Heat transfer enhancement, entropy generation and temperature uniformity analyses of shark-skin bionic modified microchannel heat sink

International Journal of Heat and Mass Transfer 146 (2020) 118846

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Heat transfer enhancement, entropy generation and temperature uniformity analyses of shark-skin bionic modified microchannel heat sink Ping Li ⇑, Dingzhang Guo, Xinyue Huang MOE Key Laboratory of Thermal Fluid Science and Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, PR China

a r t i c l e

i n f o

Article history: Received 13 May 2019 Received in revised form 2 September 2019 Accepted 5 October 2019

Keywords: Shark-skin bionic concept Heat transfer Entropy generation Temperature uniformity Microchannel heat sink

a b s t r a c t Inspired by the shark-skin bionic concept, four novel flow control devices are proposed in this study to further enhance thermal performance (TP) with low entropy generation (S/S0), as well as to improve temperature uniformity. Then, the flow structures and heat transfer characteristics of water-cooled microchannel heat sink (MCHS) modified by the proposed devices (Model A, Model B, Model C and Model D) are investigated in laminar flow regime (Re = 50–700). Results show that the variation trends of TP for different MCHS increase as Re increases, and the TP of all cases ranges from 1.1 to 3.1. And, the S/S0 of all MCHS maintain low at small Re, which increases quickly as Re further increases. When Re is small (Re = 50–250), the largest TP is obtained by Model B with the smallest S/S0. As Re is larger than 500, the TP and S/S0 of Model D both become the largest. The varied geometry of flow control devices pushes main flow towards to side walls, and the sequential contraction and expansion area of split passage enhance the fluid exchange. However, the secondary flow generated by flow control device is not intense enough to cool down side walls when Re is small. Therefore, the temperature uniformity of MCHS is improved significantly with the increase of Re. The temperature uniformity of Model D is inferior to that of Model C due to hot spots exist at the narrow split passage. Furthermore, at large Re, Model C is superior to others, because the significant improvement of TP is achieved herein with acceptable S/S0. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction The design of efficient compact size heat sink is critical for breakthrough in many industries, such as high speed component, electronic and solar thermal receivers [1–3]. Comparing with active cooling, passive cooling method is cost effective and more reliable, since the absence of driving energy and moving parts [4–6]. As one of high-tech effective cooling devices, microchannel heat sink (MCHS) has been widely employed after firstly proposed by Tuckerman and Pease [7]. Moreover, an overview about the effect of coolant types in MCHS was fulfilled by Hassan et al. [8], which indicated that liquid could provide superior cooling properties. Therefore, the water has been widely adopted as coolant due to its high heat capacity and readily availability [9–11]. The further enhancement for heat transfer performance of MCHS has been demonstrated in many researches [4–6] by disrupting the development of thermal boundary layer. For multiple microchannels, tip clearance [12] and bifurcations [13] are efficient ⇑ Corresponding author. E-mail address: [email protected] (P. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118846 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

methods. Moreover, in single microchannel, the sudden expansion of flow area [14–17] has been studied widely recently, as well as wavy walled channel [18–20]. By contrast, the rough element gains more attraction in academic research and engineering application, since it has obvious advantages in complicated heat transfer phenomena. Not only it can be added on the channel walls flexibly, but also it can be combined with above or other flow control technologies. Modified by flow control device, the friction loss is also increased obviously during enhancing heat transfer performance. Accordingly, the dimple/protrusion interests many researchers since it can decrease pressure drop penalty [21–24]. The heat transfer and flow resistance for wavy microchannel with dimples added in the throat were numerically investigated by Gong et al. [25] under constant Reynolds number 500. And, results indicated that the Nusselt number increased by 2.45 times than that of smooth channel, meanwhile, the pressure drop also increased by 2.04 times. The optimization of water-cooled MCHS with combination of dimple and pin-fin was performed in our previous study [11]. Compared to smooth rectangular microchannel, the Nusselt number was enhanced by 2.37 times with 1.82 times increment of friction loss. The above studies show that the

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P. Li et al. / International Journal of Heat and Mass Transfer 146 (2020) 118846

Nomenclature Cp Dh f H h k L m Nu q’ q’’ Re S Sf St T

fluid specific heat (J kg1 K1) hydraulic diameter (lm) Fanning friction factor microchannel height (lm) flow control device height (lm) fluid thermal conductivity (W m1 K1) microchannel streamwise length (lm) flow rate (kg s1) Nusselt number heat transfer rate per unit length (W m1) heat transfer coefficient (W m2 K1) Reynolds number entropy generation (W K1 m1) friction induced entropy generation (W K1 m1) heat transfer induced entropy generation (W K1 m1) temperature (K)

reduction of friction loss is still urgent to consider in the design of higher efficiency MCHS. The inspiration of designs could be found throughout living nature, which is serving as the basis for many new innovations. In nature, fast-swimming sharks intrigue many researchers for its low-drag characteristic [26–29]. The study of biomimetic sharkskin performed by Pu et al. [27] indicated that the high-speed and drag-reduction of shark were mainly dependent on riblet structures. And, the experimental investigation of riblet surface [28] indicated that the cross-stream velocity fluctuations inside the riblet valleys were lower than those above a flat plate, significantly. Thus, the wall shear stress was reduced by modifying the velocity distribution or fluctuation. Moreover, the mechanisms of fluiddrag for shark-skin in turbulent investigated by Dean et al. [29] showed that riblet structures can disturb the translation of vortices and reduce the vortex ejection as well as outer-layer turbulence. Above studies on the flow resistance of shark, as well as the geometry of shark-skin, indicate that the discrete gap and hump of riblet structures in shark-skin cause the reduction of flow resistance. Accordingly, based on the shark-skin bionic concept, the split protrusion was proposed by the authors [30], and results showed that the friction loss of MCHS with protrusion was decreased obviously, especially at the larger split width. Moreover, the split structure guided the part of main fluid to side walls, enhancing the secondary flow in channel. Thus, the high temperature at rear-end of protrusion and side wall corner was decreased effectively. With the development of technology, for equipment under high precision control, the deterioration of local heat transfer will influence the modulation response of system a lot, and generate additional thermal resistance. Hence, the improvement of temperature uniformity is essential to consider in the design of higher efficiency MCHS with lower pressure penalty. Moreover, the comparative investigation about different flow control devices showed that heat transfer performance of MCHS with cylinder was superior to others [31], while the increase of friction loss was also significant. Therefore, for higher heat transfer performance, better temperature uniformity and lower flow friction loss, the effect of combination of cylinder and shark skin bionic concept is worth exploring. Based on the cylinder, four novel flow control devices are proposed in this study, and all structure outlines adopted to generate above devices are inspired by shark skin. Compared with the simplified artificial riblet samples [26], the geometry similarity from shark-skin surface microstructure is further improved. Moreover,

TP Uave W DP DT

thermal performance average velocity of inlet (m s1) microchannel width (lm) pressure drop (Pa) mean temperature difference (K)

Greek symbols l fluid dynamic viscosity (Pa s) q fluid density (kg m3) Subscripts w,ave wall average f,ave fluid average 0 baselines condition

flow structures and heat transfer characteristics of MCHS with these devices are discussed in detail, as well as temperature uniformity. The entropy generation of MCHS is also the valuable reference standard for the design of MCHS [31–34], so it is also discussed herein.

2. Numerical method and validation 2.1. Geometrical configuration of models and boundary conditions The 3D model of MCHS with periodical flow control devices is shown in Fig. 1(a), which can be further extended along streamwise (Z), spanwise (X) and normalwise (Y), respectively. Moreover, internal structure of microchannel is exhibited by means of transparent wall. The fully developed periodic velocity and temperature can be obtained after fluid flows across some periodic flow control devices in MCHS, which is the main domain deciding the whole performance of heat transfer exchanger. Hence, the periodic unit of MCHS is employed as objective to carry out simulation, which has been widely adopted in many studies [11,24,31,35] to reduce computational resource. The cross-section of single MCHS is 200 lm (W)
50 lm (H), and the periodic length along streamwise direction is 150 lm (L). Working fluid water flows into the transitional domain in the positive Z direction from inlet surface, and its bulk temperature is 300 K. Moreover, the transitional periodic boundary condition is applied at both inlet and outlet, and inlet Reynolds number ranges from 50 to 700. For other surfaces of MCHS, the uniform constant heat flux of q’’ = 5
105 W m2 and no-slip boundary condition are specified. Based on the cylinder, flow control devices proposed in this study are generated by rotating special structure outline with the same rotation axis. Especially, the structure outline of Model C is based on the experiment measure of real shark skin microstructure [36]. Model B is the combination of cylinder and split, inspired of the split protrusion proposed in our previous study [30]. Moreover, the structure outlines of Model A and Model D are modified with hyperbolic function [37–39] on the basis of Model C. All these structural outlines are showed in Fig. 1(b), and the rotation axis is fixed at L/2 with y = 52.5 lm. And, the length of flow control device along streamwise direction is 100 lm. Moreover, the large spanwise width of flow control device is beneficial for fluid impinging on side surfaces, which can improve temperature uni-

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Fig. 1. Microchannel heat sink (MCHS) with periodic flow control devices: (a) Microchannel heat sink (MCHS); (b) Structure outline; (c) MCHS periodic unit models.

formity. Therefore, flow control devices are all divided into three units of geometry structure. As shown in Fig. 1(c), MCHS with different flow control devices are named according to the decrease of flow area: Model A > Model B > Model C > Model D. 2.2. Governing equations The three dimensional numerical simulations of MCHS with periodical flow control devices were carried out with ANSYS Fluent

platform. The incompressible steady Navier-Stokes equation is used to solve flow and heat transfer processes in this study. Under assumptions that the flow is (1) steady state, (2) three dimensional incompressible, (3) laminar flow and (4) constant fluid properties, the governing equations are as follows. Continuity equation

*

r u ¼0

ð1Þ

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P. Li et al. / International Journal of Heat and Mass Transfer 146 (2020) 118846

Momentum equation

  * * * q u r u ¼ rp þ lr2 u

ð2Þ

Energy equation

The entropy generation in the forced convective flow with heat transfer contains two parts: heat transfer irreversibility and fluid frictional irreversibility. It can be calculated by the following equations.

S¼

  * qC p u rT ¼ kr2 T

ð3Þ



k

l @U i

T

T

ðjrT jÞ2 þ 2

@xj

þ

 @U j @U i ¼ St þ Sf @xi @xj

ð11Þ

k ðjrT jÞ2 T2   l @U i @U j @U i þ Sf ¼ T @xj @xi @xj St ¼

ð12Þ

The SIMPLE method is used in coupling pressure and velocity. The standard scheme is used for pressure discretization. The momentum and energy equations are solved with second-order upwind scheme. The residues of continuity, energy and velocities, as well as the temperature and velocity on special points, are monitored to judge the convergence of simulation, in which convergence criteria is set as 1
106.

For an internal flow in the proposed microchannel, the rate of entropy generation per unit length can be calculated as [43–45]

2.3. Data reduction

S¼

qU av e Dh l

ð4Þ

where Uave is the average velocity of inlet, Dh is hydraulic diameter and defined by

2WH Dh ¼ W þH

hDh k

ð6Þ

Dh 2

ð15Þ

Therefore, Eq. (14) can be given as

S¼

q00 2 pDh 2 2

kT f ;av e Nu

þ

32m3 f

p q2 T f ;av e Dh 5 2

¼ St þ S f

ð16Þ

Furthermore, the baseline entropy generation (S0) can be given

S0 ¼ St0 þ Sf 0 ¼

q00 2 pDh 2 2

kT 0 Nu0

þ

32m3 f 0

ð16Þ

p q2 T 0 Dh 5 2

where T0 is the bulk temperature of inflow.

ð7Þ

where q’’ represents the heat flux, and DT is the difference of mean wall temperature Tw,ave and mean fluids temperature Tf,ave

DT ¼ T w;av e  T f ;av e

ð8Þ

The Fanning friction factor (f) is defined as

ðDP=LÞDh

ð9Þ

2qU 2av e

where DP is the pressure drop between inlet and outlet. The thermal performance (TP) is described as

 TP ¼

r¼

2.4. Model validation

q00 DT

f ¼

ð14Þ

as

where k is the thermal conductivity of water, h is the heat transfer coefficient and described as

h¼

q0 ¼ 2prq00 ;

ð5Þ

The Nusselt number (Nu) is given by

Nu ¼

1 q0 2 m3 f þ pNu kT f ;av e 2 p2 q2 T f ;av e r5

And, q’ and r can be given as

In this study, Reynolds number (Re) is defined by

Re ¼

ð13Þ

 1=3 Nu f ð Þ Nu0 f0

ð10Þ

The thermal performance [40,41] considers both heat transfer augmentation and pressure penalty, and depends on the ratios of Nu to Nu0 and f to f0. Among, f0 and Nu0 for smooth rectangular microchannel are used herein as baseline to normalize Fanning friction factor and Nusselt number, which are from research of Shah and London [42].

To balance simulation accuracy and computational resource, a grid independence validation with Model C is carried out at the case of q’’ = 5
105 W m2, Re = 350. In the validation procedure, Nu and f are selected as evaluation criteria, starting from a coarse mesh and refining it until these parameters are independent on the mesh size. As shown in Table 1, the relative discrepancies of Nu and f are similar when the mesh changes from Mesh2 to Mesh3. Therefore, Mesh2 is selected. Moreover, similar meshes are established for other MCHS periodic units. Taking the Model C as an example, the tetrahedral mesh grid applied in this study is shown in Fig. 2, including the whole mesh and mesh cut planes. It can be seen that the mesh size near the wall surfaces is refined obviously. The proposed solution method is validated by simulating flow and heat transfer in water-cooled smooth microchannel. The height, width and length of smooth microchannel computational domain are 200 lm, 50 lm and 150 lm, respectively. Compared with referenced experimental results [42], the results of verification are showed in Table 2. It can be seen that the largest difference is 0.92%, showing a very good agreement. The similar comparison can also be observed in the literatures with the same topic [46–48] and our previous studies [11,24,31]. In addition, for the

Table 1 Grid independence validation.

Mesh1 Mesh2 Mrsh3 Mesh4

Nodes

Nu

Difference %

f
10

Difference %

498,920 1,081,144 2,452,800 5,689,802

8.543 8.100 8.077 8.069

5.87 0.39 0.10 –

1.095 1.041 1.038 1.036

5.71 0.52 0.15 –

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Fig. 2. Whole mesh grid and mesh grid cut planes of Model C.

Table 2 Simulation model validation. Re

50 100 200 300

fRe

Nu

Referenced result

Proposed model

Difference %

Referenced result

Proposed model

Difference %

18.233 18.233 18.233 18.233

18.136 18.300 18.344 18.401

0.53 0.37 0.61 0.92

2.94 2.94 2.94 2.94

2.930 2.914 2.954 2.957

0.35 0.87 0.46 0.59

validation of numerical method and apparatus of fully developed laminar flow and heat transfer in microchannel, results of Shah and London [42] have been also adopted in many studies [46– 52]. Therefore, the proposed simulation method in this work can be expected accurate enough for the analysis of flow and heat transfer in MCHS.

3. Results and discussions 3.1. Analysis of performance parameters In this study, the heat transfer performance (Nu/Nu0), flow friction loss (f/f0) and thermal performance (TP) of modified MCHS are investigated in detail, as well as the entropy generation (S/S0).

Fig. 3. Variation of Nu/Nu0 in different MCHS.

It can be seen from Fig. 3 that the Nu/Nu0 of all cases ranges from 1.3 to 4.6, and the variation trends of Nu/Nu0 for different MCHS increase with the increase of Re. At the case of Re = 50, Nu/ Nu0 of MCHS are all small with little difference, while the difference of Nu/Nu0 among different MCHS is gradually obvious as Re further increases. The above phenomenon occurs due to the effect of different flow control devices on Nu/Nu0 increasing is limited by small Re. Comparing with other MCHS, the Nu/Nu0 of Model D is the largest, which is similar with that of Model B as Re increases from 50 to 250. However, the increment of Nu/Nu0 from Model B to Model D is enlarged gradually with further increase of Re. By contrast, the Nu/Nu0 of Model A always remains the smallest. When Re increases from 50 to 150, the Nu/Nu0 of Model A increases slowly, since the disturbance of fluid caused by flow control device in Model A is slightly. Moreover, comparing with Model C, the Nu/Nu0 of Model B is larger as Re ranges from 50 to 350, while it reverses when Re is larger than 500. In the studied MCHS, f/f0 is commonly categorized into friction drag and pressure drag. Friction drag is formed by interaction of the closest fluid layers to object’s surface, and pressure drag is closely related to required energy to overcome the pressure drop between the front and back of object. The development of flow boundary layer is interrupted by flow control device in MCHS, which leads to the decrease of friction drag. Meanwhile, pressure drag is increased significantly due to the appearance of flow separation near flow control device. For comparison, f0 for smooth rectangular microchannel are used herein as baseline to normalize Fanning friction, so it shows increment of friction coefficient. And, the drag reduction effect means to the comparison with the cylinder-modified MCHS. Therefore, f/f0 of all cases in this study are larger than 1, and variations of f/f0 for different MCHS increase as Re increases, as shown in Fig. 4. It is obvious that the f/f0 of Model D and Model A are much larger and smaller than that of other MCHS, respectively, and the increment of f/f0 from Model A to Model D is larger at larger Re. Moreover, at the small Re (Re = 150–250), the f/f0 of Model B is lar-

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Fig. 6. Variation of St/S0 and Sf/S0 in different MCHS. Fig. 4. Variation of f/f0 in different MCHS.

ger than that of Model C, while it increases more slowly during Re further increases from 250 to 500. Accordingly, the f/f0 of Model B and Model C become similar at the large Re (Re = 500–700). Furthermore, compared with MCHS with cylinder [31], f/f0 of all MCHS in this study are reduced significantly. Especially, the f/f0 of Model A is nearly reduced to a half. The variation of TP is similar with that of Nu/Nu0 on the whole, while there is still some difference, which is closely related to the variation of f/f0. As shown in Fig. 5, the range of TP in this study is from 1.1 to 3.1. At the small Re (Re = 50–250), comparing with Model D, the f/f0 of Model B is smaller, so the TP of Model B is slightly larger than that of Model D. However, as Re further increases, the TP of Model D becomes larger than that of others, and the largest TP = 3.1 is obtained at the case of Re = 700. By contrast, the TP of Model A always remains the smallest, and the increment of TP from Model A to Model D is also smaller than that of Nu/ Nu0. In addition, comparing with Model B, the Nu/Nu0 and f/f0 of Model C are larger and smaller at the large Re (Re = 500–700), respectively, so the TP of Model C is much larger than that of Model B at this time. To further study the comprehensive heat transfer enhancement performance, the S/S0 of MCHS is analyzed, which consists of two parts: St/S0 and Sf/S0, and the larger S/S0 means the more loss of active power. The temperature between heated wall and coolant is decreased with the increase of Nu/Nu0, so the variation trend of St/S0 is opposite to that of Nu/Nu0, which decreases with the increase of Re. As

shown in Fig. 6, the St/S0 of Model A and Model D are larger and smaller than others, respectively. The St/S0 of different MCHS are close at Re = 50, while the difference in St/S0 for different MCHS is increased suddenly at Re = 150, which decreases gradually as Re further increases. Comparing with Fig. 4, the variation trend of Sf/ S0 is similar with that of f/f0, which increase with the increase of Re. However, different from the variation of f/f0, the Sf/S0 of different MCHS are nearly close to 0 at the case of Re = 50. And then, the difference in Sf/S0 for different MCHS is increased obviously with the increase of Re. From the comparison between St/S0 and Sf/S0, it can be seen that the St/S0 is larger than Sf/S0 when Re is smaller than 150, while it reverses when Re is larger than 300. And, the difference from St/ S0 to Sf/S0 is increased obviously as Re further increases from Re = 300, so the range of Sf/S0 is much larger than that of St/S0. Furthermore, on the contrary to the variation of St/S0, the largest and smallest Sf/S0 are obtained by Model D and Model A, respectively. As shown in Fig. 7, the S/S0 of different MCHS maintain low at small Re (Re = 50–250) due to the rapid decrease of St/S0 and the slow increase of Sf/S0. However, as Re further increases, the S/S0 increases quickly, which mainly depends on the variation of Sf/S0. The range of S/S0 in this study is 0.6–2.3. Moreover, the minimum S/S0 of different MCHS are obtained at Re = 150, except Model A. And, the S/S0 of Model A is larger than that of others at small Re, while it decreases gradually with the increase of Re. Accordingly, the S/S0 of Model A becomes the smallest when Re is larger than 350. On the contrary, the S/S0 of Model D is the largest at this time. The increment of S/S0 from Model A to Model D is enlarged gradually with the increase of Re from 250 to 700. Furthermore, the S/S0 of Model B and Model C always remain similar, while the S/S0 of Model B is larger at small Re, and the S/S0 of Model C is larger at the large Re. Considering both TP and S/S0, the maximum TP and minimum S/ S0 at small Re (Re = 50–250) are achieved in Model B. However, as Re is larger than 500, Model C is superior to others, because the significant improvement of TP is achieved by Model C with acceptable S/S0. 3.2. Analysis of flow structures and heat transfer characteristics

Fig. 5. Variation of TP in different MCHS.

Due to the geometrical features of proposed flow control devices in this study, the flow area of MCHS first decreases and then increases along streamwise direction. Hence, the high-speed region appears at the location with minimum flow area, where the wall temperature decreases significantly. Moreover, part of main flow directly impinges on the leading edge of flow control device, which takes away a lot heat quickly and disturbs the devel-

P. Li et al. / International Journal of Heat and Mass Transfer 146 (2020) 118846

Fig. 7. Variation of S/S0 in different MCHS.

opment of thermal boundary layer. Furthermore, flow control device enhances spanwise fluid flow towards to side walls of MCHS, which is beneficial for the reduction of side wall temperature. As a result, both heat transfer performance and temperature uniformity of MCHS are improved by the proposed flow control devices. The cases of Re = 150 and Re = 700 are employed herein as examples to illustrate the effect of flow control device on the temperature variations. And, heat transfer characteristics highly depend on flow structures, so limiting streamlines are showed in Figs. 8 and 9 as well. In addition, the results on the associated left wall of MCHS are exhibited in its coordinate plane for clear observation. It can be seen from Fig. 8 that the temperature in the middle part of each MCHS decreases obviously at the case of Re = 150. However, the high temperature of the left surface still cannot be

7

eliminated, which is due to the secondary flow generated by flow control device is not intense enough. Comparing with other MCHS, the minimum flow area in Model D is the smallest, so the flow velocity acceleration effect is the most obvious, and the low-temperature region is the largest. Nevertheless, the high-temperature region is observed on the narrow passage walls of Model D. Moreover, in Model D, more fluid directly impinges on the leading edge of flow control device, forming three larger separation bubbles. Meanwhile, at the rear end, the flow separates in advance, which reattaches in the wake flow closer to the next channel, so the separation bubbles behind flow control device almost covers the whole wake flow region. And then, the larger separation flow enhances fluid exchange between main flow and near wall flow, both in spanwise and normalwise directions, which also results in small temperature gradient on modified wall, as well as lower temperature on side walls. Considering the above, the friction loss and heat removal of Model D both are the largest among all MCHS. Furthermore, the fluid disturbance in Model A is slight, so its heat transfer performance is inferior to that of others. As showed in Fig. 8(b), the split passage in Model B is wide and straight, and the temperature on the split passage walls decreases obviously, so the heat transfer performance of Model B is enhanced more than that of Model C. Meanwhile, the friction loss of Model B is also larger than that of Model C due to more fluid is stationary on the leading edge of flow control device. When Re increases to 700 (Fig. 9), the low-temperature region in each MCHS is enlarged obviously, and the large temperature gradient is dissipated efficiently. While, a little high-temperature region still exists on the upper side walls, which indicates that the proposed flow control devices improve heat removal of modified wall, as well as the part of side walls near it. In addition, the flow separation region of each MCHS becomes larger as well, so the friction loss increases significantly. The low-temperature region of Model D is also the largest among all MCHS, although the temperature gradient at the rear end of flow control device increases. Moreover, the flow separates

Fig. 8. Temperature contours (unit: K) and limiting streamlines on the left surface and down surface at Re = 150: (a) Model A; (b) Model B; (c) Model C; (d) Model D.

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Fig. 9. Temperature contours (unit: K) and limiting streamlines on the left surface and down surface at Re = 700: (a) Model A; (b) Model B; (c) Model C; (d) Model D.

Fig. 10. Temperature contours (unit: K) and limiting streamlines on the left surface and down surface in Model C: (a) Re = 350; (b) Re = 500.

at the rear end of flow control device, and reattaches on the wall of next periodical unit, indicating that the small separation bubbles in front of channel and large ones behind merge. Therefore, comparing with other MCHS, the heat transfer performance and friction loss of Model D still are both the largest. However, the temperature uniformity of Model D is inferior to Model C due to the hot spots exist at the split passage. Furthermore, when Re increases, the varied geometry of proposed flow control devices pushes main flow towards to side walls more intensely, and the sequential contraction and expansion area of split passage enhance the fluid and heat exchange. However, the split passage in Model B is straight, and the spanwise width of flow control device in Model B is the smallest among all MCHS, so the fluid exchange and secondary flow enhancement effect of other MCHS is more obvious. Therefore, comparing with Re = 150, the heat transfer performance of Model B becomes worse than that of Model C when Re = 700. Meanwhile, the temperature uniformity of Model B also becomes the worst among all MCHS. In addition, for Model A, three small separation

bubbles are formed when fluid impinges on flow control device, and larger separation flow can be observed in the wake flow. And, the friction loss of Model A is still smaller than that of others. From the above discussions, as Re increases, both the heat transfer performance and temperature uniformity of Model C are improved significantly with acceptable friction loss. Therefore, the limiting streamlines and temperature contours at Re = 350 and Re = 500 of Model C are showed in Fig. 10 to further discuss its performance variations. Comparing Figs. 8(c) and 10(a), the low-temperature region enlarges a lot and extends along spanwise direction when Re increases from 150 to 350. As Re further increases to 500 (Fig. 10(b)), the low-temperature region around flow control device decreases a little, while the high-temperature region on side walls decreases obviously. Moreover, the rear end separation bubbles near side walls are more streamwise, enhancing the heat removal of the side of modified wall a lot, as well as the side walls. Meanwhile, the flow separation region is enlarged at larger Re, even merge and develop to the next periodical unit,

P. Li et al. / International Journal of Heat and Mass Transfer 146 (2020) 118846

so the friction loss is increased gradually. Therefore, as shown in Fig. 9(c), the heat transfer performance and temperature uniformity both are improved obviously as Re increases to 700, while the friction loss is enlarged as well.

9

51976152) and Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2017JQ5096).

References 4. Conclusions Based on the cylinder, four novel flow control devices are proposed by inspiration of shark skin bionic concept to reduce the friction loss. Compared with MCHS with cylinder, f/f0 of all MCHS models in this study are reduced obviously. Especially, the f/f0 of Model A are nearly reduced to a half. Moreover, the ranges of f/f0 and Nu/Nu0 for all cases are 1.4–3.4 and 1.3–4.6, respectively. The conclusions of detailed analysis including TP, S/S0 and temperature uniformity are drawn as follows. (1) The variation trends of TP for different MCHS all increase with the increase of Re, and the TP in this study ranges from 1.1 to 3.1. At small Re (Re = 50–250), the largest TP is obtained by Model B. As Re further increases from 500, the TP of Model C and Model D both become the larger than that of Model B, and the largest TP = 3.1 is obtained by Model D at the case of Re = 700. Furthermore, the TP of Model A always remains the smallest among all MCHS. (2) The range of S/S0 in this study is from 0.6 to 2.3. At small Re (Re = 50–250), the S/S0 of different MCHS maintain low, which increase quickly as Re further increases. Moreover, the minimum S/S0 of different MCHS are obtained at Re = 150, except Model A. And, the S/S0 of Model A is the larger among all MCHS at small Re, while it becomes the smallest when Re is larger than 350. On the contrary, the S/S0 of Model D is small at small Re, which becomes the largest at the large Re. Furthermore, the S/S0 of Model B and Model C always remain similar, while the S/S0 of Model B is larger at small Re, which becomes smaller at the large Re. (3) The temperature uniformity of MCHS is improved significantly by the proposed flow control devices in this study. However, when Re is small, the secondary flow generated by flow control device is not intense enough to cool down side walls. As Re increases, the temperature uniformity of Model B is the worst among all MCHS. Moreover, the temperature uniformity of Model D is inferior to that of Model C due to hot spots exist at the narrow split passage. (4) When Re is small (Re = 50–250), the temperature uniformity of different MCHS is similar, and the TP and S/S0 of Model B are the largest and smallest among all MCHS, respectively. However, at large Re (Re = 500–700), comprehensively considerations of TP, S/S0 and temperature uniformity indicate that Model C is superior to other MCHS. Because the significant improvement of TP is achieved by Model C with acceptable S/S0, as well as the improvement of temperature uniformity is also the most obvious.

Declaration of Competing Interest We declare no any interest conflict. Acknowledgements The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No.

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