Hydrothermal performance of microchannel heat sink: The effect of channel design

International Journal of Heat and Mass Transfer 107 (2017) 21–44

Contents lists available at ScienceDirect

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

Review

Hydrothermal performance of microchannel heat sink: The effect of channel design Ihsan Ali Ghani a,b, Nor Azwadi Che Sidik a,⇑, Natrah Kamaruzaman a a b

Faculty of Mechanical Engineering, University Teknologi Malaysia, Skudai, Johor, Malaysia Mechanical Engineering Department, College of Engineering, Al-Mustansiriyah University, Iraq

a r t i c l e

i n f o

Article history: Received 16 August 2016 Received in revised form 8 November 2016 Accepted 8 November 2016

Keywords: Microchannel heat sink Flow disruption Microchannel design A review

a b s t r a c t This review article reports the influence of channel zone related geometrical parameters such as corrugated channel and flow disruption (FD) on the hydrothermal performance (HP) of microchannel heat sink (MCHS). Rapid increase in the power density accompanied by extreme miniaturization of electronic packages that demanded efficient cooling in MCHS is still to be explored. Despite several dedicated efforts for enhancing the heat transfer (HT) in MCHS an optimized technique is far from developed. The passive HT augmentation techniques for conventional channel also suffered from many limitations. In this context, corrugated channel appears as one of the prospective strategies due to the generation of Dean vortices (DVs) and chaotic advection (CA) in the bends. For efficient cooling, various channel shapes such as sinusoidal wavy, zigzag and convergent-divergent are introduced. The wavy MCHS with sinusoidal shape achieved high rate of HT with acceptable levels of PD compared with other shapes of zigzag and convergent-divergent MCHS. The other augmentation technique so called FD is established to be effective due to several interesting mechanisms including promotion of flow mixing, interruption of boundary layer, jetting, throttling and CA. Diverse FD methods such as grooves, cavities, ribs, hybridized ribs and grooves or cavities, offset-fin and interrupted wall channel are proposed. The hybrid techniques between ribs and either grooves or cavities have additional advantages than single technique in isolation. These features are manifested in increasing the HT area, induction of better fluid mixing and formation CA. The most important characteristic within flow disturbance techniques is found in interrupted-wall channel which manifested low PD. It is established to be the most desirable feature in MCHS applications due to its role in reducing the pump power and liquid leakage risk. We analyzed, discussed and made a comparative evaluation among various characteristics of geometrical parameters in each such technique to determine their impact on the HP of MCHS in terms of pressure drop (PD) and HT. Ó 2016 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corrugated channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Dean vortices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Chaotic advection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Corrugated MCHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Wavy MCHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Zigzag MCHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow disruption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Cavities in MCHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Ribs in MCHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22 23 23 24 25 25 28 29 30 34

Abbreviations: CA, chaotic advection; CC, corrugated channel; CD-MCHS, convergent-divergent microchannel heat sink; DVs, Dean vortices; FD, flow disruption; FF, friction factor; GMCHS, grooved microchannel heat sink; HP, hydrothermal performance; HTE, heat transfer enhancement; HT, heat transfer; MC, microchannel; MCHS, microchannel heat sink; PD, pressure drop; TR, thermal resistance; ZMCHS, zigzag microchannel heat sink. ⇑ Corresponding author. E-mail address: [email protected] (N.A.C. Sidik). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.031 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

22

4.

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

3.3. Effect of ribs and grooves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Offset strip fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Interrupted-wall channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Lately, rapid growth in the electronic industry has witnessed ultra-large-scale-integrated-circuit (ULSIC) as new generation high performing dense chip packages. However, such miniaturization causes the production of highly concentrated heat flux. This heat flux that raises the substrate temperature and creates hot spots is detrimental for the devices unless overcome. Any failure of removing such a high heat flux accelerates the meantime to failure (MTTF) and shortens the life span of electronic devices or even permanent damage [1]. Thus, appropriate thermal management of microelectronics is prerequisite to surmount the heat flux related damages. This is considered to be the major obstacle towards further development of integrated electronic technologies. According to the international technology roadmap for semiconductors (ITRS), the peak power consumption of high- and lowperformance integrated chips is expected to increase by 96% (147–288 W) and 95% (91–158 W) in 2016, respectively. The estimated amount of heat that need to be removed from the new 14 nm chip is higher than 100 W/cm2 [2]. Earlier, air-cooling method is extensively used for heat removal from integrated circuits due to its several attractive features such as low initial cost, high reliability, low operating maintenance cost, and high compatibility with micro-electronic environment [3]. However, with the rapid increase in power density and miniaturization of electronic packages this method became limited to satisfy the cooling demands. Use of various liquids as an alternative to air is proposed due to their high specific heat capacity and HT coefficient. Several micro cooling methods are developed including micro-jet impingement, micro-heat pipe, micro-electrohydrodynamic and MCHS. Among different micro-cooling methods the MCHS is appeared to be most prospective, which can remove heat at very high rate up to 790 W/cm2 [4]. The central concept of MC is relying on its ability to provide the large HT surface-tovolume ratio. MCs are used for two types of cooling such as single-phase and two-phase. Single-phase being easy for implementation is often used to remove intermediate heat fluxes. Although the two-phase can remove higher heat flux but it involves complex issues such as condensation, critical heat flux, saturation temperature, nucleation site activation etc. [5]. The flow in conventional straight MCHS is predominantly within laminar flow regime because of the tiny size of the channels, which does not allow the flow to transit to the turbulent regime. Besides, in the conventional straight MCHS the accumulation of hotter fluid at the channel wall and cooler fluid along the channel core due to continuous growth of thermal boundary layer degrades the HT in MCHS. Most of the early studies tried to improve the thermal performance of conventional straight rectangular MCHS by manipulating channel aspect ratio, channel length and wall thickness [6–9]. Some researchers manipulated the cross-section shape of MC (e.g. circular, triangular, and trapezoidal) [10–15] for the performance enhancement. Alfaryjat et al. [16] studied numerically the influence of geometrical parameters on the thermal performance of MC, where three cross-section channel shapes including hexagonal, circular and rhombus are considered. Hexagonal cross-section revealed the highest PD and HT coefficient. Channel with rhombus cross-section exhibited highest value of friction factor (FF) and thermal resistance (TR). Gunnasegaran

34 37 37 40 43

et al. [17] examined the effect of varying cross-sectional shapes (rectangular, trapezoidal and triangle) on the HP performance of MCHS. Rectangular shape channel displayed maximum HT augmentation followed by trapezoidal and triangular MCHS. Despite the implementation of complex cross-sectional shapes, a precise geometry for disrupting the thermal boundary layer beyond the entrance region and subsequent achievement of enhanced HP is yet to be developed. An optimized strategy is needed to overcome the continuous heat generation due to excessive power consumption by high-performing integrated chips. Researchers took the advantages of heat transfer augmentation methods of conventional channels and applied them in MCHS. Tao et al. [18] suggested three strategies for the single-phase HT enhancement (HTE) such as reduction of the thermal boundary layer thickness, increase of both flow disruptions and velocity gradient near the heated surface. To promote HT in MCHS, Steinke and Kandlikar [19] and Kandlikar and Grande [3] developed several techniques such as increase of surface area and HT coefficient using interrupted and staggered strip-fin design, increase of local HT coefficient by breaking boundary layer through periodic construction, incorporation of grooves and ridges, and incorporation of mixing features to improve the mixing flow. Numerous studies have attempted to review different techniques which aimed to enhance heat transfer in MCHS. Steinke and Kandlikar [19] have reviewed the applicability of passive and active heat transfer enhancement techniques in minichannels and microchannels. They also conducted a comprehensive evaluation and discuss the possibility of applying these techniques with novel applications in MCHS. These techniques include; flow disruption, channel curvature, re-entrant obstructions, secondary flows, out of plane mixing, fluid additives, surface roughness and surface treatment. Tullius et al. [20] reviewed different techniques used in efforts to modify MCHS in both single- and two-phase laminar flow. Some surface modifications discussed include adding micro-fins, adding grooves, increasing surface roughness, etc. They also focused on characteristics of using Carbon nanotubes (CNT) in the structure of MCHS to improve thermal performance due to the high thermal conductivity. Adham et al. [21] performed a comprehensive review of available studies regarding non-circular MCHS, with emphasis on rectangular MC. The review demonstrated the methodologies used to analyse and optimize the overall performance of MC systems with channel geometries, flow conditions, the coolants used, structural materials and optimization tools. Recently, Dewan et al. [22] conducted a comprehensive review of flow disruption in microchannel. They demonstrated the recent researches of using FD techniques in microchannel. Considering the rapid development, gamut research excitement and recent progress on geometrical parameters assisted enhanced HT in MCHS we provide a comprehensive review on various issues related to the role of channel zone parameters on the HP of MCHS. A special consideration has been focused on the effects of geometrical parameters and its role on the flow behaviour and heat transfer in MCHS. These effects specify the performance of proposed design MCHS based on two desired features in MCHS applications; highest rate of heat transfer at lowest pressure drop across the MCHS. This paper is organized as follows. Section 2 describes the characteristics for significant flow mixing enhancement in corrugated channel. This relates two flow mechanisms such as Dean

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Vortices and chaotic advection. An evaluation is made to determine the impact of these mechanisms on HP for various types of corrugated MCHS with varying geometrical parameters. Section 3 highlights the flow disruptions techniques for conventional channels. Various types of flow disruptions that are used in MCHS such as grooves, ribs, hybrid technique, offset strip fins and interruptedwall channel are explained. Section 4 concludes the paper. 2. Corrugated channel Certainly, corrugated channels are one of the important applications in the field of passive heat transfer augmentation methods. Using this technique a significant enhancement in the flow mixing between hotter fluid layers near channel wall and cooler fluid layers in core region is demonstrated. Induction of high flow mixing is attributed to the mechanisms of DVs and CA. It is customary to understand in details these mechanisms. 2.1. Dean vortices The fluid flow through curved trajectory inside curved channel generates centrifugal force. Consequently, the pressure becomes maximum at the outer wall and minimum at the inner wall. To balance such centrifugal force, a pressure gradient is required across the channel. This pressure gradient is manifested as a secondary flow in the form of counter-rotating roll cells pair known as Dean roll-cells [23] as depicted in Fig. 1. Dean [24,25] first made a theoretical prediction of secondary flow caused by centrifugal force,

23

where a perturbation analysis was conducted for flow in a channel with large curvature ratio (R/a). The analysis showed that the friction loss is a function of a new parameter named Dean Number p (DN = Re a/R). At higher DN, the two-cell flow become unstable due to the imbalance between the inward pressure gradient and the outward centrifugal force [23]. This instability generates another pair of counter-rotating vortices called DVs [26] as illustrated in Fig. 2 which appear close to the outer concave wall of the tube or outer wall of the channel. Various numerical studies [23,26,27] are performed to analyse the behaviour of DVs in curved duct and pipe by tracing these vortices as a function of altering DNs. It is established that DVs are transformed from two- to four- cell pattern at specific DN called critical DN (DNc). Sugiyama et al. [27] confirmed the occurrence of secondary flow pattern in curved rectangular channel using flow visualization. Experiment is carried out using the aspect ratio (AR) ranged between 0.5–2.5, curvature ratio (CR) varied from 5 to 8 and width of 20 mm. Results displayed the emergence of additional pairs of vortices near the outer concave wall, where the value of DNc is increased with decreasing aspect ratio as shown in Fig. 3. Kalb and Seader [28] examined the fully developed viscous flow in curved circular tubes and quantified the effect of DVs on the pressure loss and HT. Fully developed viscous flow and HT in curved semi-circular sector is studied numerically by Masliah and Nandakumar [29]. The enhancement factor (the ratio of Nusselt number to the FF) of curved semi-circular to the straight

Fig. 1. (a) Schematic diagram of curved rectangular channel describing the effect of centrifugal force for the formation of Dean roll-cells, and (b) velocity streamlines of Dean roll-cells [23].

Fig. 2. Schematic diagram describing the formation of Dean Vortices in circular cross-section (a) when DN < DNc, forming of pair of counter-rotating roll cells known as Dean roll-cells (b) when DN > DNc, another pair of counter-rotating vortices called DVs [26].

24

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 3. Flow visualization of curved rectangular channel with different aspect ratio describing the Dean roll-cells and DVs for: (a) AR = 0.5 and DN = 203 (b) AR = 1 and DN = 183 (c) AR = 2.5 and DN = 174 [27].

semi-circular ducts is found to be greater than unity, which is increased with the increase of both DN and Prandtl number. For curved rectangular channel, Cheng and Akiyama [30] achieved an enhancement in Nusselt number ratio up to 2 and FF ratio up to 1.8. Fletcher and co-authors [31–35] inspected a fully developed laminar flow and HT in periodic corrugated channels with different cross-section shapes, where DVs are emerged when the liquid coolant is flown through the bends. Furthermore, these vortices revealed significant effect on HT enhancement as compared to straight channel, in which the PD penalty is discerned to be much smaller than HTE. Manglik et al. [36,37] investigated numerically the laminar forced convection of air in wavy plate-fin channel in both 2D and 3D. Simulation results in 2D showed the presence of flow recirculation with lateral swirl in trough regions of the wavy channel. Conversely, the 3D results revealed symmetric pairs of DVs in the cross sections of the sinusoidal channel. In both cases, a great enhancement in the HT performance with high PD penalty is accomplished. 2.2. Chaotic advection The CA is another significant mechanism responsible for enhanced mixing and HT in tortuous passages [38,39] of MC. According to the theory of dynamical system, chaotic particle movement in the velocity field can emerge both in 2D with time-

dependence and in 3D without or with time-dependence. The enhanced mixing that is accompanied by the CA is a consequence of the rapid distortion and elongation of material interfaces [40], which also widens the effective diffusion domain. Aref [41] demonstrated this phenomenon by developing a model called blinking vortex, where a numerical study is carried out to study the flow in cylindrical tank with two agitators moving continuously or alternately. Simulation results indeed revealed a chaotic flow when the agitators underwent an alternate movement periodically. Peerhossaini and co-authors [26,38,42] performed a series of experiments with two configurations of curved pipe in heat exchanger. The first one (helical) generated a regular Dean flow inside the helical heat exchanger as illustrated in Fig. 4. The second configuration (chaotic) is designed for generating CA where each bend is rotated by 90o with respect to the neighbouring one as depicted in Fig. 5. The heat exchanger in the second configuration achieved 15–18% higher efficiency than the first one as shown in Fig. 6. Fletcher et al. [39] scrutinized the effect of CA on the flow and HT in zigzag channels having semi-circular cross-section. The Reynolds number (50–320) and Prandtl number (0.7–20) is varied for the laminar flow under consideration. The CA is found to occur for Reynolds number above 200. The emergence of CA led to the loss of periodicity of flow patterns which in turn altered the Nusselt number and FF.

Fig. 4. (a) Helical heat exchanger (b) regular Dean Flow in cross-section of helical heat exchanger Ref. [38].

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

25

Fig. 5. (a) Chaotic heat exchanger (b) schematic of bend which is rotated by 90° with respect to the neighbouring [38].

Fig. 6. Reynolds number dependent thermal performance factor for helical and chaotic configurations [38].

2.3. Corrugated MCHS The characteristics of flow passage in serpentine configuration are useful for microfluidic cooling applications including wavy, zigzag and convergent-divergent MCHS. The following sub-sections briefly explain their operational principles. 2.3.1. Wavy MCHS Sui et al. [5] examined numerically the laminar flow and HT in 3D wavy MCHS with rectangular cross-section. Using dynamic technique (Poincare section), the properties of fluid mixing is determined. The results revealed the emergence of a secondary flow (DVs) for liquid flow through wavy MCHS. Meanwhile, the quantity and the location of the vortices are found to alter along the flow direction, which created CA and enhanced the convective fluid mixing. Consequently, the HT performance of wavy MCHS is enhanced. The HT is increased with increasing waviness of the wall while the PD penalty appeared much smaller than heat transfer enhancement. To alter the relative wave amplitude along the flow direction, two novel designs are proposed. In the first design, waviness is increased along the flow direction. In second design, the waviness is locally increased at high heat flux region as shown in

Fig. 7. Interestingly, both the designs displayed high thermal performance with HTE factor ranged from 1.71 to 2.95 and the PD penalty factor ranged from 1.38 to 2. The flow and HT in sinusoidal MCHS with rectangular crosssections are experimentally investigated [43]. Each MC is consisted of ten wavy unit having depth of 404 lm, average width of 205 lm, wavy amplitudes (138 lm, 259 lm) and wavelength of 2.5 mm. Deionized water is used as a working fluid with varying Reynolds number (300 to 800). The Nusselt number of wavy MC is compared with straight MC having same cross section and footprint length. The HT performance of the wavy MCs is found to much better than that of straight one with increased HTE factor up to 211%. Furthermore, the PD penalty of wavy MCs is discerned to be much lower than the HTE with maximum increment in PD penalty factor up to 76%. Numerically simulation using particle tracking and Poincare sections verified the occurrence of CA which greatly enhanced the fluid mixing and HT. Meanwhile, the DVs that are appeared in the cross section of wavy MC displayed a significant variation in their patterns along the flow direction (Fig. 8). Sui et al. [44] examined the fully developed flow and HT in periodic wavy channel with rectangular cross-section, where the Reynolds numbers are spanned corresponding to steady laminar to transitional flow regimes. A symmetric secondary flow or DVs are observed to form when the liquid flow passed the bends. Further increase in the Reynolds number, led the flow to turn from steady state to periodic one with single frequency. In this stage, the flow is characterized by complex DVs with temporal and spatial evolution pattern along the flow direction. Nevertheless, the wavy MCHS achieved much superior HT than straight MCHS because of efficient mixing in wavy channel. Moreover, the PD penalty in wavy MCHS is determined to be much smaller than HTE. Mohammed et al. [45] investigated numerically the laminar forced convection in wavy MCHS with rectangular cross-section, where a wide range of wavy amplitude (125–500) with Reynolds number in the range of 100 to 1000 are covered. The heat sink is consisted of 25 wavy MC with hydraulic diameter of 339 lm and total length of 10 mm. The HP of wavy MC is found to enhance with increasing wavy amplitude except for 500 lm. Besides, the PD and FF are increased proportionally with the increase of wavy amplitude. Xie et al. [46,47] conducted a comparative study on HP for straight rectangular MCHS (SRC) with two kinds such as transverse wavy MCHS (TWC) and longitudinal wavy MCHS (LWC) as illustrated in Fig. 9b and c respectively. Numerical simulation is performed for laminar flow and HT with Reynolds number ranged from 100 to 230, hydraulic diameter of 160 lm and AR of 4:1. The TWC (with amplitudes TWC1 = 200 lm and TWC2 = 237.5 lm) is established superior for reducing the PD than SRC and LWC (with

26

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 7. The waviness dependent variation of temperature distribution and local Nusselt number along the MC for: (a) increased waviness along the flow direction (b) locally increased waviness in the middle of [5].

Fig. 8. (a) Poincare sections obtained from particle tracking, and (b) DVs at section 5L for wavy channel with A = 259 lm at Re = 600 [43].

amplitudes LWC1 = 25 lm and LWC2 = 30 lm). The overall evaluation of thermal resistance (TR) and PD for these three types of MCHS’s revealed that transverse wavy MCHS produced the lowest PD for the same range of TR as shown in Fig. 9a. This authenticates the superiority of transverse wavy MCHS over other types.

Abed et al. [48] examined the HT and fluid flow in wavy MCHS with square cross-section by covering a broad range of DN from 0.07 to 106.5 for two values of Prandtl number (137 and 1038). A mixture of glycerine-water is used as working fluid with varying ratios (30:70 and 10:90 in wt%) to achieve the desired Prandtl

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

27

Fig. 9. (a) Comparison of PD versus TR for; two type of transverse MCHS(TW1, TW2), two types of longitudinal MCHS(LW1, LW2) and straight rectangular MCHS, (b) generic structure of TMC (c) generic structure of LMC [46].

Fig. 10. Velocity vectors in: (a) serpentine wavy MCHS, (b) raccoon wavy MCHS [49].

numbers. The Nusselt number and FF are increased with increasing in DN due to the flow mixing enhancement. Furthermore, the thermal efficiency is increased, where Prandtl number of 137 and 1038 produced a ratio of 85% and 53%, respectively. Convergent-divergent MCHS (CD-MCHS) is another type of corrugated channels where the periodic constriction and expansion of cross-section area leads to flow acceleration and deceleration. Consequently, vortices and secondary flow arise at trough region due to the pressure gradient which significantly enhances flow mixing. Gong et al. [49] studied the 3D laminar fluid flow and HT characteristics in two types of wavy MCHS including serpentine wavy channels (SWCs) and raccoon wavy channels (RWCs) with rectangular cross-section having hydraulic diameter of 500 lm. The effects of wave amplitude, wavelength, and aspect ratio for different Reynolds numbers (50 and 150) on the HT performance are evaluated. For serpentine wavy MCHS, an increase in wave amplitude or decrease in wavelength is found to produce similar effect, where the maximum velocity got shifted from the centreline towards the trough and crest regions. This shift caused a reduction of thermal boundary layer thickness and enhanced the HT as illustrated in Fig. 10a. Furthermore, an increase in the aspect ratio is observed to reduce the boundary layers thickness. For raccoon wavy MCHS (Fig. 10b) an increase in wave amplitude and decrease in wave length led to the formation of vortices and secondary flow at furrows which in turn enhanced the HT. Meanwhile, large wave amplitude narrowed down the channels sections more and contributed to high PD. The performance factor of SWC is discerned to be superior over RWC due to the higher pressure losses. Yet,

the performance of wavy MCHS exceeded that of straight channel by up to 55%. The hydrothermal performance (HP) of CD-MCHS is numerically evaluated for fully developed flow under forced convection [2]. Effects of Reynolds number and expansion factor on the occurrence of CA are determined. The CA is found to occur at smaller expansion factor and higher Reynolds number. It indicated that a minor modification to channel geometry could create CA at high Reynolds number. The fluid flow driven improved HT performance is majorly attributed to three mechanisms. First, the HT for smaller values of waviness is increased with Reynolds number due to the increment in HT area. Second, further increase in waviness led to the creation of two counter rotating vortices in the trough region which in turn reduced the HT. Last, the mutation of flow advection towards chaos may increase the HT. These three mechanisms led to the fluctuations in Nusselt number as demonstrated Fig. 11. The performance factor showed a highest value at low waviness as illustrates in Fig. 11c. The effect of flow mixing on heat transfer enhancement (HTE) of CD-MCHS is numerically examined [50] for fully developed flow having varying Reynolds numbers (50–200). Besides, flow visualization is made using laser on enlarged transparent Perspex model. Two types of CD-MCHS such as sinusoidal and constant curvature profiles are tested. Both configurations showed similar flow pattern with the formation of a couple of symmetrical re-circulating vortices at the channel furrows which is further enlarged with increasing amplitude ratio. These vortices enhanced the flow mixing between cold fluid near central core region and hot fluid near

28

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 11. (a) Geometrical parameters of CD-MCHS S (aspect-ratio), k (waviness) and c (expansion factor) (b) wavelength dependent variation of Nusselt number for different aspect ratio (0.5–2) at Reynolds number of 600 (c) wavelength dependent variation of performance factor for different aspect ratio (0.5–2) at Reynolds number of 600 [2].

Fig. 12. Streamline plots at the upper furrow of the channel for: (a) sinusoidal CD-MCHS, and (b) constant curvature CD-MCHS at different amplitude ratios (A/L) with Re = 100 [50].

the wall. Consequently, the HT is enhanced. Larger width is found to inhibit the formation of vortices at channel furrows, while the smaller width led to the domination of vortices on flow stream. Thus, the incoming mainstream fluid flow is retarded. The optimum values of aspect ratio are found to be 0.5 and 1 under their conditions considered. Moreover, the HT is enhanced with the increase of amplitude ratio. Conversely, increasing in amplitude ratio restricted both the inlet and outlet zone. Thus, the occurrence of a significant pressure loss deteriorated the overall thermal performance of MCHS. The recirculation of vortices in the sinusoidal channel is determined to be more uniform and covered the entire furrow region than the constant curvature channel. Thus, sinusoidal CD-MCHS achieved superior HP than constant curvature one as illustrated in Figs. 12 and 13.

2.3.2. Zigzag MCHS Mohammed et al. [51] studied the effect of channels shape on the HP of MCHS. Three different shapes (same cross-section) of MCHS such as zigzag, wavy and step are considered. The performance of zigzag MCHS (ZMCHS) is compared with that of straight and wavy one. The thermal performance of ZMCHS is found to be the best with regard to temperature and HT coefficient. Furthermore, ZMCHS revealed the highest PD followed by a wavy, curvy and step types. Zheng et al. [39] examined the flow and HT characteristics of ZMCHS with semi-circular cross-section at steady conditions within a laminar regime. Reynolds number is varied from 50 to 320 and the Prandtl number is ranged from 0.7 to 20. The channel consisted of ten repeating zigzag units with smoothing joint in the inlet and outlet. Numerical results revealed

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 13. Performance factor for sinusoidal and constant curvature CD-MCHS for different amplitude ratios with Re = 50, 100, 150, and 200 [50].

the appearance of CA for Reynolds number above 200 with geometric parameter values of Rc/d = 0.51 (ratio of the radius of the curvature to the channel diameter), Lz/d = 1.75 (ratio of half unit length to channel diameter) and H = 45° (bend angle). The periodicity of flow pattern is disappeared in the chaotic regime. Besides, the PD and HT coefficient displayed fluctuations. The Nusselt number is observed to be proportional to Prandtl number of one-third exponent (Pr1/3). The effects of these three geometrical parameters on HTE and PD penalty are inspected. A decrease in the value of Lz/d is observed to increase the fluctuation in the HTE factor, implying the emergence of chaotic flow pattern (Fig. 14). Moreover, the PD is increased with decreasing value of Lz/d. The parameter Rc/d represented the degree of the sharpness in the bends. A decreasing value of Rc/d increased both HT and PD (Fig. 15). A variation of bend angle from 5 to 40° noticeably affected the HTE and PD at different Reynolds numbers. Both HT and the PD are increased with increasing bend angle as depicted in Fig. 16. Dai et al. [52] performed an experiment on a zigzag with semicircular cross-section ZMCHS having diameter of 2 mm using high-speed micro-PIV technique and measured the flow velocity for different Reynolds numbers (50–900). The effect of inlet unsteadiness on the flow features is examined. The flow transition from steady to unsteady state that occurred at critical Reynolds

29

number of 215 is found lower than the predicted value. Results revealed that the early transition is due to the flow disturbances at the inlet. Besides, the CA is observed to be very sensitive to inescapable fluctuations in the flow rate at the inlet. In another experimental study [53], they determined the HT and hydrodynamic properties for zigzag and sinusoidal MCHS having the same cross section. The use of high-speed micro-PIV technique allowed them to track and identify the 3D complex vortical structures in wavy MCHS. Results affirmed that the occurrence of flow recirculation and secondary flow at the bends are responsible for HTE. This improvement in the heat transfer is attributed to the continuous disruption to thermal boundary layer. The ZMCHS (ea = 0.91– 0.99) owing to larger HT area outperformed the sinusoidal channel (ea = 0.81–0.89). According to Table 1, taking in consideration the fabrication complexity and flexibility in application, it can be conclude that longitudinal sinusoidal wavy MCHS showed a high HTE with moderate pressure drop is more suitable electronic cooling applications. Besides, it has an ability to treat the local hot spot by increasing locally the waviness at high heat flux region.

3. Flow disruption Flow disruption (FD) is one of the HT augmentation methods. It gets manifested due to the triggering of flow instabilities which is responsible for increased flow mixing and enhancement of HT. Turbulent flow is one of common example of FD that depends on the hydraulic instability to acquire higher flow mixing. However, in many applications, the flow is unable to reach critical Reynolds number because of low velocities or small hydraulic diameters. Thus, dedicated efforts are made to utilize the geometrical modifications to the side walls of channels for promoting the flow instabilities and improved mixing. One of the effective methods for achieving it is to set up periodic disturbance promoters such as grooves, ribs, communicating and fins along the flow direction. These disturbance promoters are established to be effective for triggering the self-sustained oscillations that excite flow instabilities. Extensive studies are conducted using various disturbance promoters in conventional channels to enhance the flow mixing. Amon et al. [54] examined the effect of self-sustained oscillatory flow on HT in communicating channels, which positively impacted the HT via enhanced flow mixing. The numerical simulation of

Fig. 14. Lz/d dependent variation of (a) HTE factor eNu and (b) PD penalty factor ef [39].

30

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 15. Rc/d dependent variation of (a) HTE factor eNu and (b) PD penalty factor ef [39].

Fig. 16. Bend angle (h) dependent variation of (a) HTE factor eNu

and

(b) PD penalty factor ef [39].

Table 1 A summary of relevant literature on the effect of wavy MCHS on the HT and PD. Type of wavy MCHS

Pressure drop

Heat transfer

Reynolds number

Relative amplitude

Longitudinal wavy MCHS Transverse wavy MCHS CD-MCHS Zigzag MCHS

Moderate Very low Moderate High

High Moderate Moderate Very high

Wide range (100–800) Wide range 100–800 Moderate Re < 600 Low Re < 400

Less than 0.25 High Low –

Ghaddar et al. [55,56] on HT and fluid flow in grooved channel revealed the occurrence of resonant oscillation of the selfsustained flow that led to enhance HT by a factor of two. Greiner et al. [57] and Wirtz et al. [58] examined the influence of vgrooved channel on HT and PD. It is found that both Nusselt number and PD are increased as compared to flat channel. Several other studies [59–65] also revealed the role of grooves in HTE depending on Reynolds number value. At low Reynolds number, the periodic interruption on the surface prevented the continuous growth of thermal boundary layer. However, above the critical Reynolds number, the interruption on the surface promoted flow oscillations that allowed forming dense vortices in the grooved region with varying intensity depending on the groove dimensions and its location along the channel. Tauscher [66] stud-

ied experimentally HT in heat exchanger channel with hemicylindrical segment attached on the wall in staggered arrangement. It employed holographic interferometry to visualize the temperature fields. The interferogram showed that upstream sides of the ribs encountered the highest HT and downstream faced the lowest HT as illustrated in Fig. 17. Similar trend of HT is also reported by Cernecky et al. [67] for profiled surface as depicted in Fig. 18. 3.1. Cavities in MCHS Xia et al. [68] studied numerically the fluid flow and HT in microchannel with aligned fan-shaped reentrant cavities. A detailed analysis is carried out to determined the flow mechanisms

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

31

Fig. 17. (a) Interferogram of temperature distribution in plate heat exchanger channel with hemi-cylindrical rips for different Reynolds number (500, 1500, 2500, and 5000) and (b) channel length dependent variation of local Nusselt number [66].

Fig. 18. (a) Holographic image of temperature distribution in grooved channel with profiled surface for various Reynolds number (462, 925, and 1619) and (b) local Nusselt number as a function of channel length [67].

Fig. 19. (a) Streamlines along the mid-plain of the working fluid height and (b) flow velocity along the middle of the working fluid height [68].

32

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 20. Geometrical parameters of fan-shaped reentrant cavities [68].

inside the cavities that contributes in enhanced fluid mixing. Two main mechanisms are identified that affect significantly towards improved flow mixing: (i) the throttling effect that appears when the flow enters to the cavity and, (ii) the jet effect that occurs when the flow exit from the cavity as illustrated in Fig. 19a and b. Besides, the structure of the arcuate cavity contributes to form the swirls because of the presence of pressure gradient towards the radial direction that produce further flow mixing. At high flow rates, cooperative effects of all these mechanisms are involved for enhancing the HT and FF. At low flow rates, it is observed that flow is slipped over the cavity walls and thereby reduced the FF. Consequently, it critically hindered the HT due to the reduction in viscosity and conductivity. Thus, structural parameters analysis is performed to choose the optimal condition that fulfilled the requirements of HP with higher HT and lower PD. The abovementioned study tuned two parameters including the length ratio (L1/L2) which specify the number of cavities along the channel and the width ratio of arcuate region (W2/W1) as in Fig. 20. The achieved optimal length ratio (L1/L2) is between 0.15 and 0.2 and the most favorable width ratio (W2/W1) ranged within 1.4–2.1. Chai et al. [69] studied numerically the hydrothermal characteristics of MCHS with offset fan-shaped reentrant cavities in sidewall. The flow mechanisms and thermal performance for this design are found to be similar to the previous study except the offset in the cavities. Besides the fan-shaped reentrant cavities, Xia et al. [70] performed numerical studies on HT and fluid flow in MCHS with reentrant triangular cavities. They determined the influences of

Fig. 21. The schematic of three configurations of the MCs Ref. [71].

geometrical parameters on HT and FF. An optimization procedure is adopted to find the optimal geometric parameters according to the four variables that are selected to represent the distance and geometry of reentrant triangular cavity. The presence of reentrant triangular cavity is found to increase the CA by the vortices which are generated in the vicinity of triangular zone. Subsequently, this CA significantly improved the convective fluid mixing. Besides, the periodic interruption and redevelopment of the thermal and hydraulic boundary layers contributed in the augmentation of HT. Optimized geometrical parameters together with the corresponding Reynolds numbers achieved the maximum HT and minimum PD with overall efficiency more than 1.4. For validating the previous numerical simulation results, Xia et al. [71] conducted an experimental and numerical investigation of on HTE of MCHS with periodic expansion-construction crosssections, considered three configurations such as fan-shaped reentrant cavities (FMCHS), triangular reentrant cavities (TMCHS) and rectangular straight microchannel heat sink (RMCHS) as shown in Fig. 21. The heat sink consisted of ten parallel MCs (constant cross sections) of 0.2 mm deep and 0.1 mm wide. The effects of entrance, conjugate HT, viscous heating are evaluated to determine the temperature dependent properties. The numerical results agreed well with the experimental one in terms of Nusselt number and FF. Moreover, the average Nusselt number for expansionconstriction cross-section with triangular shape is discerned to be about 1.8 times higher than that of straight MCHS (rectangular cross-section) as in Fig. 22a. The PD in periodic expansion construction is lower for Re < 300, but it increased rapidly for Reynolds number in the range of 300–750 (Fig. 22b). All the previous numerical simulations used single MCHS without considering the effect of inlet-outlet flow arrangement and inlet-outlet headers regarding with flow distribution. Xie et al. [72] considered the effects of three inlet and outlet flow arrangements (I, C and Z-type), as well as header shapes (triangular, trapezoidal and rectangular). Additionally, the effects of three configurations namely the conventional rectangular MCHS, MCHS with triangular reentrant cavities and MCHS with offset fanshaped reentrant cavities are examined. The simulation revealed that I-type of inlet-outlet flow arrangement produced best flow distribution than other configurations. Likewise, the rectangular header shape generated better flow uniformity than other shapes. The overall evaluation for MCHS performance showed that MCHS with cavities is thermally more efficient than simple MCHS with superiority of triangular cavities over fan-shaped cavities. This enhancement in HT is attributed to the throttling and jetting effects associated with increased in PD. Later, they studied the hydrothermal features of staggered corrugated microchannel heat sink (SCMCHS) [73]. The proposed design possessed a I-type flow arrangement with rectangular header shape. The performance of SCMCHS is evaluated by comparing with rectangular microchannel heat sink (RMCHS). The PD in the proposed design is found to be higher than RMCHS. This enhancement is due to sudden-expansion of the flow area that generated vortices in reentrant cavities. Moreover, these reentrant cavities are contributed in HTE. Various techniques such as interrupting the thermal boundary layer, enlarging the heat exchanging area, increase flow mixing and chaotic advection are adopted HT improvement. The thermal performance factor is increased up to 1.24 with a reduction in TR up to 18.99%. Abouali and Baghernezhad [74] inspected the HT and fluid flow in arc (A) and rectangular (R) types of grooved MCs. These grooved are created on the floor and sidewalls of the channel. They made a comprehensive evaluation of the HTE in these MCs and compared with simple straight MC. Such grooved surface is found to have remarkable effect on the HTE and more effective than flat surface for removing the heat. Furthermore, the arc grooved MC (AGMC)

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

33

Fig. 22. Comparison of the numerical predictions and experimental data in conventional rectangular MCHS (R), MCHS with triangular reentrant cavities (T) and MCHS with fan shape reentrant cavities (F) for (a) average Nusselt number as a function of Reynolds Nu and (c) fappRe [71].

outperformed the rectangular one in terms of HT and FF. For AGMC, the increase in heat removal is about 72% and FF is 42%. Conversely, for RGMC, the increase inheat removal is 61% and FF is 25%. Additionally, the grooved MCHS (GMHS) proved their superiority over simple MCHS of minimum fin thickness. The results revealed that coefficient of performance (COP) for rectangular and arc types of GMCHS exceeded by 4.4% and 14%, respectively than that of simple MCHS. Recent researches are mostly focused on MCHS with grooves that are created on the side wall rather than that on floor due to ease fabrication. Ansari et al. [75] studied numerically the HT and fluid flow in MCHS with arched grooves organized in staggered arrangements. They determined the optimal groove shape for achieving lowest TR at minimum pump power. Multi-objective evolutionary algorithm is used with four design variables including groove pitch to channel height, groove diameter to pitch, channel width to channel height and groove depth to channel height. Pump power and TR are selected as objective functions. The GMCHS revealed much higher improvement in the thermal performance over smooth one in terms of Nusselt number and TR however at the expense of pumping power. Meanwhile, the observed reduction in the TR is ascribed to be linked with the increase of pump power. To understand the effect of other groove shapes, Kuppusamy et al. [76] studied numerically the HT and fluid flow in trapezoidal grooved microchannel heat sink (trapezoidal GMCHS) to determine the impact of geometrical parameters such as width and pitch on its HP. An enhancement in HT is achieved for minimum width is

shortened and maximum width is elongated to be closer to triangular shape. This manipulation in geometry forced the flow to deviate towards the grooved zone and led to increased flow mixing. Besides, an increase in the pitch led to an enhancement of the thermal performance. This enhancement is attributed to the reduction in PD that originated from the slipping of flow in grooves. They also examined [77] the effect of triangular GMCHS on the HP of MCHS. Three geometrical parameters (angle, depth and pitch) are considered. An enhancement in HT with the increaser of both of depth and angle is evidenced. Further flow analysis revealed that the increment in the angle and the depth led to the enlargement of the groove zone which created larger vortices and allowed improved the mixing. Nevertheless, the pitch size displayed insignificant effect on the flow pattern inside the grooves but considerably affected the number of grooves and the occurence of interruptions in the boundary layers. Ahmed et al. [78] performed an overall evaluation on three grooves geometries (triangular, trapezoidal and rectangular) to identify the optimal geometrical parameters of depth, tip length, and pitch. Besides, a new geometrical parameter called orientation ratio (r/Lg) is used, which manipulated the grooves arrangement from symmetrical (at ratio = 0) to asymmetrical arrangement (at ratio > 1) as displayed in Fig. 23. They explored the impact of geometrical parameters (depth, tip length, pitch and orientation ratio) on the performance of MCHS. It is acknowledged that trapezoidal GMCHS with specific topology can give best thermal performance at lower Reynolds number (Re = 100). This observation is

Fig. 23. Geometrical parameters of the trapezoidal GMCHS. [78].

34

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

attributed to the occurrence of high flow recirculation inside the groove at low velocity. Furthermore, thesymmetrical grooves revealed better thermal performance than asymmetrical one due to simultaneous flow expansion on both sides of the channel. This expansion generated eddies rotating in reverse direction, caused high mixing flow that carried more heat from heated walls. The highest improvement of the Nusselt number with lowest improvement in the FF is discerned to be 51.59% of 2.35%, respectively. 3.2. Ribs in MCHS Ribs are considered as another effective method in flow disruption techniques due to their ability to interrupt and redevelop thermal boundary layers and increased mixing through induced vortices. However, these configurations are accompanied with undesirable effect such as high pressure drop. Thus, the geometry of ribs such as height, pitch, width and arrangement need to be optimized for minimizing the PD with maximum HT. Chai et al. [79] studied numerically the HT and fluid flow in MCHS with fan-shaped ribs on sidewalls. They determined the proposed design dependent HT properties, PD and entropy generation. The impacts of geometrical parameters (width, height and spacing) on the HP of MCHS for two types of aligned and offset types of ribs arrangement are examined. The spacing and height of the ribs are found to have notable effect on the HT. The width showed insignificant effect on HT. These MC with aligned ribs arrangement of lower height and larger spacing revealed better HT coefficient than offset type. The fan-shaped ribs showed the ability for preventing the continuous increase of substrate temperature along the flow direction and kept the local Nusselt number at higher level. These ribs interrupted and redeveloped the boundary layer as well as induced flow recirculation that enhanced the flow mixing. Compared to smooth MCHS, the average Nusselt number in MCHS with aligned fan shaped ribs is increased by 6%–101%. Moreover, the TR is reduced by 3%–40%. The MCHS with offset fan-shaped ribs displayed an increase in the Nusselt number by 4%–103% and reduction in TR by 2%–42% [79]. In another report, Chai et al. [80] presented the effect of abovementioned geometrical parameters on the PD and FF of MCHS. An increase in rib width is observed to enhance the FF ratio (the ratio of FF of proposed design to the FF of smooth channel). Conversely, increasing ribs height and spacing led to significant enhancement in the FF. For Reynolds number in the range of 187 to 715, the FF of MCHS with aligned fan-shaped ribs revealed an increase by a factor of 1.1–8.28 times more than smooth MCHS, while the FF of MCHS with offset ribs is increased by a factor of 1.22–6.27 times only. The HT and FF mediated entropy generation is extensively investigated in the previous design [81]. Increase in the ribs height in the offset arrangement of proposed design led to enhance the thermal performance much higher than the aligned one. Further decrease in the rib spacing first increased the overall performance and then gradually deteriorated. It is asserted that an increase in the height of ribs could reduce the entropy generation due to HTE. Meanwhile, an increase in the rib height could increase the FF and therefore increase the entropy generation. For lower Reynolds number, the observed decrease in the entropy generation is attributed to the dominance of HTE over the FF which in turn improved the overall performance. For higher Reynolds number, the observed increase in entropy generation is ascribed to the increased FF that overdominated the HTE thereby reduced the overall performance. In their numerical study on the hydrothermal characteristics of MCHS with offset ribs on sidewalls, Chai et al. [82] proposed various shapes including rectangular, forward triangular (FT), backward triangular (BT), isosceles triangular (IT), and semicircular (SC). It is asserted that the existence of ribs on the sidewalls pro-

duced significant impacts on the flow structure. This created secondary flow and vortices as well as contributed to the boundary layer interruption. Additionally, it is demonstrated that the occurrence of recirculation in the downstream of the ribs enhanced the flow mixing. The Nusselt number and PD are increased proportionally with Reynolds number for all types of ribs. The Nusselt number is increased from 1.42 to 1.95 and FF in increased by a factor 1.93– 4.57 times more than the smooth MCHS. Accordingly, the overall performance is increased by a factor of 1.02–1.48 times. For Reynolds number less than 350, MCHS with FT offset ribs showed highest performance and MCHS with rectangular offset ribs revealed the lowest one. Conversely, for Reynolds number more than 400, MCHS with SC ribs displayed highest performance while the MCHS with BT ribs exhibited the lowest one. 3.3. Effect of ribs and grooves The combination between ribs and grooves is another strategy to enhance the HP of MCHS. This strategy provide many advantages such as increase in the surface area of heat transfer, increase in the flow mixing due to intensive vortices and an increment in the static pressure within cavities or grooves for recovering a high pressure drop in the ribs zone. Xia et al. [83] conducted a numerical study on the hydrothermal characteristics of MCHS using fan-shaped reentrant cavities by installing the internal semicircular ribs in the straight part between the cavities. The effect of relative rib height (the ratio of rib height to hydraulic diameter) on HP of MCHS are analyzed within laminar flow regime. The presence of ribs is found to significantly affect the flow mechanism. The flow is accelerated in the ribs zone due to the convergence of crosssection, which led to form a negative pressure in the cavity zone and positive pressure at rib zone as depicted in Fig. 24. The consequences of this mechanism leads to periodic interruption of thermal and hydraulic boundary layers. Furthermore, the periodic pressure variation caused vortices formation, flow separation and reattachment. This increased the flow mixing and in turn enhanced the thermal performance. The local Nusselt number is increased at ribs zone due to strong flow disturbances and decreased besides cavities upstream side because of the formation of a vortex. This produced thicker thermal boundary layer. The results showed an increase in average Nusselt number about 1.3–3 times higher than the rectangular channel, where the FF is increased by a factor of 6.5 times. It is established that a moderate relative rib height of e/ Dh = 0.12 at Re = 592 achieved the optimum thermal enhancement by a factor of 1.6 as in Fig. 25a. Zhai and co-authors [84] examined three new shapes of ribs (rectangular, trapezoidal and triangular) in addition to the geometry of fan reentrant cavity with circular ribs. They followed a new criteria to evaluate the performances of MCHS. The first evaluation concept is based on the relation between HT mechanism and the angles between the streamlines and the isotherms as well as the synergetic relation among velocity vector, velocity and temperature gradient. To evaluate the overall performance in the convective HT process, three parameters are considered for the synergy evaluation including the angle between the velocity vector and the temperature gradient (b), the angle between the velocity vector and the velocity gradient (a) and a dimensionless factor called synergy number (Fc). The second evaluation concept is based on evaluation of irreversibility in HT process in MCHS, which is performed by calculating the enhancement entropy generation number (Ns) that represented the ratio of entropy generation rate in enhanced MCHS to entropy generation rate in reference MCHS. The deterioration of Ns to well below unity indicated the high performance of enhanced MCHS. Thus, the new design could reduce the irreversibility. The performance is evaluated using three indicators including thermal efficiency factor (g), synergy number and

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

35

Fig. 24. (a) Magnitude of flow velocity and (b) streamlines distribution along the central plain (z = 0.25 mm) between fan-shaped reentrant cavities MCHS (e/Dh = 0.1553) and rectangular MCHS at Re = 199.5 [83].

Fig. 25. (a) Variation of thermal enhancement factor with Reynolds number and (b) geometrical parameters of fan-shaped reentrant cavities MCHS [83].

entropy generation number (Fc) to the existence of two thermal performance patterns. For Re < 300, the MCHS with fan-shaped reentrant cavities and trapezoidal ribs revealed best performance. Conversely, the MCHS with fan-shaped reentrant cavities and circular ribs showed a best performance when Re > 300 as displayed in Fig. 26a. Following the previous scheme, Zhai et al. [85] examined numerically the thermal performance of six new configurations of ribs and grooves installed on the side-walls along the channel. These configurations include triangular-cavities with circular-rib (Tri.C-C.R), triangular-cavities with triangular-rib (Tri. C-Tri.R), triangular-cavities with trapezoidal-ribs (Tri.C–Tra.R), trapezoidal-cavities with circular-rib (Tra.C-C.R),trapezoidal-cav ities with triangular-rib (Tra.C-Tri.R) and trapezoidal-cavities with trapezoid-rib (Tra.C-Tra.R) as illustrated in Fig. 27. Each of the relative cavity height and relative rib height are changed to find the optimum design. The overall performance is enhanced compared to configurations of previous study [83]. Furthermore, it showed two trends according to Reynolds number. For 100 < Re < 300, the triangular cavity with trapezoidal ribs (Tri.C–Tra.R) revealed the best performance. For 300 < Re < 600, the triangular cavities and triangular ribs (Tri.C–Tri.R) showed the best performance as illustrated in Fig. 28. The entropy generation and exergy are also anal-

ysed to evaluate the irreversibility of the system. It is demonstrated that with increasing Reynolds number, the value of entropy generation caused by heat transfer irreversibility is decreased, while the entropy generation caused by flow friction increased. Simultaneously, it is found that the effect of relative rib height on entropy generation rate and transport efficient of thermal energy is more sensitive than relative cavity height. It is further emphasized that with decreasing net temperature gradient of fluid, the irreversibility is reduced and the utilization of thermal energy is enhances. They established a new correlations for Nusselt number and friction factor of the micro heat sink (Tri.C–Tri.R) that can predict the values with an accuracy of ±10%. In another numerical study, Xie et al. [86] evaluated the hydrothermal characteristics of MCHS with grooves and obstacles using six different configurations as illustrated in Fig. 29. It is shown that the geometric arrangement of grooves and obstacles have significant influence on the HP of MC. The highest HTE (26.19) is achieved for case 4 (Fig. 28d) due to its geometric arrangement like De Laval nozzle where the flow is accelerated in the upstream half of the obstacle and then decelerated in the cavity zone which triggered vortices, flow recirculation and separation. Besides, the pressure penalty ratio reached the highest value of 110.1. To evaluate the overall performance, a comparison among

36

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 26. Reynolds number dependent variation of (a) thermal efficiency g, (b) entropy generation number Ns, (c) synergy number Fc for four types of MCHS; fan-shaped reentrant cavities with circular ribs (F-C), fan-shaped reentrant cavities with trapezoidal ribs (F-Trp), fan-shaped reentrant cavities with rectangular ribs (F-R) and fan-shaped reentrant cavities with triangular ribs (F-Tri) [84].

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 27. Schematic diagram of cavities and ribs arrangement [85] (a) Tri.C-C.R, (b) Tri.C-Tri.R, (c) Tri.C–Tra.R, (d) Tra.C-C.R, (e) Tra.C- Tri.R and (f) Tra.C-Tra.R.

all configurations is carried out by considering both HTE and PD penalty. It is concluded that case 1 (Fig. 28a) produced the best energy saving due to the lowest pressure penalty. Wang et al. [87] investigated experimentally and numerically HT and fluid flow in new design of MCHS with ribs and grooves which consisted of two parts. The upper part contained the ribs and grooves whereas the lower part is composed of rectangular straight channels. The ribs and grooves are made of SU-8 and Si, respectively. It is demonstrated that the proposed design can enhance the HT compared with smooth MCHS. The existence of

Fig. 28. Reynolds number dependent variation of overall performance for cavity-rib arrangement MCHS [85].

ribs in periodic arrangement with grooves is utilized to interrupt the thermal boundary layer and reduce the flow area. This in turn forced the flow to create a large recirculation behind the ribs and in

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

37

Fig. 29. Streamlines and temperature contour at Re = 500 (a) groove on one surface, (b) obstacle on one surface and groove on opposite surface, (c) obstacle on one surface, (d) obstacles are arranged at opposite surface, (e) grooves and obstacles are staggered on both surfaces, and (f) grooves and obstacles are aligned on both surfaces. [86].

Fig. 30. The functionality of offset-fin strips which work to split the flow and deviate its direction to spread over the entire region [89].

the grooves. These recirculation flow significantly enhanced the flow mixing between cold water in the central core zone and hot water at the walls. Thus, the study focused on the relation between the ribs height and thermal performance of the MCHS. The Nusselt number and FF is increased with increasing relative rib height. For the relative rib height of 0.85, the Nusselt number is increased up to 1.55 times than that of smooth MCHS, whereas the FF is increased up to 4.09–7.04 times. Li et al. [88] adopted a new design where the rectangular ribs are arranged in the central portion of channel and a triangular cavities are on the side-walls (TC–RR). The study analyzed numerically the effect of relative rib width and relative cavity width on the performance of flow and HT. The new design is demonstrated to acquire a significant enhancement in HT. Such enhancement is majorly attributed to the several features of the proposed design. These features included increasing HT area, jetting and throttling, interruption and redevelopment to the hydraulic thermal boundary layer. Furthermore, the combination of ribs and grooves induced better fluid mixing and formed CA. The best achieved thermal enhancement factor is 1.619 at relative rib width of 0.3, relative cavity width of 2.24 and Reynolds number of 500.

which split the flow streams and deviated their direction to move around the fins [89]. This mechanism ensured the existence of flow within a developing flow region due to flow interruption. Additionally, this technique forced the flow streams to mix with each other and dissipate more heat from the heated walls. Kishimoto and Sasaki [90] first proposed the use of offset-strip fin instead of continuous wall fin to enhance HT. They studied numerically the HT in microchannel with diamond-shaped interrupted cooling fin structure of staggered arrangement. The proposed design is found to reduce the substrate temperature by 25% less than traditional straight MC. Kandlikar and Upadhye [91] asserted the capability of this design to dissipate heat fluxes up 3 MW/m2 with PD of 35 kPa using the split flow arrangement. Steinke and Kandlikar [89] also examined experimentally the heat HT and fluid flow in silicon MCHS with offset strip fins. Four designs are used with different geometrical parameters of flow passage width and fin thickness. The results showed a significant reduction in TR of the proposed design with a value of 0.001 °C m2/W compared with TR of traditional MCHS of 0.1 °C m2/W. Besides, the COP (coefficient of performance) for proposed design (290) demonstrated a great superiority over the traditional MCHS (11). Colgan et al. [92] investigated experimentally the hydrothermal characteristics of silicon MCHS with offset strip fins in staggered arrangement which exposed to high power density greater than 300 W/cm2. The results showed that performance of the proposed design with fin pitch of 75 lm or 100 lm is superior to traditional straight MCHS having PD less than 35 kPa. Hong and Cheng [93] studied numerically the HP of offset-strip fin MCHS. The effects of geometric parameters (the ratio of fin interval to fin length and fin number) are analyzed to identify the optimal dimensions that satisfy the highest thermal performance in lowest PD. The maximum substrate temperature is maintained at 332 K by changing the flow rate via geometrical parameters manipulation. It is shown that by increasing the number of fins to a certain value one can increase the frequent interruptions of the boundary layer in addition to the increase in flow disturbance which in result enhances HT as illustrated in Fig. 31. However, an additional increase in fins number caused an enhancement in PD due to increased flow resistance. The optimal value that fulfills the minimal PD is achieved when the fin length is equal to fin interval.

3.4. Offset strip fins 3.5. Interrupted-wall channel Offset strip fin is another type of FD techniques which are used in MCHS in order to enhance HT. The concept of functional performance of offset-fin strip as illustrated in Fig. 30, where the flow moved in short passages and then encountered the offsetting fins

It is established that the HT coefficient in the entrance region of the channel is significantly larger than the downstream locations. This is because the entrance region is distinguished by thin ther-

38

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 31. The distribution of (a) velocity, (b) vorticity and (c) temperature at the midplain in MCHS with offset strip fins [93].

mal boundary layers which continue to develop towards the downstream direction causing a deterioration in HT. Thus, the entrance region’s features inspired the researchers and designers to take its advantage for enhancing the HT in thermal applications. Sparrow

et al. [94] studied numerically the HT and fluid flow in the interrupted-wall channels for the heat exchanger applications. The study aimed to explore the extent of HTE in the interruptedwall channels compared with that of parallel channel. The results showed a considerably higher HT rates predominated in the interrupted-wall channel for a wide range of Reynolds number. This enhancement is remarkably observed in relatively short channels for high Reynolds number. For micro-cooling applications, many researchers used this feature to enhance HT in MCHS. Xu et al. [95] studied experimentally the hydrothermal characteristics of silicon MCHS which consisted of ten parallel triangular microchannels separated by five transverse trapezoidal microchannels to form five discrete zones. The effects of periodic interruption of flow on HTE are determined. The results revealed that the redevelopment of thermal boundary layer at the onset of each zone significantly improved HT. This proposed MCHS is able to reduce the temperature by 14 °C as compared to conventional one. Meanwhile, the PD encountered a considerable reduction due to shortening of the effective flow length. In another study Xu et al. [96] conducted a numerical simulation on the previous geometry as shown in Fig. 32a. The study aimed to analyze the factors influencing the flow and heat transfer in interrupted and conventional MCHS. The effect of interruption technique in MCHS has a similar effect of entrance region regarding to the local Nusselt number behaviour. Fig. 32b clearly shows a periodic rise in local Nusselt number at the beginning of each zone which attributed to the redeveloping in thermal boundary layer. In conventional MCHS, the continuous growth in thermal boundary layer leads to continuous deterioration in local Nusselt number along flow direction. In regard to PD, the results indicated the existence of two effects that influence on the PD across the

Fig. 32. (a) The geometry of interrupted MCHS (b) local Nusselt number versus non-dimensional flow length for rectangular MCHS and interrupted MCHS (c) pressure distribution along flow direction for rectangular MCHS and interrupted MCHS Ref. [96].

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

39

Fig. 33. Streamlines and velocity distribution for (a) interrupted microchannel with rib (b) interrupted microchannel without rib (c) straight channel [97].

interrupted channel. First, the pressure recovery that occured when the flow exit from the main stream to the transverse channel. Second, the increment in head loss when the flow entered the next zone. It is demonstrated that the first effect suppressed the second one which indicated that overall PD of the proposed design is equal or lower than the conventional channel as displayed in Fig. 31.c. The results also referred to the slower redevelopment of the thermal boundary layer than that of hydrodynamic boundary layer. Chai et al. [97] studied the HT and fluid flow in interrupted MCHS having rectangular ribs with transverse microchambers. Experiment is performed to validate the numerical analysis for specific dimensions. It covered a broad array of parameters such as rib width, rib length, the space between two adjoining trans-

verse microchambers and the distance from the parallel microchannels to the rib row. The results revealed that the interrupted MCHS with ribs is more suitable in operating condition of Reynolds number less than 600, where the HTE is dominant over friction losses. For Reynolds number higher than 600, the results showed that interrupted MCHS without ribs possessed higher performance than the new design. This observation of HTE is attributed majorly to three main effects such as flow separation, vortices, recirculation and boundary layer separation. These effects formed within the zones of upstream and downstream to the rib as presented in Fig. 33a. Lee et al. [98] proposed a new design of interrupted-wall channel in the form of oblique cuts which are made along the channels wall to create smaller branching secondary channels. Part of flow is

Fig. 34. Schematic of a louvered-fin array [100].

40

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Fig. 35. MCHS with oblique fins [98].

the conventional MCHS. Meanwhile, the TR has decreased about 18%. It is concluded that PD in oblique finned MC is approximately the same as conventional channel for Reynolds number less than 500. A slight increase in PD is occurred in the operating conditions for Reynolds number more than 500 due to the strong momentum flow in secondary channel. In another experimental study, Lee et al. [102] employed a silicon-based MCHS with a smaller channel dimension of (12.7 mm  0.115 mm  0.387 mm). Similar results are achieved on the HTE performance with lower pressure penalty. Lee et al. [103] conducted an experiment to examine the scaling effects on the thermal performance of oblique finned MC. For channel width of 500 lm, the HT is achieved with a negligible PD penalty for Reynolds number up to 400. Further increase in Reynolds number caused additional PD penalty however still lower than HTE. For channel width of 300 lm, the shortcoming in fabrication process led to form a burr/bend at the fin edge which caused in higher PD penalty. Recently, Lee et al. [1] extensively studied the HP of silicon MCHS with oblique fins. The effect of two critical geometrical parameter such as the angle of oblique channel (15, 27, and 45°), oblique fin pitch (0.4, 80, 1.5) with two values of hydraulic diameter (0.1, 0.2) mm on the HP of such MC are examined. The smaller oblique angle is found to produce larger secondary flow with minimum flow resistance. However, the smaller pitch value created higher thermal boundary layer re-development in addition to more secondary flow generation which means further HTE. Kuppusamy et al. [104] proposed a new design exploiting the concept of secondary flow through slanted passages that formed in the channel wall between adjacent channels in alternating orientation. These slanted channels enhanced HT through two mechanisms including interruption and redeveloping to thermal boundary layer and induced flow mixing between channels. The most significant feature of this configuration is the minor PD which attained as much as 6%, while the overall thermal performance factor attained 146% and TR reduced to 76.8% compared with straight channel. Table 2 enlists a summary of relevant literature that used art of the technique to evaluate the influence of various channel zone parameters on the HP of MCHS.

Fig. 36. Comparison of PD in MCHS having oblique fin with conventional MC [98].

4. Conclusion

passed through secondary channels to the adjoining main channel for promoting the flow mixing as shown in Fig. 35. In order to provide a good balance between heat transfer and pressure drop, the proposed design of interrupted channel followed the recommendation of Suga and Aoki [99] for louvered-fin heat exchangers that the ratio of fin pitch in the spanwise direction to the fin length must be 1.5 times the tangent of the oblique angle (Fig. 34). So, the angle of oblique channel is selected to be 27° which is within the range of louvered angles of 20°–40° as in shown Fig. 35. The results showed that the combination between entrance effect and secondary flow effect has led to considerable improvement in thermal performance. Furthermore, the proposed design could reduce the TR about 19% lower than regular straight channel. Meanwhile, the local Nusselt numbers along the channel is higher almost by 80% from that of conventional channel. The most significant feature in the proposed design is the negligible pressure penalty because the pressure loss due to flow injection from oblique channel to adjacent channel is recovered with a branched flow from main channel as illustrated in Fig. 36. Later, Lee et al. [101] validated experimentally the previous proposed design using copper MCHS. The experimental results have agreed with the previous numerical study where the average Nusselt number is increased about 80% (from 8.6 to 15.8) over

Present article comprehensively overviews several leading literatures concerning the effects of geometrical parameters related to the channel zone on the HT performance of MCHS. These parameters constitute two significant heat enhancement techniques including CCs and FDs. With regards to CC technique, the superior HT performance of wavy channel with sinusoidal shape in acceptable levels of PD is emphasized. Although HT is superior in the zigzag channel but it is associated with high PD. Meanwhile, the convergent-divergent channel revealed moderate HTE at low Reynolds number. With regards to FDs technique, it is found that channel with re-entrant cavities produce fair HTE in the range of moderate to high Reynolds number. At low Reynolds number, flow is slipping over the cavity walls reduces the FF, but seriously hinder HT due to lowering viscosity and conduction level. The presence of grooves shows considerable enhancement in HT due to their ability to increase mixing of flow through induced flow recirculation. It is asserted that the HP of MCHS can be further enhanced with optimization process to the geometry of the groove. With regards to ribs configuration, it is found that ribs have the ability to interrupt thermal boundary layer and creating of secondary flow and vortices which significantly enhance HT. However, this enhancement is accompanied with high FF. Thus, there is a need to choose the appropriate shape and dimensions of ribs with specific range of flow velocities. The hybrid techniques between

Table 2 A summary of relevant literature on the effect of channel zone parameters on the HP of MCHS. Type of study

HTE factor

PD

Wavy-sinusoidal MCHS [5] Wavy-sinusoidal MCHS [43] Wavy MCHS [44]

Numerical Experimental Numerical

Wavy-sinusoidal MCHS [45]

Numerical

1.71–2.95 211% Re = 66.67, 40.5% Re = 166.7, 248.8% Superiority of wavy MCHS over straight MCHS for relative amplitude range between 0.0625 and 0.21875

1.38–2 76% Re = 66.67, 11.2% Re = 166.7, 34.8% Pressure drop of wavy MCHS is higher than straight MCHS

Wavy-transversal MCHS [46,47]

Numerical

Wavy MCHS [48]

Numerical

Convergent-divergent MCHS [49] Convergent-divergent MCHS [2] Convergent-divergent MCHS [50] Zigzag, wavy and step MCHS [51] Zigzag MCHS [39]

Numerical Numerical Numerical Numerical Numerical

Zigzag MCHS [52]

Numerical

Zigzag MCHS[53]

Numerical

MCHS with aligned fan-shaped reentrant cavities [68]

Numerical

MCHS with offset fan-shaped reentrant cavities [69] MCHS with reentrant triangular cavities [70] (i) Fan-shaped reentrant cavities (F MCHS) (ii) Triangular reentrant cavities (TMCHS) (iii) Rectangular straight microchannel heat sink (RMCHS [71] (i) MCHS with triangular reentrant cavities (ii) MCHS with offset fan-shaped reentrant cavities (iii) Rectangular straight MCHS [72] Staggered corrugated microchannel heat sink (CMCHS) [73] (i) Arc GMCHS (ii) Rectangular GMCHS [74] MCHS with arched grooves in staggered arrangements [75] Trapezoidal GMCHS [76] Triangular GMCHS [77] (i) Triangular GMCHS (ii) Trapezoidal GMCHS (iii) Rectangular GMCHS [78] (i) Aligned fan-shaped ribs (ii) Offset fan-shaped ribs [79], [80] MCHS with offset ribs: (i) Rectangular (ii) Forward triangular (iii) Backward triangular (iv) Isosceles Triangular (v) Semicircular [82] MCHS with Fan-shaped reentrant cavities and internal ribs circular ribs F-C [83]

Numerical Numerical Experimental

Pr = 137, 85% Pr = 1038, 53% Re P 50, 55% 20% 50% Zigzag MCHS is superior over step and wavy MCHS (i) HT is increased with decreasing value of Lz/d (ii) HT is increased with decreasing value of Rc/d (iii) HT is increased with increasing value of bend angle

Zigzag channels provide significant heat transfer intensification with much higher surface area utilisation (ea = 0.91–0.99) than sinusoidal channels (ea = 0.81–0.89) Optimum HT enhancement with length ratio L1/L2 between 0.15 and 0.2 and width ratio between 1.4 and 2.1 The HTE is highly dependent on Reynolds number value Overall efficiency more than 1.4 TMCHS is the best with heat enhancement about 1.8 time than RMCHS

Transverse wavy MCHS produced the lowest PD than longitudinal wavy MCHS and straight MCHS Pr = 137, 39% Pr = 137, 2% PD is higher than straight MCHS PD is higher than straight MCHS PD is higher than straight MCHS PD in zigzag MCHS is higher than step and wavy MCHS (i) PD is increased with decreasing value of Lz/d (ii) PD is increased with decreasing value of Rc/d (iii) PD is increased with increasing value of bend angle The flow transition from steady to unsteady flow occurs at a relatively low Reynolds number (Rec = 215) PD in zigzag MCHS is larger than sinusoidal MCHS

Optimum PD with length ratio L1/L2 between 0.15 and 0.2 and width ratio between 1.4 and 2.1 PD is higher than straight MCHS PD is higher than straight MCHS

Numerical

Triangular cavities configuration is the best compared with other configurations

PD is higher than straight MCHS

Numerical and Experimental Numerical

1.24 times more than straight MCHS

PD is higher than straight MCHS

(i) Arc GMCHS 72% (ii) Rectangular GMCHS 61% Grooved micro-channel exhibited a lower thermal resistance over a smooth micro-channel but at the expense of pumping power 91.42% 1.78 times higher than straight MCHS 51.59% more than straight MCHS

(i) Arc GMCHS 42% (ii) Rectangular GMCHS 25% PD is higher than straight MCHS

Numerical Numerical Numerical Numerical

Numerical Numerical

Numerical

1–6%–101% 4–103% (i) Re < 350 forward triangular offset ribs showed a highest performance (ii) Re > 400 semicircular ribs showed highest performance (iii) Increase in Nusselt number (1.42)–(1.95)

1.3–3 times more than straight MCHS

PD is much lower than HT PD in triangular GMCHS is higher than straight MCHS 2.35% more than straight MCHS

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Ref.

(i) 1.1–8.28 times (ii) 1.22–6.27 times (1.93–4.57) times more 1.93–4.57 times higher higher than straight MCHS

6.5 times more than straight MCHS (continued on next page) 41

42

Table 2 (continued) Ref.

Type of study

HTE factor

PD

MCHS with fan-shaped reentrant cavities and: (i) Rectangular ribs F-R (ii) Trapezoidal ribs F-Trp (iii) Triangular ribs F-Tri [84]

Numerical

PD is higher than straight MCHS

MCHS with Grooves and obstacles of six cases [86] Ribs and grooves [87] MCHS with triangular cavities and rectangular ribs (TC–RR) [88] MCHS with offset strip fins [91] MCHS with offset strip fins [89] MCHS with offset strip fins [92] MCHS with offset strip fins [93]

Numerical Numerical Numerical

(i) Re < 300, (ii) F-Trp is the best. (iii) Re > 300, F-C is the best Case 4–26.19 1.55 times Overall thermal enhancement 1.619

35 kPa

Interrupted wall channel MCHS [95]

HT is higher than straight MCHS HTE is dominant over friction losses for Re < 600

PD is the same as in straight MCHS PD is higher than straight MCHS

80% 80%

Negligible pressure penalty Negligible pressure penalty

MCHS with oblique fins [102]

Experimental and numerical Numerical Experimental and numerical Numerical Experimental and numerical Numerical

Dissipates heat fluxes up 3 MW/m2 C.O.P = 290 Dissipates heat fluxes up 300 W/cm2 The best thermal performance at lower PD is achieved when the ratio of the fin interval to the fin length is equal to one HT is higher than straight MCHS

Negligible PD compared with conventional straight MCHS

MCHS with oblique fins [103]

Experimental

MCHS with oblique fins [1]

Experimental

MCHS with slanted channels in alternating orientation [104]

Numerical

Nusselt number increased by 55% more than conventional straight MCHS Nusselt number increased by 103% more than conventional straight MCHS 47% at Re = 680 Optimal angle 27° 146%

35 kPa

PD is the same as in straight MCHS

Small PD Negligible PD 6%

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

Interrupted wall channel MCHS [96] Interrupted MCHS with rectangular ribs in transverse microchambers [97] MCHS with oblique fins [98] MCHS with oblique fins [101]

Numerical Numerical Experimental Numerical

Case 4–110.1 4.09–7.04 PD is higher than straight MCHS

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

ribs and either grooves or cavities have additional advantages than single technique in isolation. These features are manifested in increasing the HT area, induction of better fluid mixing and formation CA. The offset-strip fins configuration is another FD technique which forces the flow streams to mix with each other and dissipate more heat from the heated walls. Furthermore, the performance of this configuration is related to the optimal geometrical parameters such as fin length, fin number and fin interval. The most important characteristic within flow disturbance techniques is found in interrupted-wall channel which manifested low PD. It is established to be the most desirable feature in MCHS applications due to its role in reducing the pump power and liquid leakage risk. Besides, the secondary flow in slanted channels in the wall-fin notably contributes in increasing the flow mixing and continuous interruption to the thermal boundary layer and therefore enhances HT. So, it can be concluded that MCHS with oblique fins (or slanted channels) has achieved best performance with high heat transfer rate at negligible pressure drop. Although many research have focused on studying the effects of geometrical parameters in both above techniques, but there is a need to further studies focusing on: 1. More studies are needed to adopt a combination between wavy MCHS and FD techniques for more thermal performance. 2. The combination between grooves and ribs in central channel has achieved a higher performance than using individual technique of ribs or grooves. An optimization of geometrical parameters for grooves and ribs with different shapes is needed to acquire more reduction in PD associated with higher rate of heat transfer. This all-inclusive and edifying review article is expected to serve as taxonomy for navigating and understanding the state of the art developments towards improvement of HP in MCHS.

References [1] Y.J. Lee, P.K. Singh, P.S. Lee, Fluid flow and heat transfer investigations on enhanced microchannel heat sink using oblique fins with parametric study, Int. J. Heat Mass Transfer 81 (2015) 325–336. [2] H. Ghaedamini, P.S. Lee, C.J. Teo, Developing forced convection in converging– diverging microchannels, Int. J. Heat Mass Transfer 65 (2013) 491–499. [3] S.G. Kandlikar, W.J. Grande, Evaluation of single phase flow in microchannels for high heat flux chip cooling—thermohydraulic performance enhancement and fabrication technology, Heat Transfer Eng. 25 (2004) 5–16. [4] N.H. Mohamad Noh, A. Fazeli, N.A. Che Sidik, Numerical simulation of nanofluids for cooling efficiency in microchannel heat sink, J. Adv. Res. Fluid Mech. Therm. Sci. 4 (2014) 13–23. [5] Y. Sui, C.J. Teo, P.S. Lee, Y.T. Chew, C. Shu, Fluid flow and heat transfer in wavy microchannels, Int. J. Heat Mass Transfer 53 (2010) 2760–2772. [6] S.B. Abubakar, N.A. Che Sidik, Numerical prediction of laminar nanofluid flow in rectangular microchannel heat sink, J. Adv. Res. Fluid Mech. Therm. Sci. 7 (2015) 29–38. [7] M.M. Rahman, F. Gui, Experimental measurements of fluid flow and heat transfer in microchannel cooling passages in a chip substrate, in: The ASME International Electronics Packaging Conference, Binghamton, NY, USA, 1993, pp. 685–692. [8] G. Gamrat, M. Favre-Marinet, D. Asendrych, Conduction and entrance effects on laminar liquid flow and heat transfer in rectangular microchannels, Int. J. Heat Mass Transfer 48 (2005) 2943–2954. [9] I.A. Ghani, The significant effect of secondary flow in wavy microchannel for augmentation of heat transfer, J. Adv. Res. Fluid Mech. Therm. Sci. 25 (2016) 1–18. [10] W. Owhaib, B. Palm, Experimental investigation of single-phase convective heat transfer in circular microchannels, Exp. Therm. Fluid Sci. 28 (2004) 105– 110. [11] J.P. McHale, S.V. Garimella, Heat transfer in trapezoidal microchannels of various aspect ratios, Int. J. Heat Mass Transfer 53 (2010) 365–375. [12] Y. Chen, C. Zhang, M. Shi, J. Wu, Three-dimensional numerical simulation of heat and fluid flow in noncircular microchannel heat sinks, Int. Commun. Heat Mass Transfer 36 (2009) 917–920. [13] S.B. Abubakar, N.A. Che Sidik, A.S. Ahmad, The use of Fe3O4-H2O4 nanofluid for heat transfer enhancement in rectangular microchannel heatsink, J. Adv. Res. Mater. Sci. 23 (2016) 15–24.

43

[14] H. Mohammed, P. Gunnasegaran, N. Shuaib, The impact of various nanofluid types on triangular microchannels heat sink cooling performance, Int. Commun. Heat Mass Transfer 38 (2011) 767–773. [15] A.A. Razali, A. Sadikin, CFD simulation study on pressure drop and velocity across single flow microchannel heat sink, J. Adv. Res. Des. 8 (2015) 12–21. [16] P.-S. Lee, S.V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, Int. J. Heat Mass Transfer 48 (2005) 1688–1704. [17] P. Gunnasegaran, H. Mohammed, N. Shuaib, R. Saidur, The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes, Int. Commun. Heat Mass Transfer 37 (2010) 1078–1086. [18] W.Q. Tao, Y.L. He, Q.W. Wang, Z.G. Qu, F.Q. Song, A unified analysis on enhancing single phase convective heat transfer with field synergy principle, Int. J. Heat Mass Transfer 45 (2002) 4871–4879. [19] M.E. Steinke, S.G. Kandlikar, Review of single-phase heat transfer enhancement techniques for application in microchannels, minichannels and microdevices, Int. J. Heat Technol. 22 (2004) 3–11. [20] J.F. Tullius, R. Vajtai, Y. Bayazitoglu, A review of cooling in microchannels, Heat Transfer Eng. 32 (2011) 527–541. [21] A. Mohammed Adham, N. Mohd-Ghazali, R. Ahmad, Thermal and hydrodynamic analysis of microchannel heat sinks: a review, Renewable Sustainable Energy Rev. 21 (2013) 614–622. [22] A. Dewan, P. Srivastava, A review of heat transfer enhancement through flow disruption in a microchannel, J. Therm. Sci. 24 (2015) 203–214. [23] L. Wang, T. Yang, Bifurcation and stability of forced convection in curved ducts of square cross-section, Int. J. Heat Mass Transfer 47 (2004) 2971–2987. [24] W.R. Dean, XVI. Note on the motion of fluid in a curved pipe, London Edinburgh Dublin Philos. Mag. J. Sci. 4 (1927) 208–223. [25] W.R. Dean, LXXII. The stream-line motion of fluid in a curved pipe (Second paper), London Edinburgh Dublin Philos. Mag. J. Sci. 5 (1928) 673–695. [26] A. Mokrani, C. Castelain, H. Peerhossaini, The effects of chaotic advection on heat transfer, Int. J. Heat Mass Transfer 40 (1997) 3089–3104. [27] S. Sugiyama, T. Hayashi, K. Yamazaki, Flow characteristics in the curved rectangular channels: visualization of secondary flow, Bull. JSME 26 (1983) 964–969. [28] C. Kalb, J. Seader, Heat and mass transfer phenomena for viscous flow in curved circular tubes, Int. J. Heat Mass Transfer 15 (1972) 801–817. [29] J.H. Masliyah, K. Nandakumar, Fully developed viscous flow and heat transfer in curved semicircular sectors, AIChE J. 25 (1979) 478–487. [30] K. Cheng, R.-C. Lin, J.-W. Ou, Fully developed laminar flow in curved rectangular channels, J. Fluids Eng. 98 (1976) 41–48. [31] N.R. Rosaguti, D.F. Fletcher, B.S. Haynes, Laminar flow and heat transfer in a periodic serpentine channel, Chem. Eng. Technol. 28 (2005) 353–361. [32] N.R. Rosaguti, D.F. Fletcher, B.S. Haynes, Laminar flow and heat transfer in a periodic serpentine channel with semi-circular cross-section, Int. J. Heat Mass Transfer 49 (2006) 2912–2923. [33] P.E. Geyer, N.R. Rosaguti, D.F. Fletcher, B.S. Haynes, Thermohydraulics of square-section microchannels following a serpentine path, Microfluid. Nanofluid. 2 (2005) 195–204. [34] P.E. Geyer, N.R. Rosaguti, D.F. Fletcher, B.S. Haynes, Laminar flow and heat transfer in periodic serpentine mini-channels, J. Enhanced Heat Transfer 13 (2006). [35] P.E. Geyer, D.F. Fletcher, B.S. Haynes, Laminar flow and heat transfer in a periodic trapezoidal channel with semi-circular cross-section, Int. J. Heat Mass Transfer 50 (2007) 3471–3480. [36] H. Metwally, R.M. Manglik, Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels, Int. J. Heat Mass Transfer 47 (2004) 2283–2292. [37] R.M. Manglik, J. Zhang, A. Muley, Low Reynolds number forced convection in three-dimensional wavy-plate-fin compact channels: fin density effects, Int. J. Heat Mass Transfer 48 (2005) 1439–1449. [38] C. Chagny, C. Castelain, H. Peerhossaini, Chaotic heat transfer for heat exchanger design and comparison with a regular regime for a large range of Reynolds numbers, Appl. Therm. Eng. 20 (2000) 1615–1648. [39] Z. Zheng, D.F. Fletcher, B.S. Haynes, Laminar heat transfer simulations for periodic zigzag semicircular channels: chaotic advection and geometric effects, Int. J. Heat Mass Transfer 62 (2013) 391–401, 7//. [40] R.H. Liu, M.A. Stremler, K.V. Sharp, M.G. Olsen, J.G. Santiago, R.J. Adrian, et al., Passive mixing in a three-dimensional serpentine microchannel, J. Microelectromech. Syst. 9 (2000) 190–197. [41] H. Aref, Stirring by chaotic advection, J. Fluid Mech. 143 (1984) 1–21. [42] H. Peerhossaini, C. Castelain, Y. Le Guer, Heat exchanger design based on chaotic advection, Exp. Therm. Fluid Sci. 7 (1993) 333–344. [43] Y. Sui, P.S. Lee, C.J. Teo, An experimental study of flow friction and heat transfer in wavy microchannels with rectangular cross section, Int. J. Therm. Sci. 50 (2011) 2473–2482. [44] Y. Sui, C. Teo, P. Lee, Direct numerical simulation of fluid flow and heat transfer in periodic wavy channels with rectangular cross-sections, Int. J. Heat Mass Transfer 55 (2012) 73–88. [45] H. Mohammed, P. Gunnasegaran, N. Shuaib, Numerical simulation of heat transfer enhancement in wavy microchannel heat sink, Int. Commun. Heat Mass Transfer 38 (2011) 63–68. [46] G. Xie, J. Liu, Y. Liu, B. Sunden, W. Zhang, Comparative study of thermal performance of longitudinal and transversal-wavy microchannel heat sinks for electronic cooling, J. Electron. Packag. 135 (2013) 1–9.

44

I.A. Ghani et al. / International Journal of Heat and Mass Transfer 107 (2017) 21–44

[47] G. Xie, J. Liu, W. Zhang, B. Sunden, Analysis of flow and thermal performance of a water-cooled transversal wavy microchannel heat sink for chip cooling, J. Electron. Packag. 134 (2012) 1–11. [48] W.M. Abed, R.D. Whalley, D.J.C. Dennis, R.J. Poole, Numerical and experimental investigation of heat transfer and fluid flow characteristics in a micro-scale serpentine channel, Int. J. Heat Mass Transfer 88 (2015) 790– 802. [49] L. Gong, K. Kota, W. Tao, Y. Joshi, Parametric numerical study of flow and heat transfer in microchannels with wavy walls, J. Heat Transfer 133 (2011) 1–13. [50] J. Yong, C.J. Teo, Mixing and heat transfer enhancement in microchannels containing converging-diverging passages, J. Heat Transfer 136 (2014) 041704. [51] H. Mohammed, P. Gunnasegaran, N. Shuaib, Influence of channel shape on the thermal and hydraulic performance of microchannel heat sink, Int. Commun. Heat Mass Transfer 38 (2011) 474–480. [52] Z. Dai, Z. Zheng, D.F. Fletcher, B.S. Haynes, Experimental study of transient behaviour of laminar flow in zigzag semi-circular microchannels, Exp. Therm. Fluid Sci. 68 (2015) 644–651. [53] Z. Dai, D.F. Fletcher, B.S. Haynes, Impact of tortuous geometry on laminar flow heat transfer in microchannels, Int. J. Heat Mass Transfer 83 (2015) 382–398. [54] C. Amon, D. Majumdar, C. Herman, F. Mayinger, B. Mikic, D. Sekulic, Numerical and experimental studies of self-sustained oscillatory flows in communicating channels, Int. J. Heat Mass Transfer 35 (1992) 3115–3129. [55] N. Ghaddar, K. Korczak, B. Mikic, A. Patera, Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and self-sustained oscillations, J. Fluid Mech. 163 (1986) 99–127. [56] N. Ghaddar, M. Magen, B. Mikic, A. Patera, Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement, J. Fluid Mech. 168 (1986) 541–567. [57] M. Greiner, R.-F. Chen, R. Wirtz, Enhanced heat transfer/pressure drop measured from a flat surface in a grooved channel, J. Heat Transfer 113 (1991) 498–501. [58] R. Wirtz, F. Huang, M. Greiner, Correlation of fully developed heat transfer and pressure drop in a symmetrically grooved channel, J. Heat Transfer 113 (1999) 590–596. [59] C. Herman, E. Kang, Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel, Heat Mass Transfer 37 (2001) 87–99. [60] S. Lorenz, D. Mukomilow, W. Leiner, Distribution of the heat transfer coefficient in a channel with periodic transverse grooves, Exp. Therm. Fluid Sci. 11 (1995) 234–242. [61] C. Herman, F. Mayinger, Experimental analysis of forced convection heat transfer in a grooved channel, Adv. Heat Transfer (1992) 900–913. [62] L. Wang, B. Sundén, Experimental investigation of local heat transfer in a square duct with various-shaped ribs, Heat Mass Transfer 43 (2007) 759–766. [63] C. Herman, E. Kang, Heat transfer enhancement in a grooved channel with curved vanes, Int. J. Heat Mass Transfer 45 (2002) 3741–3757. [64] Y. Islamoglu, C. Parmaksizoglu, The effect of channel height on the enhanced heat transfer characteristics in a corrugated heat exchanger channel, Appl. Therm. Eng. 23 (2003) 979–987. [65] E.A.M. Elshafei, M.M. Awad, E. El-Negiry, A.G. Ali, Heat transfer and pressure drop in corrugated channels, Energy 35 (2010) 101–110. [66] A. Hartmann, A. Lucic, Application of the holographic interferometry in transport phenomena studies, Heat Mass Transfer 37 (2001) 549–562. [67] J. Cernecky, J. Koniar, Z. Brodnianska, The effect of heat transfer area roughness on heat transfer enhancement by forced convection, J. Heat Transfer 136 (2014) 041901. [68] G. Xia, L. Chai, M. Zhou, H. Wang, Effects of structural parameters on fluid flow and heat transfer in a microchannel with aligned fan-shaped reentrant cavities, Int. J. Therm. Sci. 50 (2011) 411–419. [69] L. Chai, G. Xia, M. Zhou, J. Li, Numerical simulation of fluid flow and heat transfer in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall, Int. Commun. Heat Mass Transfer 38 (2011) 577–584. [70] G. Xia, L. Chai, H. Wang, M. Zhou, Z. Cui, Optimum thermal design of microchannel heat sink with triangular reentrant cavities, Appl. Therm. Eng. 31 (2011) 1208–1219. [71] L. Chai, G. Xia, L. Wang, M. Zhou, Z. Cui, Heat transfer enhancement in microchannel heat sinks with periodic expansion–constriction cross-sections, Int. J. Heat Mass Transfer 62 (2013) 741–751. [72] G.D. Xia, J. Jiang, J. Wang, Y.L. Zhai, D.D. Ma, Effects of different geometric structures on fluid flow and heat transfer performance in microchannel heat sinks, Int. J. Heat Mass Transfer 80 (2015) 439–447. [73] G. Xia, D. Ma, Y. Zhai, Y. Li, R. Liu, M. Du, Experimental and numerical study of fluid flow and heat transfer characteristics in microchannel heat sink with complex structure, Energy Convers. Manage. 105 (2015) 848–857. [74] O. Abouali, N. Baghernezhad, Numerical investigation of heat transfer enhancement in a microchannel with grooved surfaces, J. Heat Transfer 132 (2010) 1–10. [75] D. Ansari, A. Husain, K.-Y. Kim, Multiobjective optimization of a grooved microchannel heat sink, IEEE Trans. Comp. Packag. Technol. 33 (2010) 767–776. [76] N.R. Kuppusamy, H.A. Mohammed, C.W. Lim, Numerical investigation of trapezoidal grooved microchannel heat sink using nanofluids, Thermochim. Acta 573 (2013) 39–56. [77] N.R. Kuppusamy, H.A. Mohammed, C.W. Lim, Thermal and hydraulic characteristics of nanofluid in a triangular grooved microchannel heat sink (TGMCHS), Appl. Math. Comput. 246 (2014) 168–183.

[78] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal and rectangular grooved microchannel heat sinks, Int. Commun. Heat Mass Transfer 66 (2015) 47–57. [79] L. Chai, G.D. Xia, H.S. Wang, Parametric study on thermal and hydraulic characteristics of laminar flow in microchannel heat sink with fan-shaped ribs on sidewalls – Part 1: heat transfer, Int. J. Heat Mass Transfer 97 (2016) 1069–1080. [80] L. Chai, G.D. Xia, H.S. Wang, Parametric study on thermal and hydraulic characteristics of laminar flow in microchannel heat sink with fan-shaped ribs on sidewalls – Part 2: pressure drop, Int. J. Heat Mass Transfer 97 (2016) 1081–1090. [81] L. Chai, G.D. Xia, H.S. Wang, Parametric study on thermal and hydraulic characteristics of laminar flow in microchannel heat sink with fan-shaped ribs on sidewalls – Part 3: performance evaluation, Int. J. Heat Mass Transfer 97 (2016) 1091–1101. [82] 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. [83] G. Xia, Y. Zhai, Z. Cui, Numerical investigation of thermal enhancement in a micro heat sink with fan-shaped reentrant cavities and internal ribs, Appl. Therm. Eng. 58 (2013) 52–60. [84] Y.L. Zhai, G.D. Xia, X.F. Liu, Y.F. Li, Heat transfer in the microchannels with fan-shaped reentrant cavities and different ribs based on field synergy principle and entropy generation analysis, Int. J. Heat Mass Transfer 68 (2014) 224–233. [85] Y. Zhai, G. Xia, X. Liu, Y. Li, Exergy analysis and performance evaluation of flow and heat transfer in different micro heat sinks with complex structure, Int. J. Heat Mass Transfer 84 (2015) 293–303. [86] Y. Xie, Z. Shen, D. Zhang, J. Lan, Thermal performance of a water-cooled microchannel heat sink with grooves and obstacles, J. Electron. Packag. 136 (2014) 1–13. [87] G. Wang, D. Niu, F. Xie, Y. Wang, X. Zhao, G. Ding, Experimental and numerical investigation of a microchannel heat sink (MCHS) with micro-scale ribs and grooves for chip cooling, Appl. Therm. Eng. 85 (2015) 61–70. [88] Y. Li, G. Xia, D. Ma, Y. Jia, J. Wang, Characteristics of laminar flow and heat transfer in microchannel heat sink with triangular cavities and rectangular ribs, Int. J. Heat Mass Transfer 98 (2016) 17–28. [89] M.E. Steinke, S.G. Kandlikar, Single-phase liquid heat transfer in plain and enhanced microchannels, in: ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, 2006, pp. 943–951. [90] T. Kishimoto, S. Saski, Cooling characteristics of diamond-shaped interrupted cooling fin for high-power LSI devices, Electron. Lett. 23 (1987) 456–457. [91] S.G. Kandlikar, H.R. Upadhye, Extending the heat flux limit with enhanced microchannels in direct single-phase cooling of computer chips, in: 2005 IEEE Twenty First Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2005, pp. 8–15. [92] E.G. Colgan, B. Furman, M. Gaynes, W.S. Graham, N.C. LaBianca, J.H. Magerlein, et al., A practical implementation of silicon microchannel coolers for high power chips, IEEE Trans. Comp. Packag. Technol. 30 (2007) 218–225. [93] F. Hong, P. Cheng, Three dimensional numerical analyses and optimization of offset strip-fin microchannel heat sinks, Int. Commun. Heat Mass Transfer 36 (2009) 651–656. [94] E. Sparrow, B. Baliga, S. Patankar, Heat transfer and fluid flow analysis of interrupted-wall channels, with application to heat exchangers, J. Heat Transfer 99 (1977) 4–11. [95] J.L. Xu, Y.H. Gan, D.C. Zhang, X.H. Li, Microscale heat transfer enhancement using thermal boundary layer redeveloping concept, Int. J. Heat Mass Transfer 48 (2005) 1662–1674. [96] J. Xu, Y. Song, W. Zhang, H. Zhang, Y. Gan, Numerical simulations of interrupted and conventional microchannel heat sinks, Int. J. Heat Mass Transfer 51 (2008) 5906–5917. [97] L. Chai, G. Xia, M. Zhou, J. Li, J. Qi, Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers, Appl. Therm. Eng. 51 (2013) 880–889. [98] Y.-J. Lee, P.-S. Lee, S.-K. Chou, Enhanced microchannel heat sinks using oblique fins, in: ASME 2009 InterPACK Conference collocated with the ASME 2009 Summer Heat Transfer Conference and the ASME 2009 3rd International Conference on Energy Sustainability, 2009, pp. 253–260. [99] K. Suga, H. Aoki, Numerical study on heat transfer and pressure drop in multilouvered fins, J. Enhanced Heat Transfer 2 (1995) 231–238. [100] N.C. DeJong, A.M. Jacobi, Localized flow and heat transfer interactions in louvered-fin arrays, Int. J. Heat Mass Transfer 46 (2003) 443–455. [101] Y.-J. Lee, P.-S. Lee, S.-K. Chou, Experimental investigation of oblique finned microchannel heat sink+, in: 2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 2010, pp. 1–7. [102] Y.-J. Lee, P.-S. Lee, S.-K. Chou, Experimental investigation of silicon-based oblique finned microchannel heat sinks, in: 2010 14th International Heat Transfer Conference, 2010, pp. 283–291. [103] Y. Lee, P. Lee, S. Chou, Enhanced thermal transport in microchannel using oblique fins, J. Heat Transfer 134 (2012) 101901. [104] N.R. Kuppusamy, R. Saidur, N. Ghazali, H. Mohammed, Numerical study of thermal enhancement in micro channel heat sink with secondary flow, Int. J. Heat Mass Transfer 78 (2014) 216–223.