Thermo-hydraulic investigation of two stepped micro pin fin heat sink having variable step size

. To achieve enhanced flux dissipation, microchannels heat sink are being effectively implemented in various engineering processes. Here, a numerical analysis is to be carried out on an open stepped micro pin fin heat sink (MPFHS) with different step size. The stepped pin fin heat sink (PFHS) having varied fin height in an array of two fins having inline arrangement. For the simulation purpose, a single-phase water was used as working fluid with variable thermophysical properties. The present configuration has operated for Reynolds number =100-500, heat flux of 500 kW/m 2 . The step variation of 100 µm, 200 µm and 300 µm has been considered. It was observed that with increase in step size, the heat transfer augmentation also increases. However, at higher Reynold number, the present studies does not provide effective results in terms of sustainability.


Introduction
Classical thermodynamics defines heat sinks as devices that can reject any amount of heat without raising its temperature.It forms the basis of various thermodynamics systems which are currently giving their service in various thermal plants, electronic companies.Management of heat intake and heat that is released to environment is very important because performance of system has a lot to depend on this intake and outgoing of heat.Various techniques have been developed to tackle this flow of heat in and out of system for large systems that are no doubt operating exceptionally.But systems with micro heat sink are difficult to examine for heat flow.On the other hand, these systems are physically impossible to construct.Heat sinks, whether industrial or commercial, work on the same principle: they use thermal contact to absorb useless heat which generates in various operations.In the recent past, the electronic industry has experienced dramatic reductions in component size after the introduction of transistors.Heat dissipation is always linked to the flow of electric current via any electrical device.As a consequence, a drastic increase in the produced heat in a unit volume has been sought.In the foreseeable future, it will probably certainly approach 1000 W/cm 2 and that too is expected to increase further at a higher pace [1].The inadequate management of heat dissipation can lead to diminish of efficiency due to excessive heat and perhaps cause irreversible harm to the equipment.More than half of all electronic (VLSI) circuit failures, according to Pedram and Nazarian [2], are due to poor thermal management.Efforts must be taken to construct an appropriate cooling system so that it can be used safely and for a longer time.Because, typical cooling technologies that use medium of cooling via natural or forced air (through a fan or fins) are unable to disperse heat in these devices [3,] better arrangements are necessary to dissipate a large amount of heat from a limited space.These systems are also huge, noisy, and tremble.When compared to liquids, air has a low thermal conductivity, resulting in meagre heat dissipation.Observations received discovered that cooling through liquids provide 4-10 times the heat flux of a system cooled with air.The results displayed by microchannels heat sink (MCHS) has necessitates the research fraternities to switch from conventional techniques like jet impingement, micro heat pipe, thermoelectric, spray cooling, etc. [4,5].This is due to its intrinsic properties of high Surface/volume ratio [6] and effortlessness of application.Tuckerman and Pease [7], for example, were among the first to adopt microchannels for heat dispersion, emphasizing its implementation in cooling of electronic devices.This makes the basis of microchannels heat sink applications to improve design modifications and thermal performance for its feasibility and viability.

Literature review and objective
The existing literature describes both active and passive methods for enhancing heat transmission through micro-channels.Microchannels are combined with additional approaches such as vibration and electrostatic forces in active procedures.Passive methods are used to change the fundamental characteristics of microchannel heat sinks.Passive techniques include micro-channel design alterations, the use of alternate working fluids such as nanofluids, and operating conditions of coolant [8][9][10][11].Strategy revisions include configurations of pin fin for MCSH.Micro pin fin configurations offer higher area of convective surface, enhanced mingling of fluid, secondary flow, and disturbance caused by boundary layer.To improve the performance of micro PFSH, several researchers have experimented with varying pin fin forms, sizes, orientations, and densities [12][13][14][15].The parameters of tip clearance were found to be improved thermal performance while minimizing pressure dropin microchannel heat sinks.Prajapati [16] discovered that height of fin ranging 0.8 to 0.85 of height of channel is considered to be ideal.In their numerical analysis, Bhandari and Prajapati [12] made a similar observation.Figure 1 shows how pin fins are used in a stepwise fashion to improve the performance of open microchannel layouts.As per the recent publications [14][15][16][17][18][19][20], stepped pin fins in 3 and 4-rows arrays outperform two-row arrays.They also discovered that increasing the number of pin fins outperformed decreasing the pin fin numbers in terms of overall performance.

Page layout Geometry and numerical modeling\
Figure 2 shows isometric diagram of micro PFHS.Pin fins have a lower height than channel height, as shown in Figure 3(a).Heat sink (3Dimensional) geometries, was numerically solved in this study for different substrate materials.L×W×H = 21.50×12.50×2.00mm is the overall dimension of the computing domain.The heat sink was architected in a manner that square pins in series was made having variation in pin heights comprising the total number of pin fins rows are 20 and that each row of heat sink contains 10 fins.As a result, 200 fins having square size of similar dimensions with a footmark area of 0.5×0.5 mm 2 are arranged at pitch distance of 1.0 mm.

Fig. 2 Isometric view of micro pin fin heat sink
Two side walls having a dimension of 0.5 mm x 1 mm were used on the opposite side of heat sink that permits the flow of fluid between them.In addition to it, 1 mm of plenums were provided at inlet as well as outlet that authorizes organized and smooth flow of working medium.Needless to mention, with suitable physical properties of water, it is therefore used as working fluid in the current simulation.The current model's details are shown in Table 1.Fig. 3.Side view of two stepped micro pin fin heat sink (i) 0.6 mm-0.7 mm (ii) 0.6 mm-0.8 mm (iii) 0.6 mm-0.9 mm

Governing equations
The conjugate technique was applied in solving the problem with working fluid as a water in single phase.For the sake of simplicity, some assumptions are considered in the condition of steady state: Where V = velocity matrix.The thermo-physical properties of the water was regarded as temperature's polynomial function to predict better results [12].These relationships hold true for a range of 5-95°C, which matches the current operating range perfectly.The said relationships were taken into account by Fluent when designing the coolant properties.In this investigation, the Reynolds number (Re) was computed as follows: Where, uniform velocity uin was assumed at the inlet plenum's.Dh is the micro pin fin heat sink's hydraulic diameter, which in present configuration is 0.5 mm.The hydraulic diameter for all three configurations is same i.e. 0.5 mm.The heat transfer coefficients has been calculated as , c , ) ( - The following expression was applied in computation of average Nusselt number (NU).
, c , ) ( - Tavg,cw = mean temperature of contact surface of solid and liquid, and Tbulk,l is the bulk fluid temperature accessible of heat sink at any given time in the equation above.The area weighted average temperature, Tavg,cw, is calculated, and the volume average temperature, Tbulk,l, is estimated for the fluid domain.qeff stands for the effective heat flux, which is determined using the equation below.The bottom wall surface area is Abw, while the solid-liquid contact surface area is Acw.For all configurations, bottom wall surface area is constant i.e. 268.75 mm 2 , while the convective surface area is 550.25 mm 2 , 568.25 mm 2 and 590.25 mm 2 for 0.6 mm-0.7 mm, 0.6 mm-0.8 mm and 0.6 mm-0.9 mm configuration, respectively.The present simulation was performed on commercial code ANSYS 18.0 (Fluent module).Calculations of governing equations were made with the help of scheme of SIMPLE to which convergence criteria was kept to 1×10 -4 for continuity equation.However, for the velocity in three directions i.e., x, y, and z, the convergence criteria were kept to 1×10 -6 .For the simplifications of energy equation, 1×10 -7 was kept as convergence criteria.

Results and discussion
To examine the effect of step size on thermal and hydraulic characteristics, 3 different step sizes were chosen.The stepped (inline) configuration has been simulated for these heat sink materials at heat flux of 500 kW/m 2 .Heat transfer coefficients variation for different step size has been depicted in fig. 4. Similar trend is also observed for the average NU in Fig. 5 as the step size increases, average NU increases.However the slope of curve flattens at higher Reynold number.The variation of T bw ̅̅̅̅̅ for different substrate material is illustrated in fig.6.and it was found that significant augmentation is achieved when step size varies from 100 µm to 200µm.But, this behaviour degrades when step size varies from 200 µm to300µm.In present work, drop in pressure was determined as inlet and outlet pressure difference.Figure 7 display the change in drop in pressure against different Re.As obtained from figure 7, it is to be found that highest drop in pressure was achieved for the case of 0.6-0.9mm whereas lowest was obtained for the case of 0.6-0.7 mm.This may be due to increased flow obstruction in the 0.6-0.9mm case.

Conclusion
Two stepped microchannel heat sink with inline arrangement has been simulated for different step size.The step size has been varied from 100 µm-300µm.Using single phase of flow of water and pin fins of square shape for the comparative numerical analysis under operating conditions of heat flux of 500 kW/m 2 and Re = 100-500.On the basis of present study, it can be concluded that 200µm step size has shown better thermo-hydraulic performance compared to 100 µm and 300 µm.

Fig. 1
Fig. 1 Various microchannel configurations opted in literature The current study is dealing to understand the influence of step size on thermo hydraulic performance of MCHS.The stepped configuration in inline arrangement has been used in present work.The next section focuses on detailed dimensions of present heat sink model.The stepped configuration is chosen as it has shown better performance compared to uniform configurations due to improved fluid mixing, increased 3-D of fluid flow, and disruption of the boundary layers occurs due to thermo-hydraulic effects.On the basis of the foregoing discussion, a numerical comparison of 3 step size of open micro pin fin heat sinks for single phase fluid flow was conducted.
(a) working fluid is incompressible follows and law of Newtonian.(b) flow is assumed as constant.(c) No slip boundary conditions are assumed at the interface.(d) Effect of radiation is not considered.(e) Except for the bottom wall, all surface walls are adiabatic.With respect to the assumption as made in the study, mass conservation, momentum, energy, equation of continuity and Navier-Stokes Equations were applied to descirbe fluid flow and phenomena of heat transfer.Below expressions are used to express the laws (1-4).

Fig. 4 :
Fig. 4: Variation of heat transfer coefficients with Re for different configuration at heat flux of 500kW/m 2

Fig. 5 :
Fig. 5: Variation of Nu ̅̅̅̅ with Re for different substrate material at heat flux of 500 kW/m 2

Fig. 6 :
Fig. 6: Variation ofT bw ̅̅̅̅̅ with Re for different substrate material at heat flux of 500 kW/m 2

Table 1 .
The heat sink's dimensional parameter In present simulation, two stepped open MCHS has been opted.The different configurations considered are depicted in Fig.3.The first configuration has fin height variation in 0.6 mm -0.7 mm order, second one is having 0.6 mm-0.8 mm and last one has 0.6 mm -0.9 mm order.