An Experimental Study on Heat Transfer Enhancement of Non-Newtonian Fluid in a Rectangular Channel With Dimples/Protrusions

Transcription

1 Di Zhang Key Laboratory of Thermal Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi an Jiaotong University, Xi an, Shaanxi Province , China Lu Zheng Key Laboratory of Thermal Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi an Jiaotong University, Xi an, Shaanxi Province , China Gongnan Xie Engineering Simulation and Aerospace Computing (ESAC), School of Mechanical Engineering, Northwestern Polytechnical University, P.O. Box 552, Xi an, Shaanxi Province , China Yonghui Xie 1 Professor School of Energy and Power Engineering, Xi an Jiaotong University, Xi an, Shaanxi Province , China yhxie@mail.xjtu.edu.cn An Experimental Study on Heat Transfer Enhancement of Non-Newtonian Fluid in a Rectangular Channel With Dimples/Protrusions Dimple and protrusion play important roles in the heat transfer enhancement and flow characteristic in cooling channels, which widely employed within electronic cooling systems. Non-Newtonian fluid has significant differences with Newtonian fluid, such as water, in fluid characteristic. In this study, an experiment on the viscosity of three different kinds of non-newtonian fluids, i.e., xanthan gum solution, Carbopol 934 solution, polyacrylamide solution, was first accomplished to acquire the viscosity with different mass fractions. Then, experimental measurements on heat transfer and friction characteristics of non-newtonian fluid in a rectangular channel with dimples and protrusions were conducted. The overall Nusselt numbers (Nu) and Fanning friction factors at different dimple/protrusion structures were obtained with various inlet flow rates and mass fractions. The results show that only xanthan gum solution has the significant shear thinning effect within the concentration range of this study, and the dimples/protrusions both have great effect on the heat transfer enhancement in the rectangular channel, and that the heat transfer of the case with the protrusions and crossing arrangement can be further enhanced with the higher Nu when compared to the case with the dimples and aligned arrangement. Moreover, an increase in Nu with the higher non-newtonian fluid mass fraction is observed. [DOI: / ] Keywords: non-newtonian fluid, heat transfer enhancement, dimple/protrusion, experimental 1 Introduction Due to the development of integrated electronic devices, the desires of miniaturization, high performance and the output power, the cooling requirement of chips have been increased gradually. When the chip temperature is too high, the stability and efficiency will deteriorate, so the problem of heat dissipation has become a bottleneck for the development in the electronic industry. To enhance cooling of electronic devices, heat transfer inside flow passages is needed to be enhanced so as to improve cooling effectiveness by using passive augmented heat transfer devices such as rib-turbulators, pin fins, dimples, and protrusions. Such these heat transfer enhancement techniques have particular applications for electronic cooling devices and internal turbine cooling and so on. Arik and Bunker [1] discussed the synergies between electronic cooling and turbine cooling, and highlighted the cooling technologies of gas turbines could be implemented straightforwardly into electronic cooling, but the fluid scales and fluidstructure interactions should be validated for the anticipated flow regimes and geometries. Numerous non-newtonian fluids, such as fusion plastics, paint and toothpaste, are widely used in the manufacturing industry, and the non-newtonian fluid characteristic also has a great influence on the productive process, such as the rheological properties. For non-newtonian fluids, the material properties operating depend critically on the kinematics of the flow [2]. There existed 1 Corresponding author. Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received July 29, 2013; final manuscript received October 10, 2013; published online April 29, Assoc. Editor: Gary Miller. many experimental and numerical researches on non-newtonian fluids. Bharti et al. [3] reported the role of the Reynolds number and the power-law index on the flow past unconfined circular cylinder. They found that the shear thinning fluids reduced the recirculation zone length and delayed the separation. The results of the pressure and the friction coefficients on the surface of the unconfined circular cylinder were also provided extensively. Acrivos et al. [4] performed a theoretical analysis of laminar natural convection heat transfer to non-newtonian fluids. By employing the power-law model, an asymptotic solution of the appropriate laminar boundary layer equation was obtained, and an expression for computing the average rate of heat transfer in laminar free convection was presented. Sharma and Adelman [5] conducted an experiment of natural convection heat transfer to non-newtonian fluids from isothermal vertical plates, and a successful correlation for predicting natural convective heat transfer coefficients for non-newtonian fluids from flow behavior index 0.2 to 1.0 inclusive was developed. Most heat transfer augmentations affect the boundary layer in such a way as to make it thinner or partially break it, which often results in a higher flow resistance. Previous research works have shown that dimples can provide substantial heat transfer enhancement in confined channels with relatively low pressure loss penalty compared to other types of augmented heat transfer devices such as fins, pins, and rib turbulators. Silva et al. [6] performed a literature review of numerical and experimental works with dimpled surfaces and a numerical simulation of heat transfer in a dimpled channel. The results showed that the dimple technology offered the potential of improved heat transfer in microelectronic systems. Wei et al. [7] numerically simulated laminar heat transfer insider a microchannel with one dimpled surface, and stated that Journal of Electronic Packaging Copyright VC 2014 by ASME JUNE 2014, Vol. 136 /

2 an effective heat transfer enhancement could be achieved by adding dimples in microchannels. Small et al. [8] conducted an experiment and a simulation on enhanced heat transfer in heat sinks for electronic cooling applications, and found that dimples improved heat transfer capability of the heat sinks. Xie et al. [9] compared thermal performance of a blade tip-wall with pins, dimples and protrusions, and showed that the dimples had best overall performance for the internal blade tip cooling. Kim et al. [10] experimentally studied on the detailed heat transfer coefficients in a rotating smooth and dimpled rectangular channel by the transient liquid crystal technique. Results showed that the heat transfer coefficient on the trailing surface was higher than that on the leading surface. Chen et al. [11] experimentally investigated heat transfer enhancement in dimpled coaxial-pipe heat exchanger tubes. Despite the extremely simple design, this outperformed almost all heat transfer enhancements recommended in the literature. Ligrani et al. [12,13] performed flow visualization, pressure and velocity measurements on the flow structure of a dimpled wall. They observed a primary vortex pair shed periodically from the center of each dimple, and two additional secondary vortex pair formed near the spanwise edges of each dimple. They researched the heat transfer combined with influences of aspect ratio, temperature ratio, Reynolds number, and flow structure. Elyyan and Tafti [14] investigated of flow and heat transfer in a channel with dimples and protrusions with large eddy simulation. They showed that dimples and protrusions might not be viable heat transfer augmentation surfaces when the flow was steady and laminar based on the geometry studied. Alshroof et al. [15] numerical studied the effect of combinations of spherical dimples and protrusions on flow and heat transfer in a shallow rectangular channel in the laminar regime. The addition of a protrusion downstream of the dimple led to an increase of 30% in heat transfer augmentation above that which pertained for the isolated protrusion without any increase in the pressure drop. Hwang et al. [16,17] investigated the local heat transfer and thermal performance on periodically dimple-protrusion patterned walls for compact heat exchangers. They found various secondary flows generated from the dimple/protrusion coexist and the vortices induced from the upstream affect strongly on the downstream pattern on the single-side patterned walls. Rao et al. [18] conducted an experimental study to investigate the effects of dimple depth on the pressure loss and heat transfer characteristics in a pin fin-dimple channel, where dimples were located on the endwall transversely between the pin fins. The result showed that, compared to the baseline pin fin channel, the pin fin-dimple channels had further improved convective heat transfer performance by up to 19.0%, and the pin fin-dimple channel with deeper dimples showed relatively higher Nu values. Rao et al. [19] also conducted experimental and numerical studies to investigate the flow and heat transfer characteristics in channels with pin fin-dimple combined arrays of different configurations, where dimples are located transversely or both transversely and streamwise between the pin fins. They found that, compared to the pin fin channel, depending on the configurations of the pin fin-dimple combined arrays the pin fin-dimple channel could have distinctively further improved convective heat transfer performance by %, whereas lower or slightly higher friction factors were found over the studied Reynolds number range. They also carried out experimental and numerical studies to investigate the flow friction and heat transfer performance in rectangular channels with staggered arrays of pin fin-dimple hybrid structures and pin fins in the Reynolds number range of ,000, and to investigate the effects of dimple depth on the flow and heat transfer characteristics in a pin fin-dimple channel, where dimples were located spanwise between the pin fins [20,21]. Afanasyev et al. [22] conducted the experimental research on the heat transfer and pressure loss characteristics of the shallow dimples on panels, and the results showed that the performance of heat transfer increases by 30 40% without the significant increase in pressure loss; Burgess and Ligrani [23] completed the experimental measurements on the heat transfer in the channels with deep dimples, obtaining the friction coefficient, local Nu and average Nu. It was shown that the deep dimple enhanced the vortex structure inside the dimple, such as the secondary flow, and the three-dimensional turbulent, which mainly appeared in the local region of dimples and the edge region of the rear of dimples. Moon et al. [24] studied the flow and heat transfer characteristics in the channel with one-side arrangement dimples, and it was shown that the increased resistance coefficient ranged from 1.6 to 2.0, with the constant enhanced heat transfer coefficient at 2.1, which was almost independent of the height of the channel. Most recently, Xie et al. [25] predicted numerically flow structure and heat transfer in a square channel with nonspherical dimples. They reported that the augmented heat transfer depended on dimple surface geometry transitions and surface curvature diameters. From the above-mentioned works, it is clear that various dimples/protrusions have potential advantages of moderate heat transfer augmentation with relatively low pressure drop that they produced. However, previous researches with dimpled/protruded surfaces mainly pay attention to Newtonian fluids (air, water, etc.), and no related research focusing on non-newtonian fluids with dimpled/protruded heat transfer is available. Therefore, the motivation of this paper is to investigate non-newtonian flow and heat transfer characteristics in cooling channels with dimples and protrusions for electronic cooling applications. In this paper, an experiment on the viscosity of three different kinds of non- Newtonian fluids, xanthan gum solution, Carbopol 934 solution, polyacrylamide solution, was accomplished first, acquiring the viscosity with different mass fractions, which provided the basis for the experiment on the heat transfer of non-newtonian fluids. Another experiment on heat transfer enhancement of non- Newtonian fluid in rectangular channels with an array of dimples or protrusions was completed. The overall Nu s and Fanning friction factors at different cases were obtained under various flow rates and mass fractions of non-newtonian fluid. A comparison among cases with different dimple protrusion structures and mass fractions was also performed. 2 Experiment on Viscosity of Non-Newtonian Fluids As a sort of fluid dynamic viscosity changes with the variation in shear rate, non-newtonian fluid can fall into three categories: shear thickening fluid, shear thinning fluid and plastic fluid. The relationship between the dynamic viscosity and the shear rate of the non-newtonian fluid can be correlated by l ¼ kc n (1) where l is the fluid dynamic viscosity, k is the consistency coefficient, c is the shear rate, and n is the rheological index. The non-newtonian fluid with larger n and smaller than 0 are shear thickening fluid and shear thinning fluid, respectively. Consequently, it is necessary to conduct a preliminary experiment on the power-law relationship of the non-newtonian fluids to provide a reference for the heat transfer experiment. In this study, three alternative non-newtonian fluids were selected for test: xanthan gum solution, Carbopol 934 solution and polyacrylamide solution. The shear rate, c, was obtained with the rotational viscometer (NDJ-9S). Figure 1 shows the change of dynamic viscosity (l) with shear rate (c) at different solution mass fractions (x) of xanthan gum solution. It is shown in the figure that when mass fractions (x) is below 0.1%, the dynamic viscosity has not evident change with mass fractions, however, decreases significantly with increasing the shear rate (c) when mass fractions (x) reaches 0.1%, suggesting that the xanthan gum solution begins to show the shear thinning property. For higher mass fractions (x), the shear thinning property develops more distinctly, especially with the relative low shear rate (c), indicating that the shear thinning property can be / Vol. 136, JUNE 2014 Transactions of the ASME

3 Fig. 1 Change of the dynamic viscosity with shear rate of xanthan gum solution at two ranges of mass fraction: (a) from 0.04% to 0.1% and (b) from 0.2% to 0.5% Fig. 2 Change of the dynamic viscosity with shear rate: (a) Carbopol 934, (b) polyacrylamide solution, and (c) water Fig. 3 Fitted l c curves of three selected solution of xanthan gum solution: (a) 0.1%, (b) 0.2%, and (c) 0.3% apparently presented in xanthan gum solution with the mass fraction (x) of no less than 1%. Figure 2 shows the change of dynamic viscosity (l) with shear rate (c) at different mass fractions (x) of Carbopol 934 solution, polyacrylamide solution and water. It is shown in Fig. 2(a) that Carbopol 934 solution begins to express the shear thinning property when the mass fraction (x) is 2.7% with poor fluidity, especially for the higher mass fractions (x). As shown in Fig. 2(b), for polyacrylamide solution, there is no relative obvious shear thinning property with mass fractions (x) being lower than 1%. Since that the monomer of polyacrylamide (acrylamide) has toxicity and the dissolving may result in the decomposing of polyacrylamide, the upper limit of mass fractions (x) was set to be 1%. On the other hand, the dynamic viscosity (l) of water holds steady with shear rate (c), which is in a great agreement with the fluid characteristic of Newtonian fluids, as shown in Fig. 2(c). This also implies that the validity of the viscosity experiment in this paper has been proved based on the tested result of water. Table 1 Fitted results and corresponding standard error x (%) Analysis formula Standard error-l Standard error-c 0.1 l ¼ 0:2655 c 0: l ¼ 1:18075 c 0: l ¼ 8:05574 c 0: Journal of Electronic Packaging JUNE 2014, Vol. 136 /

4 Fig. 4 Schematic sketch of an experiment system for flow and heat transfer tests Fig. 5 Two arrangements and cross sections of the dimple and protrusions. All dimensions are given in millimeters / Vol. 136, JUNE 2014 Transactions of the ASME

5 It can be concluded that xanthan gum solution and Carbopol 934 solution show the shear thinning property in this study, and the corresponding mass fraction of Carbopol 934 solution is relative high, resulting the distinct descend in fluidity, which is inappropriate for the following experiment on heat transfer. Therefore, the xanthan gum solution with three mass fractions (x) at 0.1%, 0.2%, 0.3% were selected to be the solution for heat transfer experiment as well as water to be compared, considering the influence on fluidity of high mass fraction (x). The fitted l c curves of the experiment solution were also correlated, as shown in Fig. 3. The fitted results and the corresponding standard error are listed in Table 1. The maximum standard errors of dynamic viscosity (l) and shear rate (c) are and 0.019, respectively, suggesting that the rationality of correlations. 3 Experiment on Heat Transfer in Rectangular Channel 3.1 Experiment System and Cases. The sketch of the experiment system is schematically shown in Fig. 4. The experiment solution flows into the channel from Inlet and out from the Outlet, and the circulation is maintained with centrifugal pump (2). The rotate speed is adjusted according to the cases by adjustable-speed motor (1). The distances between Inlet and the first dimple (protrusion) is long enough to ensure a fully developed flow, and the distance between Outlet and the last dimple (protrusion) is also enough to avoid the outlet effect. Two arranged manners of dimple/protrusion are considered in this study: aligned (so called parallel) arrangement and crossing (so called staggered) arrangement, as shown in Fig. 5. For the aligned manner, there are 10 streamwise rows with the pitch of 25 mm and 5 spanwise rows with the pitch of 20 mm, thus in total 50 dimples/protrusions are placed. For the crossing manner, 5 and 6 spanwise rows are placed in each odd and even streamwise row, respectively. The spanwise pitch is kept to be 20 mm while the streamwise pitch is changed to be mm. In this case, such manner seems much denser, and there are in total 55 dimples/protrusions. The cross sections of the dimple and protrusion are also schematically shown in Fig. 5. The dimples and protrusions have the same configurations but with different orientations. The printed diameter and depth of the dimples are 10 mm and 2 mm, respectively. The protruded diameter and height of the protrusions are also 10 mm and 2 mm, respectively. In this study, four structures are designed for tests: aligned arrangement of protrusions, crossing arrangement of protrusions, crossing arrangement of dimples and the smooth structure without dimples/protrusions. The flow pressure difference was measured using the differential manometer (4), and the thermal resistance thermodetector (51,52,53,54) was installed to measure the T o,w, T i,w, T o,f, T i,f, which stand for the temperature in the outlet-wall, inlet-wall, outlet-fluid, and inlet-fluid, respectively. The flow rate was measured with the turbine flowmeter (7). The temperature of the solution was measured and controlled at room temperature with the thermostat (8), and the solution heater (9) will start if necessary. All the experiment solution was placed in the water tank (10). The test section with dimples/protrusions was packed with the heat insulation cotton, creating an adiabatic boundary to prevent the excess heat dissipation. The thermal resistance thermodetectors (5) need to be revised before the experiment to minish the error from thermal resistances. The practical experiment system is shown in Fig. 6. In the experiment, seven flow rates are tested: 3 l/min, 3.5 l/ min, 4 l/min, 4.5 l/min, 5 l/min, 5.5 l/min, and 6 l/min with four mass fractions (x): 0, 0.1%, 0.2%, and 0.3%. Thus, there are in total 112 tested cases: 84 for xanthan gum and 28 for water, as listed in Table Parameter Definition. The Nu in this paper is defined as follows: Fig. 6 Photograph of the practical experiment system Nu ¼ hd h k where D h is the hydraulic diameter based on the cross-sectional area and wetted perimeter of the rectangular channel and k is the fluid thermal conductivity. h is the fluid heat transfer coefficient, which is given as h ¼ q (3) DT where q is the wall heat flux, DT is the fluid wall temperature difference, which is determined by log-mean valuing of wall temperature and fluid temperature as (2) DT ¼ ðt o;w T o;f Þ ðt i;w T i;f Þ ln T (4) o;w T o;f T i;w T i;f where T o,w, T i,w, T o,f, and T i,f, are the temperature in the outletwall, inlet-wall, outlet-fluid, and inlet-fluid, respectively. The wall temperatures above mean the temperatures of internal wall, and can be obtained from the measured temperature of external wall, using heat conduction equation with Fourier-law DT r ¼ qdx k wall (5) where Dx is the wall thickness, and k wall is thermal conductivity of the wall. The tested data show that the temperature of external wall is higher than that of internal wall by 0.26 K. The Fanning friction factor is defined by Dp D h L f ¼ 2qU 2 (6) Table 2 Different cases and conditions Channel structure V (10 5 m 3 /s) x (%) Group A Alignedprotrusion 5.00/5.83/6.67/7.50/8.33/9.17/ /0.1/0.2/0.3 Group B Crossingprotrusion 5.00/5.83/6.67/7.50/8.33/9.17/ /0.1/0.2/0.3 Group C Crossingdimple 5.00/5.83/6.67/7.50/8.33/9.17/ /0.1/0.2/0.3 Group D Smooth 5.00/5.83/6.67/7.50/8.33/9.17/ /0.1/0.2/0.3 Journal of Electronic Packaging JUNE 2014, Vol. 136 /

6 Fig. 7 Variations of Nu with flow velocity at different mass fractions: (a) x 5 0% and (b) x 5 0.1%; (c) x 5 0.2%, and (d) x 5 0.3% where DP and L are the differential pressure between the inlet and outlet, and the test section length, respectively. q is the fluid density, and U is the flow velocity. 4 Results and Analysis 4.1 Heat Transfer. Figure 7 shows the change of Nu with flow velocity (U) at different cases with different mass fractions (x). It is shown that Nu increases obviously with U at all cases regardless of Newtonian fluid or non-newtonian fluid. The channel with crossing protrusion has the maximum Nu due to the strong flow impinge on the protrusion upstream. Obviously, the arrangement of crossing protrusion can receive the flow impingement more easily and it is stronger than aligned arrangement which can greatly enhance the heat transfer. In addition, the vortices structures surrounding the protrusion or downstream the protrusion are affected little by the adjacent protrusion for crossing protrusion. Form the figure, the smooth channel has the minimum one, indicating that protrusion and dimple both distinctly enhanced the convective heat transfer in the channel. Besides, the heat transfer enhancements in the channel with protrusion and crossing arrangement are stronger than that of the channel with dimple and aligned arrangement, respectively. For dimple structure, the heat transfer enhancement is mainly improved by the directly flow impingement on the downstream boundary and the strengthened flow mixing by vortices structure forming in the downstream and adjacent flat area. Additionally, the flow impingement in protrusion structure is obviously stronger than dimple structure in the same geometric dimensions. Accordingly, a high heat transfer can be expected for crossing protrusions if the flow impingement plays the dominant role in improving the heat transfer. The difference in Nu between different structures gradually rises with the increase in x and U. Besides, it is shown that the Nu with crossing-dimple is smaller than that of aligned-protrusion only in the case with x ¼ 0%. When x reaches 0.1% or larger, the Nu with crossing-dimple begins to exceed that with alignedprotrusion when U is higher. At a high velocity or a large fluid viscosity, the dimple structure have a larger heat transfer enhancement than aligned-protrusion which can be explained by the intensified vortices structure at high Reynolds numbers or high fluid viscosity. From the figure, the heat transfer enhancement of crossing-dimple evidently surpasses that of aligned-protrusion with a higher U or x. Since the heat transfer enhancement is mainly done by flow impinge for crossing dimple, the higher pressure loss penalty can also be predicted for crossing-protrusion arrangement than crossing-dimple arrangement. Figure 8 shows the change of Nu with flow velocity (U) at different cases with different structures. It is shown that in different cases, there is a significant increase in Nu with a higher x, indicating that the convective heat transfer is further enhanced / Vol. 136, JUNE 2014 Transactions of the ASME

7 Fig. 8 Nu s subjected to flow velocity of different channel structures: (a) aligned-protrusion and (b) crossing-protrusion; (c) crossing-dimple, and (d) smooth channel apparently with the increase in x. The effect of the case with x ¼ 0.1% is inconspicuous but prominent when x reaches 0.2% or higher. Moreover, the enhancement is strengthened when the flow velocity is larger. For high flow velocity or large fluid viscosity, the flow impingement and secondary vortices structures are strengthened. In addition, the recirculation flow shrinks and the reattachment moves forward with the high fluid viscosity which also acts in enhancing the heat transfer. The development of the thermal boundary layer is impeded by the protrusion or dimple, enhancing the local heat transfer in the reattachment region and wake region, and increasing the Nu in the channel. Since that xanthan gum is a kind of shear thinning fluid, and the shear rate on the wall differs from that in the middle of the channel, the high normal viscosity difference and normal stress difference appear, resulting in the secondary flow, which prominently enhances the heat transfer. It is also shown that the reattachment moves forward, and the flow separation size reduces when the non-newtonian fluid is applied, strengthening the heat transfer. Moreover, the intensity of the shear flow rises as a consequent of the high viscosity and the structure of the protrusion and dimple, increasing the heat transfer enhancement. In summary, the heat transfer enhancement is mainly caused by the secondary flow from the shear thinning property, so does the high-strength shear flow. Thus, it is critically important to select a suitable working fluid to realize the great combination with the flow structure, so that the heat transfer could be enhanced greatly. 4.2 Flow Resistance. The change of friction factor (f) with flow velocity (U) at cases with different mass fraction (x) is illustrated in Fig. 9. In all cases, Fanning friction factor (f) reduces observably with the increase in U, and f in the channel with protrusion and crossing arrangement are larger than that of the channel with dimple and aligned arrangement, respectively, which are all larger than that of the smooth channel, suggesting the protrusion and dimple both increase the flow resistance, no matter for Newtonian fluid or non-newtonian fluid. For the dimple or protrusion structure, the flow separation and reattachment exist, which lead to the larger pressure loss compared with smooth channel. The difference between f in the channels with protrusion/dimple and that of the smooth channel is relative distinct. Such difference decreases with the increase of U. It is observed that when U is larger than 0.16 m/s, the difference has become small. This is caused by that, according to the l c curve (Fig. 3), the viscosity of xanthan gum decreases significantly with the increase in U, especially with the relative low shear rate, which is in a good agreement with the result in this section. It can be suggested that the drag reduction of xanthan gum will be more significant when the flow velocity increases, and might even superior than water. Figure 10 shows the change of friction factor (f) with flow velocity (U) for different channel structures. It is found that there is an apparent increase of friction factor (f) with a higher mass fraction (x), particularly in the cases with x ¼ 0.2% and 0.3%, agreeing with the result of the experiment on viscosity of Journal of Electronic Packaging JUNE 2014, Vol. 136 /

8 Fig. 9 Variations of friction factor with flow velocity at different mass fractions: (a) x 5 0% and (b) x 5 0.1%; (c) x 5 0.2%, and (d) x 5 0.3% non-newtonian fluids. It is also found that with a higher x, the variation range and gradient of f both distinctly rise, indicating an increasing shear thinning effect with a higher x. The development of the flow boundary layer is impeded by the protrusion and dimple, leading the decrease in the channel frictional resistance. Nevertheless, the pressure resistance increases as a result of the flow separation in the dimple inside, leading and trailing edge areas of the protrusion. In the present working conditions, the increase in the pressure resistance exceeds the decrease in the frictional resistance, resulting in an increase in f. Based on above comparison between the aligned-protrusion and crossingprotrusion, it is inferred that the development of the flow boundary layer is disturbed more frequently with the crossingprotrusion, and the flow separation is aggravated by the interaction of the protrusions, result in a higher f. Besides, through the comparison between the crossing-protrusion and crossing-dimple, it is inferred that when dimples are arranged, the flow separation mainly appears in the dimple inside. However, there are two flow separation regions: leading edge and trailing edge of the protrusion, which further increases the pressure resistance, leading a higher f that of dimples. For the non-newtonian fluid with shear thinning property, the shear rate in the flow boundary layer and protrusions/dimples both increase when the flow velocity increases, resulting in the decrease in the fluid viscosity and the delay of the flow separation. The reattachment moves forward, and the pressure resistance and frictional resistance both are reduced markedly. It should be noted that only laminar flow is studied in this paper. Compared to the Newtonian fluid in this paper (water), the drag reduction effect has not been obviously shown, though f starts to reduces more markedly, which indicates that f rises with the shear thinning fluid within laminar flow in the channel with protrusions or dimples. What is more, f of the non-newtonian fluid gradually gets closer to that of water at a higher U. In the current studies, the shear thinning fluid expresses the drag reduction effect well within turbulence flow [26 28]. 5 Experimental Error Analysis The main experimental errors are as follows: The temperature difference between the internal wall and external wall, which has been revised in the data processing in this paper. The thermal resistances are stacked to the wall with silica gel, which may bring in the measured temperature difference. The thermal resistance is also sheathed, and it may disturb the flow distribution surrounded. The solubleness of xanthan gum in water may produce several solid particles, leading to the error in the mass concentration. The heat from the rotatory pump may break the thermal balance of the circulation circuit, leading the unsteady state of the experiment system / Vol. 136, JUNE 2014 Transactions of the ASME

9 Fig. 10 Friction factors subjected to flow velocity of different channel structures: (a) aligned-protrusion and (b) crossingprotrusion; (c) crossing-dimple and (d) smooth channel Since the measurement space is limited, there exists difference in the positions of the measurement points of fluid temperature and wall temperature in the flow direction, which may bring in the measurement error. 6 Summary and Conclusion An experiment on the viscosity of three different kinds of non- Newtonian fluids, xanthan gum solution, Carbopol 934 solution, polyacrylamide solution, has been accomplished to acquire the viscosity with different mass fractions. Another experiment on heat transfer enhancement of non-newtonian fluid in rectangular channel with dimples/protrusions has also been completed, and the Nu and Fanning friction factor (f) at different cases were obtained. A comparison among different cases was achieved, and the main conclusions are summarized as follows: (1) Only xanthan gum shows apparent shear thinning property in the concentration range considered in this study without destroying the fluidity. (2) For Newtonian fluid and non-newtonian fluid, the friction factor distinctly reduces with the increase in flow velocity, which rises when dimples or protrusions are arranged. The friction factor of the channel with protrusion and crossing arrangement is larger than that of the channel with dimple and aligned arrangement. At high mass fraction, the friction factor increases significantly, but the difference is gradually decreased with the increase of flow velocity. (3) For Newtonian fluid and non-newtonian fluid, the Nu increases obviously with increasing the flow velocity at all cases and the heat transfer is enhanced when dimples or protrusions are arranged. The Nu in the channel with protrusion and crossing arrangement is higher than that of the channels with dimple and aligned arrangement. The heat transfer enhancement is remarkable at high mass fraction. (4) The flow resistance of non-newtonian fluid gets closer to that of Newtonian fluid with a relative high flow velocity. The enhancement of heat transfer is further strengthened when xanthan gum is selected to be the working fluid, especially at a higher flow velocity. In summary, the enhancement is further promoted with non-newtonian fluid and the structure of crossing-protrusion. Acknowledgment The authors would like to acknowledge financial support from the National Natural Science Foundation of China ( , ). The authors would like to thank Ping Li, KeYang, Keke Gao, Wei Zhao of Xi an Jiaotong University, China, for their kind supports of the research associated with this paper. Nomenclature A ¼ cross-sectional area (m 2 ) D h ¼ hydraulic diameter (m) Journal of Electronic Packaging JUNE 2014, Vol. 136 /

10 f ¼ Fanning friction factor h ¼ heat transfer coefficient (W/m 2 K) k ¼ consistency coefficient L ¼ test section length (m) n ¼ rheological index Nu ¼ Nusselt number P ¼ wetted perimeter (m) q ¼ wall heat flux (W/m 2 ) T ¼ temperature (K) U ¼ flow velocity (m/s) V ¼ volumetric flow rate (10 5 m/s) Greek Symbols c ¼ shear rate (s 1 ) Dp ¼ differential pressure (Pa) DT ¼ temperature difference (K) Dx ¼ wall thickness (m) k ¼ thermal conductivity (W/m K) l ¼ fluid dynamic viscosity (Pa S) q ¼ fluid density (kg/m 3 ) x ¼ solution mass fractions (%) Subscripts i,f ¼ inlet, fluid i,w ¼ inlet, wall o,f ¼ outlet, fluid o,w ¼ outlet, wall r ¼ revise wall ¼ wall References [1] Arik, M., and Bunker, R. S., 2006, Electronics Packaging Cooling: Technologies From Gas Turbine Engine Cooling, ASME J. Electron. Packag., 128, pp [2] B ohme, G., 1987, Non-Newtonian Fluid Mechanics, Elsevier Science & Technology, Amsterdam, Netherlands, Chap. 2. [3] Bharti, R. P., Chhabra, R. P., and Eswaran, V., 2006, Steady Flow of Power- Law Fluids Across a Circular Cylinder, Can. J. Chem. Eng., 84, pp [4] Acrivos, A., Shah, M. J., and Petersen, E. E., 1965, On the Solution of the Two-Dimensional Boundary-Layer Flow Equations for a Non-Newtonian Power Law Fluid, Chem. Eng. Sci., 20, pp [5] Sharma, K. K., and Adelman, M., 1969, Experimental Study of Natural Convection Heat Transfer From a Vertical Plate in a Non-Newtonian Fluid, Can. J. Chem. Eng., 47, pp [6] Silva, C., Marotta, E., and Fletcher, L., Flow Structure and Enhanced Heat Transfer in Channel Flow With Dimpled Surfaces: Application to Heat Sinks in Microelectronic Cooling, ASME J. Electron. Packag., 129, pp [7] Wei, X. J., Joshi, Y. K., and Ligrani, P. M., 2007, Numerical Simulation of Laminar Flow and Heat Transfer Inside a Microchannel With One Dimpled Surface, ASME J. Electron. Packag., 129, pp [8] Small, E., Sadeghipour, S. M., and Asheghi, M., 2006, Heat Sinks With Enhanced Heat Transfer Capability for Electronic Cooling Applications, ASME J. Electron. Packag., 128, pp [9] Xie, G. N., Sunden, B., and Zhang, W. H., 2011, Comparisons of Pins/Dimples/Protrusions Cooling Concepts for an Internal Blade Tip-Wall at High Reynolds Numbers, ASME J. Heat Transfer, 133(6), p [10] Kim, S., Choi, E. Y., and Kwak, J. S., 2012, Effect of Channel Orientation on the Heat Transfer Coefficient in the Smooth and Dimpled Rotating Rectangular Channels, ASME J. Heat Transfer, 134(6), p [11] Chen, J., M uller-steinhagen, H., and Duffy, G. G., 2001, Heat Transfer Enhancement in Dimpled Tubes, Appl. Therm. Eng., 21, pp [12] Ligrani, P. M., Harrison, J. L., Mahmood, G. I., and Hill, M. L., 2001, Flow Structure Due to Dimple Depression on a Channel Surface, Phys. Fluids, 13, pp [13] Mahmood, G. I., and Ligrani, P. M., 2002, Heat Transfer in a Dimpled Channel: Combined Influences of Aspect Ratio, Temperature Ratio, Reynolds Number, and Flow Structure, Int. J. Heat Mass Transfer, 45, pp [14] Elyyan, M. A., and Tafti, D. K., 2008, Large Eddy Simulation Investigation of Flow and Heat Transfer in a Channel With Dimples and Protrusions, ASME J. Turbomach., 130(4), p [15] Alshroof, O., Reizes, J., Timchenko, V., and Leonardi, E., 2009, Flow Structure and Heat Transfer Enhancement in Laminar Flow With Protrusion-Dimple Combinations in a Shallow Rectangular Channel, Proceedings of ASME Heat Transfer Summer Conference, San Francisco, CA, July 19-23, ASME Paper No. HT [16] Hwang, S. D., Kown, H. G., and Cho, H. H., 2010, Local Heat Transfer and Thermal Performance on Periodically Dimple-Protrusion Patterned Walls for Compact Heat Exchangers, Energy, 35, pp [17] Hwang, S. D., Kown, H. G., and Cho, H. H., 2008, Heat Transfer With Dimple/Protrusion Arrays in a Rectangular Duct With a Low Reynolds Number Range, Int. J. Heat Fluid Flow, 29, pp [18] Rao, Y., Wan, C. Y., and Xu, Y. M., 2012, An Experimental Study of Pressure Loss and Heat Transfer in the Pin Fin-Dimple Channels With Various Dimple Depths, Int. J. Heat Mass Transfer, 55, pp [19] Rao, Y., Wan, C. Y., and Zang, S. S., 2012, An Experimental and Numerical Study of the Flow and Heat Transfer in Channels With Pin Fin-Dimple Combined Arrays of Different Configurations, ASME J. Heat Transfer, 134(12), p [20] Rao, Y., Xu, Y. M., and Wan, C. Y., 2012, An Experimental and Numerical Study of Flow and Heat Transfer in Channels With Pin Fin-Dimple and Pin Fin Arrays, Exp. Therm. Fluid Sci., 38, pp [21] Rao, Y., Xu, Y. M., and Wan, C. Y., 2012, A Numerical Study of the Flow and Heat Transfer in the Pin Fin-Dimple Channels With Various Dimple Depths, ASME J. Heat Transfer, 134(7), p [22] Afanasyev, V. N., Chudnovsky, Y. P., Leontiev, A. I., and Roganov, P. S., 1993, Turbulent Flow Friction and Heat Transfer Characteristics for Spherical Cavities on a Flat Plate, Exp. Therm. Fluid Sci., 7, pp [23] Burgess, N., and Ligrani, P., 2005, Effects of Dimple Depth on Channel Nusselt Numbers and Friction Factors, ASME J. Heat Transfer, 127, pp [24] Moon, H., O Connell, T., and Glezer, B., 2000, Channel Height Effect on Heat Transfer and Friction in a Dimpled Passage, ASME J. Eng. Gas Turbines Power, 122, pp [25] Xie, G. N., Liu, J., Ligrani, P. M., and Zhang W. H., 2013, Numerical Predictions of Heat Transfer and Flow Structure in a Square Cross-Section Channel With Various Non-Spherical Indentation Dimples, Numer. Heat Transfer, Part A, 64(3), pp [26] Peixinho, J., Desaubry, C., and Lebouche, M., 2008, Heat Transfer of a Non- Newtonian Fluid (Carbopol Aqueous Solution) in Transitional Pipe Flow, Int. J. Heat Mass Transfer, 51, pp [27] Pawar, S. S., and Sunnapwar, V. K., 2013, Experimental Studies on Heat Transfer to Newtonian and Non-Newtonian Fluids in Helical Coils With Laminar and Turbulent Flow, Exp. Therm. Fluid Sci., 44, pp [28] Zhang, G. G., Zhang, M. Y., and Yang, W. Y., 2007, Drag Reduction in Turbulent Pipe Flows of Aqueous Xanthan Gum Solutions, J. Xi an Jiaotong Univ., 41, pp (in Chinese) / Vol. 136, JUNE 2014 Transactions of the ASME