A transient study on two phase adiabatic flow over micro circular pin heat sinks

Computers and Mathematics with Applications xxx (xxxx) xxx

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A transient study on two phase adiabatic flow over micro circular pin heat sinks Mohammadreza DaqiqShirazi a , Azeez A. Barzinjy c,b , Samir M. Hamad d,e , ∗ Rezvan Alamian f , Mostafa Safdari Shadloo g,h , a

Department of Material Science, University of Turin, Turin, Italy Department of Physics, College of Education, Salahaddin University-Erbil, Kurdistan Region, Iraq Department of Physics Education, Faculty of Education, Tishk International University, Erbil, Kurdistan Region, Iraq d Computer Department, Cihan University-Erbil, Erbil, Kurdistan Region, Iraq e Scientific Research Centre, Soran University, Soran, Kurdistan Region, Iraq f Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran g Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam h Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam b c

article

info

Article history: Available online xxxx Keywords: Micro heat sink Two phase flow Enhanced heat transfer Pin diameter Surface tension Pressure drop

a b s t r a c t In the present work, a transient numerical study on two-phase flow over circular staggered and inline micro pin fins is conducted. Pin diameter, fluid density ratio, and surface tension have been taken into account. Diameters of micro pins are in the range of 50 to 250 µm; moreover, a variation of 100 fold in the surface tension and density ratio are considered. In order to solve the numerical model of a micro heat sink, a volume of fluid (VOF) method using open package Gerris Flow Solver (GFS) is employed. Pressure drop, flow velocity, as well as void fraction for all cases are presented and discussed. Based on the results, transient nature of flow is observed even after the first transition phase. Flow mixing as an essential phenomenon in heat transfer is thoroughly discussed. Our study proves that with an increase of pin diameter the flow mixing near micropins is hindered. Moreover, bridge formation in staggered conformation was observed which may reduce the heat transfer. Additionally higher surfaces tension ratio yielded a better flow mixing. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction In the past two decades, the main focus of micro scale heat transfer research was concentrated on the heat dissipation in small devices. Amongst proffered methods to improve heat transfer rate in micro scale devices, enhanced surfaces manifest a superior capability [1–3], in spite of the fact that pressure drop is higher in them compared to ordinary micro channels. Advances in micro fabrication in last two decades enhanced the use of micro pin heat sinks as a powerful cooling method in mini structures. A considerable amount of research was dedicated to this field that was aimed at the study of fluid flow and heat transfer characteristics dissipated from the hot surfaces experimentally. Amongst them, some studies dealt with a single-phase flow in the form of sub-cooled or saturated state. On the other hand, some researchers ∗ Corresponding author at: [email protected] (Mostafa Safdari Shadloo). E-mail addresses: [email protected] (M. DaqiqShirazi), [email protected] (A.A. Barzinjy), [email protected] (S.M. Hamad), [email protected] (R. Alamian), [email protected] (M. Safdari Shadloo). https://doi.org/10.1016/j.camwa.2019.10.019 0898-1221/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Nomenclature

ρ Rein D t U p

µ δ σ κ n¯ c

Density of fluid Reynold’s number of the flow at the inlet of the microchannel Diameter of the micropins Time Velocity of flow Pressure of the fluid Viscosity of the fluid Dirac distribution function Surface tension Curvature Normal to the surface Volume fraction of the first fluid

numerically studied the case of microchannels [4–6]. However, the number of studies and parameters studied by this method is still much lower than the number of experimental studies [7]. One of the interesting properties to observe and control in micro pin finned devices is the pressure drop. Reviews of predictive methods for pressure drop in mini and micro channels can be found extensively in references [8–11]. As an example, Kuppusamy et al. [12] conducted research about a particular case of a micro channel where they employed secondary flow to reduce the pressure drop and increase the heat transfer. In fact, their case resembles an elongated trapezoid pin fin bank. Other researchers investigated the two-phase flows passing through these micro structures; trying to find a methodology to formulate pressure drop or flow patterns. Some of them focused their studies on simple micro channels; for instance, to comprehend their characteristics in refrigeration. Lee and Mudawar [13] measured the pressure drop for two-phase flows in a micro-channel heat sink. They employed refrigerant R134a for their study. Qu and Mudawar [14] also discussed major flow patterns and instabilities in micro channels. They concluded that the instability in the cycle was completely suppressed by throttling a control valve situated upstream of the heat sink. On the other hand, an abundance of studies about enhanced micro surface structures is available. Siu-Ho et al. [15,16] conducted experiments to analyze the pressure drop and heat transfer of de-ionized water over square micro pins in the form of sub cooled fluid. Qu and Siu-Ho [17–19] surveyed adiabatic and diabatic pressure drops of several staggered micro pin fins banks. Konishi et al. [20] performed an experimental study on single-phase flow to evaluate the pressure drop across square micro-pin-fins having diameters of 200 µm. However, in all these studies, water played the role of working fluid, Koşar and Peles [21] considered both single-phase and two-phase heat transfer using R-123 as the working fluid. A broad gamut of working fluids and configurations has been taken into account in previous researches [22]. In addition to the latter work, two-phase flows over enhanced surfaces are present in manifold works: Koşar and Peles [23] studied the flow of de-ionized water over a shrouded micro pin fin structure. Nitrogen–water mixture was used by Kirishnamurthy and Peles [24] to study the circular micro pins . Wei et al. [25] studied cooling of electronics devices with 30 and 50 µm thick fin pins. Furthermore, they employed FC-72 as the working fluid. Koşar et al. [26] expanded their research for three different micro pin heat sinks utilizing two different working fluids, namely R134a and water. Konishi et al. [27] investigated the two-phase pressure drop of water liquid–vapor, excluding heat transfer from their study. Jasperson et al. [28] also performed a comparison between these two routes of heat dissipation from three different aspects: thermal performance, hydraulic performance, and cost of manufacturing. In recent years more researchers became interested in dielectric chemically inert HFE-7200 for cooling. As an example, Reeser et al. [29] implemented an investigation of this fluid over both staggered and inline configurations. They observed no major differences between the cooling ability of inline and staggered pin banks ;In addition to this work, in references [30–32], researchers employed HFE-7200 as working fluid, and a collection of similar studies were presented in their works. Kirishnamurthy and Peles [33] studied a form of enhanced surface with a single row of micro pins under boiling conditions observing three major flow patterns: bubbly flow, multiple flows, and wavy-annular flow. Law et al. [34] analyzed another case of boiling fluid over the oblique-finned surface in order to extract heat transfer and pressure drop characteristics. Chang et al. [35] investigated sub-cooled flow as well as boiling heat transfer and bubble characteristics of FC-72 on a heated square micro-pin-finned. They concluded that micro pin effectively augments the flow boiling heat transfer coefficient. In the last decade due to advances in computational tools and the need to characterize the flow with more detail, some researchers employed numerical methods to scrutinize pressure drop and heat transfer related phenomena in micro structures with enhanced surfaces. John et al. [36] solved the case of single-phase flow over circular and square micro pins banks with the use of commercial software CoventorWareTM . Their results reveal better performance in circular pin fins for lower Re numbers. Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 1. The view of micro pin fin bank including its main parameters (dimensions are in mm) (a) two dimensional inline (b) two dimensional staggered (c) three dimensional (the arrow shows the flow direction).

Lee et al. [37] employed direct numerical simulation to model the finned surfaces. Shafeie et al. [38] numerically studied the laminar flow in micro heat sinks with the micro pin-fin structure on a 1 cm × 1 cm substrate. Izci et al. [39] modeled numerically a channel with different shape single micro pin-fins using software COMSOL Multiphysics 3.5a. Zhao et al. [40] performed a numerical investigation on square pin fins. Square pin angle and porosity were optimized in their study. Two issues are mostly considered in both simple and micro channels with enhanced surfaces; improving the heat transfer and controlling the pressure drop. The primary goal of a micro heat sink is to enhance heat transfer and dissipation. In this regard, the optimum design of such a system is based on the increment of the device heat transfer. However, such improvement is accompanied by an increase in pressure drop of the device. Understanding the fluid flow in these chambers gives researchers a better tool to overcome the aforementioned difficulty. In the current study, the emphasis is on capturing the physical behavior of flow due to its transient nature in order to inspect the hydraulic behavior of the flow as well as the present mixing which correlates with the ability of the fluid to remove heat from the micro pins surfaces. Researchers benefited from many different numerical skims in their multiphase studies such as smoothed particle hydrodynamics (SPH) [41–44], lattice Boltzman method (LBM) [45–48] and volume of fluid (VOF) [49–52]. Anyway, in current research a VOF approach accompanied by an adaptive meshing is used (see Section 2 for more details). A glance over current literature in the field of micro enhanced surfaces reveals the usage of an extensive collection of working fluid as well as the need to formulate and studying the performance of this device in transition, especially in the presence of two fluids. 2. Methodology 2.1. Problem description The case of adiabatic two-phase flow over staggered and inline micro fin banks are considered in this study. Flow over a pin fin bank is studied for a time lapse of 0.1s in order to capture the transient nature of the flow in this sort of devices. Initially, the 1.8 mm × 1.8 mm microchannel was filled to its half by each fluid. Both fluids enter the micro fin bank having the same velocity in x-direction which is indicated in figures by dimensionless Reynold’s number (Rein ). Density ratios between 1 to 100, pin fin diameters in the range of 50-250 µm and surface tension as well as pin fin configuration – staggered or inline – are analyzed (Fig. 1). In order to have a good overview of all cases, Tables 1–4 summarized the geometrical, initial, boundary conditions and modeling conditions in this study. In order to have a good overview of all cases, Tables 2–4 summarized the geometrical, performed simulations and boundary conditions. It is worth mentioning that static refinement on geometry and dynamic refinement of vorticity, pressure, void fraction and velocity were applied; which means that cells are refined whenever gradients in these variables exist to 28 . Also a threshold of at least 0.02 percent in gradient of these variables are kept. Moreover, for assuring the numerical convergence of the adaptive mesh; mesh levels of 6, 7 and 8 are studied and no meaningful difference between two latter levels was observed. Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al. / Computers and Mathematics with Applications xxx (xxxx) xxx Table 1 Initial and boundary conditions utilized in current study. Property

Value

Initial velocity Inlet velocity Wall BC Refinement level

Fluids are at rest Uniform velocity calculated based on Re no slip condition Level 8

Table 2 Test cases in order to study the effect of density ratio. Rein = 100, inline Rein = 100, staggered

ρ2 /ρ1

ρ2 /ρ1

ρ2 /ρ1

1 1

2 2

100 100

Table 3 Test cases in order to study the effect of diameter variation D. Rein = 100, ρ2 /ρ1 = 1, inline Rein = 100, ρ2 /ρ1 = 1, staggered

D

D

D

D

D

50 µm 50 µm

100 µm 100 µm

150 µm 150 µm

200 µm 200 µm

200 µm 200 µm

Table 4 Test cases in order to study the effect of surface tension. D = 150 µm, inline, ρ2 /ρ1 = 1 D = 150 µm, Staggered, ρ2 /ρ1 = 1

Surface tension

Surface tension

Surface tension

1 1

10 10

100 100

2.2. Governing equations We employed incompressible, and two-dimensional Navier–Stokes equations for two immiscible fluids in this study, which can be written in the form of:

ρ(

∂ + U ∆U) = −∆p + µ∆2 U + σ κδ n¯ ∂t

∆U = 0

(1) (2)

In Navier–Stokes and continuity equations (1) and (2) U = U(u, v ), ρ = ρ (x, t) and µ = µ(x, t) represent fluid velocity, fluid density and fluid dynamic viscosity; δ , σ , κ , n¯ are Dirac distribution function, surface coefficient, curvature and normal to interface, respectively. For two-phase flow, a VOF method was used where fluid density and viscosity are expressed as a function of c, volume fraction of the first fluid. Thus, the advection equation of density can be replaced with advection of equation of volume fraction [53]:

∂c + ∇ (Uc) = 0 ∂t

(3)

Velocity boundary condition was exerted on the inlet; moreover, no-slip condition on pins and microchannel walls were assumed. The numerical equations were solved using a finite volume method. This numerical problem was solved using the open-source package Gerris [54] which was initially validated by the code author. Moreover the code was validated and utilized for many applications such as nucleate boiling [55], bubble formation [56] and collapse [57]. In this method, a quad/octree discretization skim is employed which uses a finite difference based discretization on different coarse/fine levels which enables one to model complex surfaces and interfaces efficiently [58,59]. 3. Results and discussion In the micro heat sink, the flow passes through the micro pillars that are constructed to improve the heat transfer with an escalation in the heat transfer area. The observed fluid flow demonstrates a transient behavior (look at Fig. 2 as an example). In the present work, three different parameters are examined, including the density ratio of two flows, pin diameter, and surface tension. In Fig. 2 the flow inside the micro pinned micro channel is illustrated (ρ2 /ρ1 = 1 and Rein = 100). It depicts the transient nature of the flow. In this case, the flow is developed for the first 0.0034 s of the simulation. Subsequently, an oscillation occurs after the micropins, which increases flow mixing, and therefore enhances the convective heat transfer. From the FFT transform analysis, it can be concluded that a periodic motion in the channel (≈ 1.5 Hz) exists (Fig. 3). Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 2. Velocity distribution in x-direction for ρ2 /ρ1 = 1 for inline configuration at different time steps, Rein = 100, D = 150 µm.

Fig. 3. FFT analysis of the pressure difference in the enhanced micro channel for the case of D = 150 µm and ρ2 /ρ1 = 1.

An exhaustive parametric study, over calculation time (tfinal = 0.1s), was performed. The first parameter for analysis is the density ratio. As discussed earlier, different types of coolants ranging from water to dielectric fluids were taken as the working fluid which shows the necessity to examine different fluid density ratios. Pressure drop versus simulation time for various density ratios of two fluids is presented in Fig. 4. Pressure fluctuates at the beginning of the simulation, as flow develops. Then, pressure drop reaches to an almost steady value; though pressure fluctuation due to transient behavior of the flow still persists, nonetheless, its variations diminish. When the microchannel is filled with two fluids with higher density ratios; the fluctuations become smaller. Normally, micropins distract the heavier fluid. Therefore, the heavier fluid squeezes the lighter one and causes higher velocity in the lighter fluid (Fig. 5). Besides, the lowest value of pressure drop in the study of density ratio belongs to the ratio of two. In this ratio, after initial transitional flow, almost all major fluctuations disappear, and flow becomes much more stable than the ratio one (Fig. 6). However, density augmentation causes higher pressure drops in density ratio of hundred. In this regard, the flow only oscillates near the pin surfaces. On the other hand, in staggered configuration the flow disturbance, due to the presence of staggered micro pins, becomes more widespread in comparison to inline configuration; yet, the flow preserves its discussed behavior (Fig. 7). One of the major characteristics of a microchannel with a micro pin enhanced surface is known to be the diameter of the micro pins. In order to fully understand the flow behavior inside the chamber, different diameters with inlet Re number of 100 are examined. For excluding the effect of density ratio, this parameter is set to be one. Fig. 8 illustrates the pressure difference in the channel between inlet and outlet positions. As it can be inferred from the figure, pressure drop for the case with 250 µm pins is drastically more than the other cases. When the diameter of the pins is very small, the pins do not alter the flow extensively. Thus the flow becomes more similar to a microchannel Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 4. Pressure difference in the channel in the inline configuration case for three different density ratios, D = 150 µm, Rein = 100.

Fig. 5. Void fraction in the microchannel for ρ2 /ρ1 = 100 from t = 0 s to t = 0.1 s, Rein = 100, D = 150 µm.

Fig. 6. Velocity distribution in the micro channel due to density ratio difference at t = 0.005 s, Rein = 100, D = 150 µm. Velocity is in range of [0,1] and is indicated by a color map that spans from low (blue) to high (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

without micropins. However, the flow is slightly changed, which will lead to an improvement in the ability of flow to dissipate the heat through convection in comparison to a case without such structures. Proportional to the enlargement of the micropins, the ability of the flow to pass pillars easily drops down. Therefore, the pressure drop increases. In cases of thicker pins such as D = 200 µm and 250 µm flow exits the pin bundle similar to some jets. Even though this phenomenon promotes heat transfer due to the better mixing (for example, look at Fig. 9(e)) throughout the channel, it is culpable for the extreme pressure drop experienced in these cases. Another salient point is that the trailing flow seems to form a stream at the middle of the channel. This stream tends to constrict proportional to the micro pin diameters; in this way, heat dissipation from near-wall regions afflicts. In addition to this, pressure drop has the least value for the Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 7. Velocity distribution in the micro channel with staggered micro fins for different time instances, ρ2 /ρ1 = 1, Rein = 100, D = 150 µm. Velocity is in range of [0,2] and is indicated by a color map that spans from low (blue) to high (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. Pressure difference in the channel in the inline configuration and five different diameters, ρ2 /ρ1 = 1, Rein = 100.

case with pin diameters of 100 µm. Fig. 9 justifies this behavior as this case has the minimum instabilities in the trailing region of the pins bundle. When the micro channel is filled with staggered pins, the pressure difference between inlet and outlet flops as the diameter of the pins varies from D = 50 µm to D = 150 µm, then the pressure gets its maximum drop at D = 200 µm (Fig. 10). The pressure drop trend commensurates with instabilities and chaotic behavior of the flow (Fig. 10). The pressure loss consists of three components: frictional loss, drag loss, and vortex loss. It is important to pay attention to this fact that frictional loss happens not only near the solid surfaces but also when adjacent layers of fluid have different velocities. As the flow behaves in a chaotic manner, a large amount of energy dissipates (Fig. 11). It is also noticeable that two flows have a tendency to be mixed. In this regard, when they pass over the micro pin bundle, some elongated bubbles are formed after the pins. Fig. 12(e) shows the velocity in x-direction for various staggered pin diameters. As the microchannels area blockage due to the presence of micro pins rises, fluid flow hinders. This fact bears testimony to the fact that vortex formations and fluid mixing play a more important role in the pressure drop in micro pinned enhanced microchannels. The study of surface tension on the flow field in the microchannel is conducted by two surveys (inline and staggered configurations). Fig. 13 presents the pressure drop for three different surface tensions of the flow in the microchannel in the case of Rein = 100 for both fluids and density ratio (ρ2 /ρ1 = 1) over inline micro pins with D = 200 µm. The pressure drop variations appear to be steady for σ = 0.1 and σ = 0.01 with some small variation after the first flow development. On the other hand, the fluctuations become violent for σ = 1. As it is obvious from Fig. 14, rapid changes in pressure drop in the case of σ = 1 does not correspond to any physical phenomenon as the flow field remains tranquil during the simulation and only some small waves appear; we suspect that the numerical instabilities are culpable for this behavior. Physically speaking, the increase in surface tension yields a better mixing as more waves emerge after the micro pin bundle, which can increase heat transfer ability of the device (Fig. 14). Fig. 15 presents the pressure drop behavior of the flow for three different surface tensions in the microchannel (the case with Rein = 100 and ρ2 /ρ1 = 1 over staggered micropins with D = 200 µm). The flow behavior is quite similar Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 9. Velocity field for 5 different inline micro pin diameters at t = 0.05 s and Rein = 100, ρ2 /ρ1 = 1. Velocity is in range of [0,1.5] and is indicated by a color map that spans from low (blue) to high (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. Pressure difference in the channel in the staggered configuration case with inlet Reynolds of a hundred for both fluids and five different diameters, ρ2 /ρ1 = 1, Rein = 100.

Fig. 11. Void fraction for 5 different staggered micro pin diameters at t = 0.05 s and ρ2 /ρ1 = 1, Rein = 100.

Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 12. Velocity field in x direction for 5 different staggered micro pin diameters at t = 0.05 s and ρ2 /ρ1 = 1, Rein = 100. Velocity is in range of [0,1.7] and is indicated by a color map that spans from low (blue) to high (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 13. Pressure difference in the channel with the inline configuration case with Rein = 100 for both fluids and three different surface tensions ρ2 /ρ1 = 1, D = 200 µm.

Fig. 14. Void fraction in the microchannel for three different surface tension, D = 200 µm, ρ2 /ρ1 = 1 and Rein = 100.

to the inline case; however, a better flow mixing in the upstream of the micro pins happens in the channel. Only in the case of σ = 0.01 a pressure drop remains almost steady through the simulation. Another phenomenon that is observed in staggered case is that the flow makes some bridges between micropins, so the flow movement around these pillars and consequently the heat transfer from pin surfaces are decreased (Fig. 16). Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Fig. 15. Pressure difference in the channel with the staggered configuration case with Rein = 100 for both fluids and three different surface tensions

ρ2 /ρ 11 = 1, D = 200.

Fig. 16. Void fraction in the microchannel for three different surface tensions, D = 200, ρ2 /ρ1 = 1 and Rein = 100.

4. Conclusion In the current study, two-phase flow over micro pinned surface microchannels is investigated from a hydrodynamical point of view. The flow behavior due to variation of three main parameters (i.e., density ratio, micro pin diameter, and surface tension) are scrutinized in the presence of two fluids. The flow solver Gerris with a tree-based and adaptive approach is utilized to solve the flow in a two-dimensional enhanced surface micro channel. Pressure drop, void fraction, and flow velocity field are presented in several figures to illustrate the flow behavior in such systems. Main points that are deduced from this work are as follows:

• A small fluctuation remains in the flow even after the first transition phase. Although these flow movements enhance flow mixing, they increase the pressure drop.

• The lowest pressure drop happens at density ratio of two in which most of the fluctuations are damped. • With an increase in the pin diameter, the flow mixing near walls is impaired. • A better mixing happens with an increase in the surface tension of the fluids. However, in staggered configuration due to bridge formation in the micro pin bundle, a reduction in heat transfer is expected. References [1] T. Ambreen, A. Saleem, C.W. Park, Numerical analysis of the heat transfer and fluid flow characteristics of a nanofluid-cooled micropin-fin heat sink using the Eulerian-Lagrangian approach, Powder Technol. 345 (2019) 509–520. [2] A. Mohammadi, A. Koşar, Review on heat and fluid flow in micro pin fin heat sinks under single-phase and two-phase flow conditions, Nanoscale Microscale Thermophys. Eng. 22 (3) (2018) 153–197. [3] M.V. Bozorg, M.H. Doranehgard, K. Hong, Q. Xiong, CFD Study of heat transfer and fluid flow in a parabolic trough solar receiver with internal annular porous structure and synthetic oil–Al2O3 nanofluid, Renew. Energy 145 (2020) 2598–2614. [4] A.G. Fedorov, R. Viskanta, Three-dimensional conjugate heat transfer in the microchannel heat sink for electronic packaging, Int. J. Heat Mass Transfer 43 (3) (2000) 399–415. [5] A. Weisberg, H.H. Bau, J. Zemel, Analysis of microchannels for integrated cooling, Int. J. Heat Mass Transfer 35 (10) (1992) 2465–2474. [6] W. Qu, I. Mudawar, Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink, Int. J. Heat Mass Transfer 45 (12) (2002) 2549–2565. [7] R. Sadeghi, M.S. Shadloo, M. Hopp-Hirschler, A. Hadjadj, U. Nieken, Three-dimensional lattice Boltzmann simulations of high density ratio two-phase flows in porous media, Comput. Math. Appl. 75 (7) (2018) 2445–2465. [8] J.R. Thome, Boiling in microchannels: a review of experiment and theory, Int. J. Heat Fluid Flow 25 (2) (2004) 128–139. [9] X.-y. Shi, H. Gao, V.I. Lazouskaya, Q. Kang, Y. Jin, L.-P. Wang, Viscous flow and colloid transport near air–water interface in a microchannel, Comput. Math. Appl. 59 (7) (2010) 2290–2304.

Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.

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Please cite this article as: M. DaqiqShirazi, A.A. Barzinjy, S.M. Hamad et al., A transient study on two phase adiabatic flow over micro circular pin heat sinks, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.10.019.