom of the tested microchannels with a horizontal spacing of 16 mm for wall temperature measurements. The distance between the microchannel base and the thermocouples is 1 mm. The designed positions are shown in Fig. 4. 2.3. Data reduction This section presents the relevant formulas used to calculate the characteristics of heat transfer and fluid flow in microchannels. The energy balance equation for a counter-flow microchannel heat sink is expressed by
Data acquision P
Cover plate Heang water inlet
Q cool ¼ e Q hot
ð1Þ
P
PC
Test secon Peristalc pump
Volume flow meter
MC-OSR MC-BSR MC-S
Heater
Thermostac water bath Fig. 1. Experimental apparatus.
Container Fig. 3. Tested microchannels.
4
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Table 1 Structural parameters of the experimental microchannels. Microchannel
MC-S
MC-OSR
MC-BSR
Microchannel width (B) Microchannel height (H) Microchannel length (L) Rib width (b) Rib height (h) Hydraulic diameter (Dh)
1 mm 1 mm 100 mm – – 1 mm
1 mm 1 mm 100 mm 0.5 mm 0.5 mm 1 mm
1 mm 1 mm 100 mm 0.5 mm 0.5 mm 1 mm
where q is the mean density of deionized water, u is the velocity and l is the mean viscosity. The pressure drop is obtained from experimental observations, and the theoretical formulas is as follows [29]:
DP ¼ Pin Pout DPin DPout
ð11Þ
where DP in is the inlet pressure loss of the microchannel and DPout is the outlet pressure loss.
DPin ¼ q hf
ð12Þ
DPout ¼ q hf
ð13Þ
P P 2 li þ le X u þ ni hf ¼ kl di 2
ð14Þ
where hf is the energy loss of the pipeline system, kl is the friction P factor of the pipeline, li is the total length of the straight pipe, P le is the total equivalent length of valves, di is the inner diameter P of the pipe, and ni is sum of local drag coefficients. The friction factor is defined as:
f ¼
2DPDh qu2 L
ð15Þ
The thermal performance index, which was used to evaluate the heat transfer changes at a constant pumping power, was introduced by Webb [30–32]: Fig. 4. Measurement points.
g¼
13 Nu f Nu0 f0
ð16Þ
where Q cool denotes the heat transfer rate of the cooler, Q hot denotes the heat transfer rate of the microchannel and e denotes actual effectiveness.
where Nu0 and Nu are the Nusselt numbers of a smooth microchannel and a microchannel with ribs respectively, and f 0 and f are the corresponding friction factor.
Q cool ¼ Cpcool wcool ðt out tin Þ
ð2Þ
2.4. Uncertainty analysis
Q cool ¼ Cphot whot ðT out T in Þ
ð3Þ
where Cpcool and Cphot are the specific heat values of the corresponding fluid, wcool and whot are the mass fluxes, t out and T out are the outlet temperatures and t in and T in are the inlet temperatures.
w¼V q
ð4Þ
where V is the volumetric flow rate and q is the density. The average heat transfer coefficient is calculated by
hav e ¼
Q cool A Dt m
ð5Þ
where A is the heat transfer area. In this case, Dt m is the logarithmic mean temperature difference, which is calculated as follows.
Dt m ¼
DT 1 DT 2 ln DDTT 12
3.1. Validation of the experimental results
DT 2 ¼ T out tin
ð8Þ
ð9Þ
where Dh is the hydraulic diameter of the microchannel and k is the thermal conductivity of deionized water. The Reynolds number is defined as
q u Dh l
The variation of the Nusselt number against Reynolds number for the MC-S is described in Fig. 5. The result of Ref. [33] is adopted Table 2 Maximum uncertainties.
The average Nusselt number is calculated by
Re ¼
ð17Þ
3. Results and discussion
ð7Þ
hav e Dh k
" #12 n X DR DY i 2 ¼ R Yi i¼1
ð6Þ
DT 1 ¼ T in t out
Nu ¼
All temperatures were measured with T-type thermocouples, and all pressures were measured with pressure transducers. All data except the volumetric flow rate were collected using a data acquisition system. The inlet volumetric flow rates of the microchannel and the cooler were controlled by a peristaltic pump and a volumetric flow meter, respectively. The maximum uncertainty of each experimental parameter is given in Table 2 based on the following equation.
ð10Þ
Parameters
Maximum uncertainty
Temperature Volumetric flow rate Pressure Reynolds number Heat transfer coefficient Nusselt number Friction factor Thermal performance index
±0.1 K ±0.35% ±0.5% ±2.15% ±2.17% ±2.68% ±2.41% ±3.92%
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Fig. 5. Variation of the Nusselt number with Re for the MC-S.
5
Fig. 7. Variations in the Nusselt number with the inlet temperature for the MC-S, MC-OSR and MC-BSR.
to validate. The results show the same trend. Furthermore, the Nusselt number of reference is lower than that of present work. It could be due to the uneven temperature distribution in multiple microchannels. The variation of calculated friction factor in MC-S with Reynolds number is compared with theoretical correlation of Shah and London [34] as shown in Fig. 6. The friction factor obtained by the experiment presents the same trend with the theoretical calculation curve. There is some discrepancy between them which can be referred to the multiple vertical bending at inlet and outlet of the microchannel. 3.2. The effect of the inlet temperature Fig. 7 shows the variations in the Nusselt numbers of the tested microchannels with the inlet temperature when the volumetric flow rate is 90 ml/min. The Nusselt number increases with increasing inlet temperature because the viscosity of the fluid decreases with increasing inlet temperature, which causes the thermal and hydraulic boundary layers to easily break up. At different inlet temperatures, MC-OSR displays the highest Nusselt number. Fig. 8 displays the variations in the friction factor with the inlet temperature for the MC-S, MC-OSR and MC-BSR. With increasing temperature, the friction factor in the microchannels decreases
Fig. 8. Variations in the friction factor with the inlet temperature for the MC-S, MCOSR and MC-BSR.
slightly, which is attributed to the decrease in the viscosity of the fluid. 3.3. The effect of the volumetric flow rate
Fig. 6. Variation of the friction factor with Re for the MC-S.
The variations in the Nusselt number with the volumetric flow rate for the three microchannels are illustrated in Fig. 9. The Nusselt number increases with increasing volumetric flow rate, and the slopes of the Nusselt number curves decrease with increasing volumetric flow rate. The Nusselt numbers of the three microchannels are relatively similar at low volumetric flow rates. By comparison, the Nusselt numbers of the MC-OSR and MC-BSR are higher than that of the MC-S. This finding indicates that the ribs enhance heat transfer by increasing the heat transfer area, the jetting and throttling effects and the chaotic advection caused by ribs. Simultaneously, the MC-OSR displays the best thermal performance. When the ribs are placed on one side, the fluid flow on both sides is asymmetrical, which causes an obvious heat transfer enhancement due to boundary layer breakup and intensified chaotic mixing.
6
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Fig. 9. Variations in the Nusselt number with the volumetric flow rate for the MC-S, MC-OSR and MC-BSR.
Fig. 10. Variations in the friction factor with the volumetric flow rate for the MC-S, MC-OSR and MC-BSR.
Fig. 11. Variations in the thermal performance index with the inlet temperature for the MC-S, MC-OSR and MC-BSR.
Fig. 12. Variations in the thermal performance index with the volumetric flow rate for the MC-S, MC-OSR and MC-BSR.
3.4. Thermal performance index As illustrated in Fig. 10, the trend of the friction factor curves is downward when the volumetric flow rate is less than 60 ml/min. And then there is a mutation in the friction factor curve which indicates the transition of flow state. The friction factor for the MC-OSR and MC-BSR are lower than that for the MC-S. This result suggests that the flow area enlargement caused by the ribs can reduce the pressure loss. At low volumetric flow rate, the velocity of recirculation is small which cause the formation of flow stagnation regions [27,28]. The main stream slips over the ribs and the friction coefficient between the fluid and the microchannel walls is partly replaced by that between the fluid and the fluid in the MC-OSR or MC-BSR. Obviously, friction resistance between the fluids is smaller than that between the fluid and the microchannel walls. When the volumetric flow rate is greater than 60 ml/min, the recirculation and the jetting and throttling effects [14,21,27,28] enhance by the ribs. The difference of friction factor for the microchannel with or without ribs is smaller. Additionally, the MC-OSR has a slightly larger friction factor than the MC-BSR because of the asymmetrical flow.
The purpose of the proposed novel structure is to develop a microchannel heat exchanger with high thermal performance and a low pressure drop. The thermal performance index, which represents the Nusselt number ratio divided by the friction factor ratio to the power of one-third, is used to evaluate the overall performance of each microchannel in this study. The value of the performance index indicates the thermal effectiveness relative to the pressure drop. Therefore, the higher the performance index value is (greater than 1), the better the performance of the microchannel. The variations in the performance index with the inlet temperature and volumetric flow rate are presented in Figs. 11 and 12 respectively. The performance index exhibits a slight decrease with increasing inlet temperature. This result clearly shows that the viscosity of the fluid has a certain effect on the heat transfer enhancement as demonstrated by the small negative trend. The performance index values of the MC-OSR and MC-BSR are directly proportional to the flow rate, except at high
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
flow rates, when the performance index slightly decreases. This finding indicates that increasing the flow rate is not an effective method of improving performance when the flow rate reaches a certain value. The performance index of the MC-OSR is superior compared with that of the MC-BSR. When the main flow with a constant volumetric flow rate crosses the expanded flow area, the ribs placed on one side of domain disrupt the flow and lead to the breakup of the hydraulic and thermal boundary layers due to asymmetry more obviously. The superiority of the thermal performance of the microchannels with ribs can be attributed to many reasons: (1) the increase in the heat transfer area due to the presence of ribs leads to increased heat transfer and a slight reduction in the pressure loss; (2) the jetting and throttling effects caused by the ribs lead to flow disruption, which promotes flow instabilities and flow mixing; and (3) although the fluid entering the rib region is partially trapped, which leads to the formation of flow stagnation regions, the ribs are able to enhance heat transfer due to the transverse convection [28] between the partial fluid in the ribs region and the main flow in the central region.
7
3.5. Wall temperature distribution and temperature difference analysis Figs. 13–15 illustrate the wall temperature distributions and temperature differences at different inlet temperatures for the MC-OSR, MC-BSR and MC-S, respectively. Figs. 13(a), 14(a) and 15(a) indicate that the trend of the wall temperature distribution is nonlinear in the flow direction for different inlet temperatures. For five temperature measurement points at x ¼ 18; 34; 50; 66; and 82 mm along the length of the microchannel, the wall temperature increases with increasing inlet temperature. The wall temperatures of the MC-OSR and MC-BSR are higher than that of the MC-S. For the MC-OCR, MC-BSR and MC-S, the wall temperature differences in the flow direction are displayed in Figs. 13(a), 14(a) and 15(a), respectively. The height of the first column represents the temperature difference between the first and second temperature measurement points, and the subsequent corresponding differences are shown in the next three columns. At a fixed inlet temperature, the wall temperature difference gradually decreases in the flow direction, as shown by the blue arrow. The temperature
Fig. 13. (a) Wall temperature distribution for the MC-OSR at different inlet temperatures; (b) Wall temperature differences for the MC-OSR at different inlet temperatures.
Fig. 14. (a) Wall temperature distribution for the MC-BSR at different inlet temperatures; (b) Wall temperature differences for the MC-BSR at different inlet temperatures.
8
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
Fig. 15. (a) Wall temperature distribution for the MC-S at different inlet temperatures; (b) Wall temperature differences for the MC-S at different inlet temperatures.
Fig. 16. (a) Wall temperature distribution for the MC-OSR at different volumetric flow rates; (b) Wall temperature differences for the MC-OSR at different volumetric flow rates.
Fig. 17. (a) Wall temperature distribution for the MC-BSR at different volumetric flow rates; (b) Wall temperature differences for the MC-BSR at different volumetric flow rates.
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
9
Fig. 18. (a) Wall temperature distribution for the MC-S at different volumetric flow rates; (b) Wall temperature differences for the MC-S at different volumetric flow rates.
of the partial fluid in the ribs and the main stream in the central region both decrease along the length of microchannels. For low temperature, the dynamic viscosity of fluid is large and the thermal conductivity coefficient of the fluid is low which lead to the formation of local flow stagnation regions and weaken the heat transfer. This condition is dominant in the MC-OSR and MC-BSR. As the inlet temperature increases, the heights of the four columns decrease. The four columns are highest at T in ¼ 358K. It indicate that the thermal boundary layer is thinner at the entrance and the extent of the interruption and redevelopment of thermal boundary layer caused by reflux is wider which can be referred to the physical properties of fluids at high inlet temperature. The wall temperature distribution and temperature differences at different volumetric flow rates are depicted in Figs. 16–18. As shown in Figs. 16(a), 17(a) and 18(a), the wall temperature displays nonlinear growth in the flow direction for different volumetric flow rates. The wall temperature of the MC-OSR is the highest, and that of the MC-S is the lowest. According to Figs. 16(a), 17(a) and 18(a), the heights of the columns gradually decrease, as shown by the blue arrow for a fixed flow rate. With increasing flow rate, the height of the first column decreases. At low flow rates, the thermal boundary layer is thinner at the entrance of the microchannel which causes the smaller thermal resistance. The heat transfer enhancement caused by the entrance effect is more obvious than the effect of the interruption and redevelopment of thermal boundary layer caused by reflux. In contrast, the height of the remaining three columns increases with the flow rate. This result indicates that the interruption and redevelopment of thermal boundary layer is severer. The rate of thermal boundary layer development is slower due to the lower thermal resistance, which enhance the heat transfer at higher flow rates. The height of the first column for the MC-OSR and MC-BSR is larger than that for the MC-S, mainly because of the more obvious entrance effect for the MC-OSR and MC-BSR due to the ribs. In addition, the asymmetric ribs have a significant effect on the temperature difference compared with the symmetric ribs due to the intensification of flow instabilities and flow mixing. 4. Conclusions In this paper, the heat transfer and flow performance of the MC-OSR and MC-BSR are compared with that of the MC-S based on experimental studies. The heat transfer enhancement effect and mechanism of the ribs were explored by analyzing the effects
of the volumetric flow rate and the inlet temperature on the Nusselt number and friction factor considering the wall temperature distribution. The following conclusions can be extracted from the results. (1) The Nusselt number increases and friction factor decreases with increasing inlet temperature. Considering the Nusselt number difference, the inlet temperature has a smaller effect on the increased heat transfer than does the volumetric flow rate. (2) As the volumetric flow rate increases, the Nusselt number increases, the friction factor decreases and the slopes of the Nusselt number curves decrease. At a low flow rate, the use of ribs has a notable influence on the enhanced heat transfer. When the volume flow rate is around 60 ml/min, there is a transition of flow state. (3) Under the given working conditions, the MC-OSR has the highest Nu, and the MC-BSR has the lowest friction factor. The performance index exhibits a slight decrease with increasing inlet temperature. The MC-OSR displays the best overall performance. Specifically, when the volume flow rate is around 75 ml/min, the MC-OSR has the highest thermal performance index value. (4) The wall temperature is distributed nonlinearly in the flow direction. The wall temperature increases with the flow rate or inlet temperature. As the flow rate increases, the first temperature difference decreases, but the remaining three temperature differences increase. Compared to those for the MC-S, the entrance effects for the MC-OSR and MC-BSR are more obvious. (5) The heat transfer enhancement of the ribbed channels can be referred to the recirculation and the jetting and throttling effects caused by ribs. The formation of local flow stagnation regions can decrease frictional pressure loss at low flow rate.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors acknowledge the financial support provided by the National Natural Science Foundation of China (Nos. 51776095 and
10
J. Li et al. / International Journal of Heat and Mass Transfer 143 (2019) 118482
51606103) and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (No. 15KJB470007). References [1] A. Dewan, P. Srivastava, A review of heat transfer enhancement through flow disruption in microchannel, J. Therm. Sci. 24 (3) (2015) 203–214. [2] A. Bergels, Enhanced heat transfer: endless frontier, or mature and routine?, Enhanc Heat Transf. 6 (1999) 79–88. [3] R. Webb, N. Kim, Principle of enhanced heat transfer, second ed., Taylor & Francis, Boca Ration, 2005, p. 28. [4] M.E. Steinke, S.G. Kandlikar, Review of single-phase heat transfer enhancement techniques for application in microchannels, microchannels and microdevices, Int. J. Heat Technol. 22 (2) (2004) 3–11. [5] N. Zhao, C. Qi, T.T. Chen, et al., Experimental study on influences of cylindrical grooves on thermal efficiency, exergy efficiency and entropy generation of CPU cooled by nanofluids, Int. J. Heat Mass Transf. 135 (2019) 16–32. [6] A. Rawool, S. Mitra, S. Kandlikar, Numerical simulation of flow through microchannels with designed roughness, Microfluid. Nanofluid. 2 (3) (2006) 215–221. [7] M. Kharati-Koopaee, M. Zare, Effect of aligned and offset roughness patterns on the fluid flow and heat transfer within microchannels consist of sinusoidal structured roughness, Int. J. Therm. Sci. 90 (2015) 9–23. [8] X. Yuan, Z. Tao, H.W. Li, et al., Experimental investigation of surface roughness effects on flow behavior and heat transfer characteristics for circular microchannels, Chin. J. Aeronaut. 29 (6) (2016) 1575–1581. [9] Y.P. Liu, G.Q. Xu, J.N. Sun, et al., Investigation of the roughness effect on flow behavior and heat transfer characteristics in microchannels, Int. J. Heat Mass Transf. 83 (2015) 11–20. [10] H. Miao, Y. Huang, H.G. Chen, Flow and heat transfer characteristics in laminar flow through random rough microchannels, J. Beijing Univ. Aeronaut. Astronaut. 37 (6) (2011) 738–742. [11] N. Kang, H.Y. Wu, F.Y. Xu, et al., Flow and heat transfer characteristics in silicon-based pin-fin microchannels, J. Eng. Thermophys. 36 (7) (2015) 1572– 1577. [12] X.Q. Zhang, J.Y. Hua, X.B. Zhao, et al., Study on the flow and heat-transfer properties of microchannel heat sink with different pin-fin shapes, J. Nanjing Normal Univ. (Eng. Technol. Ed.) 18 (1) (2018) 47–55. [13] L. Chai, G.D. Xia, M.Z. Zhou, et al., Numerical simulation of fluid flow and heat transfer in a microchannel with fan-shaped reentrant cavities, J. Harbin Inst. Technol. 43 (6) (2011) 2725–2730. [14] L. Chai, G.D. Xia, M.Z. Zhou, et al., Heat transfer enhancement characteristics of parallel-microchannel silicon heat sink with expansion-constriction cross section, J. Aerosp. Power 28 (12) (2013) 2725–2730. [15] L. Chai, G.D. Xia, H.S. Wang, Numerical study of laminar flow and heat transfer in microchannel heat sink with offset ribs on sidewalls, Appl. Therm. Eng. 92 (2016) 32–41. [16] L. Chai, L. Wang, X. Bai, Thermohydraulic performance of microchannel heat sinks with triangular ribs on sidewalls – Part 1: Local fluid flow and heat transfer characteristics, Int. J. Heat Mass Transf. 127 (2018) 1124–1137.
[17] L. Chai, L. Wang, X. Bai, Thermohydraulic performance of microchannel heat sinks with triangular ribs on sidewalls – Part 2: Average fluid flow and heat transfer characteristics, Int. J. Heat Mass Transf. 128 (2019) 634–648. [18] G.L. Wang, N. Qian, G.F. Ding, Heat transfer enhancement in microchannel heat sink with bidirectional rib, Int. J. Heat Mass Transf. 136 (2019) 597–609. [19] S.J. Zeng, B.D. Shao, L.F. Wang, et al., Numerical analysis of micro-channel with an isosceles triangle grooves, Int. Commun. Heat Mass Transf. 66 (2015) 47– 57. [20] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal and rectangular grooved microchannel heat sinks, J. Liaoning Tech. Univ. (Nat. Sci.) 36 (12) (2017) 47–57. [21] D.X. Deng, L. Chen, X.L. Chen, et al., Heat transfer and pressure drop of a periodic expanded-constrained microchannels heat sink, Int. J. Heat Mass Transf. 140 (2019) 678–690. [22] D.D. Ma, G.D. Xia, W. Wang, et al., Study on thermal performance of microchannel heat sinks with periodic jetting and throttling structures in sidewalls, Appl. Therm. Eng. 158 (2019). [23] M.Q. Pan, H.W. Wang, Y.J. Zhou, Experimental investigation of the heat transfer performance of microchannel heat exchangers with fan-shaped cavities, Int. J. Heat Mass Transf. 134 (2019) 1199–1208. [24] E. Bayrak, A.B. Olcay, M.F. Serincan, Numerical investigation of the effects of geometric structure of microchannel heat sink on flow characteristics and heat transfer performance, Int. J. Therm. Sci. 135 (2019) 589–600. [25] H. Ghaedamini, P.S. Lee, C.J. Teo, Developing forced convection in converging– diverging microchannels, Int. J. Heat Mass Transf. 65 (2013) 491–499. [26] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal and rectangular grooved microchannel heat sinks, Int. Commun. Heat Mass Transf. 66 (2015) 47–57. [27] Y.F. Li, G.D. Xia, D.D. Ma, Characteristics of laminar flow and heat transfer in microchannel heat sink with triangular cavities and rectangular ribs, Int. J. Heat Mass Transf. 98 (2016) 17–28. [28] I. Ghani, N. Kamaruzaman, N. Sidik, Heat transfer augmentation in a microchannel heat sink with sinusoidal cavities and rectangular ribs, Int. J. Heat Mass Transf. 108 (2017) 1969–1981. [29] Q. Xia, S.Y. Jia, Unit operations of chemical engineering (I), Tianjin University Press, 2012. [30] R. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transf. 24 (4) (1981) 715– 726. [31] R. Webb, M. Scott, A parametric analysis of the performance of internally finned tubes for heat exchanger application, J. Heat Transf. 102 (1) (1980) 38– 43. [32] D.L. Gee, R. Webb, Forced convection heat transfer in helically rib-roughened tubes, Int. J. Heat Mass Transf. 23 (8) (1980) 1127–1136. [33] Q. Esmaili, A.A. Ranjbar, S. Porkhial, Experimental analysis of heat transfer in ribbed microchannel, Int. J. Therm. Sci. 130 (2018) 140–147. [34] R.K. Shah, A.L. London, Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data, Academic Press, New York, USA, 1978.