1 Introduction

With rapid development in power electronics, thermal management of small-sized electronic components has become a highly challenging problem for designer. The components are highly delicate and the critical factor which determines the life span is the operating temperature. Care has to be taken to maintain the maximum surface temperature beyond safe limit, failing would hinder long term operation of electronic devices. Presently, the researcher has proposed a solution to dissipate larger heat flux by employing micro pin fin heat sink and micro channel heat sink for efficient cooling. These heat sink are fabricated using micro machining techniques and are deemed to be advantageous where parameters like thermal resistance and heat transfer coefficient are concerned. They exhibit low thermal resistance, high heat transfer coefficient, greater heat transfer surface area and required minimum inventory which are favorable for heat dissipation. Moreover, these heat sinks are slightly modified by having either staggered or inline pin fin arrangements which proved to be more effective. The heat sink had the potential to dissipate larger magnitude of heat through smaller areas with an appreciable increase in the pressure drop.

The concept of micro channel was first proposed by Tuckerman and Pease [1], Shafeie et al [2] numerically studied the performance of heat sink with staggered and oblique arrangement and observed that oblique pin fin performs better compared to staggered for a given pumping power. Hydrodynamic and heat transfer characteristics have been explored numerically for heat sink with pin fin structures by Turker Izci et al [3], Hasan et al [4] numerically compared hydrodynamic and heat transfer characteristics of micro pin fin heat sink of different shapes using water and Nano fluids. Sohail et al [5] proposed pin fin array of various shapes to reduce maximum surface temperature. Later Abdoli et al [6] numerically investigated the influence of different pin fin shapes for cooling of electronic chips and reported pin fin with convex and hydrofoil shape performed better compared to circular cross section. Carlos et al [7] proposed variable fin density heat sink of different shapes namely circle, square, elliptical and flat plate to maintain uniform temperature of integrated chips. Flat shaped pin fins were observed to be superior compared to other shapes. Liu et al [8] experimentally proved that pin fin shape has significant effect on heat transfer at larger Reynolds number. Yavo poles et al [9] experimentally proved that the thermal resistance can be greatly reduced by employing pin fin heat sink. Zhao et al [10] experimentally showed that elliptical pin fin has better stream line with low thermal resistance and triangular pin fin has larger flow resistance compared to other shapes. John et al [11] proposed a non-dimensional zed parameter to access the performance of pin fin heat sink and proved circular fins are effective for Reynolds number smaller than 300 and square fins are better for Reynolds number greater than 300. Kosar and Peles et al [12] compared the performances of micro pin fin heat sink of different shapes namely circular, rectangular, hydrofoil, and cone-shaped. They concluded that at high Reynolds number pin fin with denser configuration has better performance, whereas sparsely configuration is better at low Reynolds number. Bayram Sahin et al [13] experimentally proved heat sink with square pin fin results in heat transfer enhancement and developed correlation for enhancement efficiency.

Judy et al [14] investigated pressure drop through micro channels with different cross sections. Lee et al [15] experimentally investigated heat transfer in rectangular micro channels, effect of surface roughness on micro channel heat sink was studied by Giulio et al [16]. Welin Qu et al [17, 18] conducted experiments through micro channel heat sink and compared the experimental results using three-dimensional conjugate model numerically, later viscosity model and roughness viscosity model were proposed to interpret experimental data. Dorin lelea et al [19] experimentally studied the performance of micro tubes using distilled water. Reiyu cheien et al [20] numerically investigated micro channel heat sink with different inlet and outlet arrangements and concluded heat sink performs better when coolant is collected vertical. Harms et al [21] reported that micro channel heat sink with smaller width and larger depth performs better. Marino et al [22] reported experimental results for heat transfer in micro channel heat sink. Peng et al [23] experimentally studied the influence of geometry on the performance of micro channel and concluded heat transfer under laminar regime is highly dependent on aspect ratio. Wu et al [24] experimentally predicted transition zone for flow inside microchannel and showed hydrodynamic and heat transfer characteristics increased with surface roughness. Zhang et al [25] proposed parallel and counter flow micro channel heat sink with bifurcations to minimize micro channel heat sink temperature. Results reveal that counter flow heat sink performs better than parallel flow and by employing bifurcation the thermal performance can be greatly enhanced. Yadav et al [26] studied the performance of micro channel with extended surface at different position.

As discussed above, studies available in open literature are mostly focussed on heat sink with different pin fin shapes and rectangular micro channel heat sink. None of the studies reports the combined effect of pin fin heat sink and micro channel heat sink. The prime focus of the present investigation is to study the combined effect of pin fin heat sink and micro channel heat sink for different pin fin shapes.

2 Description of physical model

2.1 Unfinned micro channel heat sink

The three dimensional arrangement of unfinned micro channel heat sink and its top is shown in figure 1(a) and figure 1(b) respectively. An aluminum substrate of size 11.5 mm × 6 mm with a total of 5 channels are considered for the present work. The geometrical parameters of rectangular micro channel heat sink are channel width 0.75 mm (Wch), Channel Height 1 mm (Hch), heat sink width 1.125 mm (Ws), Wall Thickness 0.375 mm (Wt), substrate thickness 0.375 mm (Ts). Owing to symmetric condition and to reduce the computational time, single element of micro channel heat sink is considered for computational model as shown in figure 1(b). Unfinned micro channel heat sink is considered to be the base line heat sink to compared the performance of pin fin heat sink and micro channel pin fin heat sink. This is taken as unfinned-MCHS.

Figure 1
figure 1

(a) Three-dimensional arrangement of unfinned micro channel heat sink. (b) Top view of single element micro channel heat sink.

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2.2 Pin fin heat sink

A three-dimensional heat sink of dimensions 11.5 mm × 6 mm × 1 mm with 50 circular pin fins of diameter 0.5 mm, height 0.5 mm and 50 square pin fins of size 0.5 mm*0.5 mm, height 0.5 mm is considered for square pin fin heat sink [HS-SPF] and circular pin fin heat sink [HS-CPF] as shown in figures 2(a), 2(b), 2(c) and 2(d), respectively . Further, staggered arrangement of fins spaced with distance of 0.5 mm is considered. Ten pin fins are considered in longitudinal direction and five in traverse direction. Longitudinal and transverse distance between pin fin are Sx = Sz = 0.5 mm, [4].

Figure 2
figure 2

(a) Three-dimensional arrangement of staggered heat sink with square pin fin (HS-SPF). (b) Top view of Staggered arrangement of heat sink with circular pin fin. (c) Three-dimensional arrangement of staggered heat sink with circular pin fin(HS-CPF). (d) Top view of staggered arrangement of heat sink with circular pin fin.

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2.3 Micro channel pin fin heat sink

A micro channel pin fin heat sink of size 11.5 mm × 6 mm with a total of 5 channels are considered. The geometrical parameters of micro channel pin fin heat sink are channel width 0.75 mm (Wch), Channel Height 1 mm (Hch), heat sink width 1.125 mm (Ws), Wall Thickness 0.375 mm (Wt), substrate thickness 0.375 mm (Ts). Ten pin fins are considered in the longitudinal direction. The dimensions of square pin fin are 0.5 mm × 0.5 mm and diameter of circular pin fin is 0.5 mm. The spacing fin distance are Sx = 0.125 mm and Sz = 0.5 mm, respectively. Owing to symmetric condition and to reduce the computational time, single element of micro channel pin fin heat sink is considered for computational model as shown in figures 3(a) and 3(b), respectively. To investigate flow and heat transfer characteristics of heat sink, water was used as working fluid and aluminum heat sink with constant properties [4] as shown in table 1.

Figure 3
figure 3

(a) Top view of single element micro channel heat sink with square pin fin (MCHS-SPF). (b)Top view of single element micro channel heat sink with circular pin fin (MCHS-CPF).

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Table 1 Properties of coolant and heat sink.
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2.4 Assumptions

The following assumptions were made to simplify the problem

  1. i)

    Flow is steady and laminar

  2. ii)

    Fluid is Newtonian and incompressible

  3. iii)

    No slip condition at walls.

  4. iv)

    There is no viscous dissipation

  5. v)

    Body forces are neglected.

2.5 Governing Equation and parameter defnition

Based on the above assumption, the following equation is solved to compute velocity and temperature distribution

Continuity equation

$$ \nabla .(\rho .V) = 0 $$
(1)

Momentum equation

$$ (u.\nabla )\rho V = - \nabla P + \mu \nabla^{2} V $$
(2)

Energy equation

$$ V.\nabla T = \frac{k}{{\rho C_{p} }}\nabla^{2} T $$
(3)

Governing equation for heat sink is given by

$$ \nabla^{2} T = 0 $$
(4)

Reynolds number at inlet is defined as

$$ \text{Re} = \frac{{\rho ud_{h} }}{\mu } $$
(5)

Where ρ is the fluid density, u is the inlet velocity, dh is the hydraulic diameter and µ is the fluid dynamic viscosity.

The maximum thermal resistance is evaluated using the relation

$$ R_{\text{max}} = \frac{T_{\text{max}} - T_{\text{in}}}{q} $$
(6)

Tmax is the maximum temperature of the bottom substrate and q is the heat flux dissipated by the bottom substrate.

The average nusselt number is computed using the relation

$$ Nu = \frac{{\text{h}_{\text{m}}\text{d}_{\text{h}}}}{k} $$
(7)
$$ h_m = \frac{Q}{nA(T_{avg} - T_{in})} $$
(8)

The required friction factor is calculated using the relation

$$ f = \frac{2.\Delta P}{{\rho .u^{2}_{\hbox{max} } }} $$
(9)

The thermal-hydraulic performance of pin fin and micro channel pin fin heat sink is accessed using a non-dimensional parameter performance index, ratio of heat transfer enhancement to rise in pressure drop. unfinned micro channel is taken as the reference for comparison with other cases. Performance Index is given by

$$ \eta = \frac{{{\raise0.7ex\hbox{${Nu}$} \!\mathord{\left/ {\vphantom {{Nu} {Nu_{o} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Nu_{o} }$}}}}{{{{(\Delta P} \mathord{\left/ {\vphantom {{(\Delta P} {\Delta P_{o} }}} \right. \kern-0pt} {\Delta P_{o} }})^{1/3} }} $$
(10)

2.6 Computational grid and boundary condition

All three-dimensional fluid flow and conjugate heat transfer analysis presented in this paper were carried out using FLUENT software. Hyper mesh was used as the computational grid generation tool. Computational domain for pin fin heat sink, unfinned micro channel heat sink and micro channel heat sink with pin fin has been discretized using structured grids of hexahedral and few tetrahedron volume elements distributed uniformly, except near the finned surface. Finer mesh has been generated for pin fin walls with a cell ratio of 1.02, as flow and heat transfer parameters are sensitive in this regions. For all the heat sink configuration, aspect ratio is less than 2, warp angle less than 5 degree. A sample mesh for staggered square and circular pin fin heat sink with zoomed view around the pin fin is shown in figures 4 and 5, respectively.

Figure 4
figure 4

(a) Meshed configuration of square pin fin heat sink. (b) Zoomed view around pin fin.

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Figure 5
figure 5

(a) Meshed configuration of circular pin fin heat sink. (b) Zoomed view around pin fin.

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The fluid velocity was computed based on flow Reynolds number \( \text{Re} = \frac{{\rho ud_{h} }}{\mu } \) and imposed at inlet where dh is the hydraulic diameter. The inlet fluid temperature at the entry was set to be Tin = 293 K.

$$ \begin{aligned} {\text{u}} & = {\text{v}} = 0{\text{ and w}} = {\text{w}}_{\text{in}} \\ {\text{T}} & = {\text{T}}_{\text{in}} \\ \end{aligned} $$

The flow is assumed to be fully developed at the outlet of the channel and zero velocity is defined at the solid boundaries. Uniform heat flux is imposed upon the bottom surface of the solid substrate, adiabatic condition was assumed for side walls in case of pin fin heat sink and symmetry condition for micro channel heat sink with pin fin, the upper wall was considered to be adiabatic. Thus, \( \frac{\partial T}{\partial x} = 0 \) and \( \frac{\partial T}{\partial y} = 0 \).

All heat sink configurations considered in the present study have same characteristic dimension. To have geometry has the only variable, the material characteristic of each pin fin is assumed to be same and uniform heat flux is applied at the bottom. The heat dissipation area for all the configuration discussed are kept constant.

2.7 Solution methodology

The governing conservative continuity, momentum and energy equations was solved using the Finite Volume Method. Convective terms was discretized using second order upwind scheme and a simple algorithm was adopted for pressure-velocity coupling to obtain the pressure field. Segregated solver was used to solve the conservation scheme. For convergence residual criteria 10−6 was used for continuity equation and velocity in all direction, whereas 10−7. for energy equation. The convergence criteria for conservative equations was set to 10−6. The entire work was carried out using FLUENT software.

2.8 Mesh independence

The grid independency was studied for heat sink with square pin fin with bottom wall temperature maintained at 373 K for Reynolds number 100 with pure water as coolant. To ensure grid independency of the results, a detailed study was carried out for various element size. The outlet temperature and pressure drop for different element size are tabulated in table 2. The percentage change in outlet temperature and pressure drop between two successive grid sizes was around 0.04% for computational grid greater than 2, 21,661 elements. Hence a computational grid with 2, 21,661 elements was sufficient for the study, which gives same result with minimum computational time and minimum memory requirement.

Table 2 Mesh independent study.
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3 Results and discussion

3.1 Validation

The present work was validated with the experimental results from literature [18].The model presented consists of rectangular micro channel of dimensions 231 µm × 731 µm. Deionized water was employed as coolant and test was conducted for 100 W/cm2 for Reynolds number ranging between 200 and 1600. The difference between the present simulation and analytical solution was very negligible. The results are validated for pressure drop and temperature drop. Figure 6 shows comparison of computed pressure drop with experimental values for increasing Reynolds number. Since pressure drop is directly proportional to square of velocity, pressure drop increases with Reynolds number. Computed pressure drop from the present work slightly under predicts experimental values. The deviation may be due to losses with sudden expansion and contraction at entry and exit of micro channel. Which is not considered while carrying out computational work.

Figure 6
figure 6

Comparison of pressure drop computed from the present work with experimental results [18].

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Figure 7 shows comparison of measured temperature drop with experimental values and analytical values obtained from energy balance. Pw = ρfCpf(Tout − Tin).

Figure 7
figure 7

Comparison of temperature drop (Tout-Tin) computed from the present work with experimental results and energy balance values [18].

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The numerically measured temperature drop decreases with Reynolds number and are in good agreement with experimental results and analytical values, indicating power supplied by heater are effectively removed by water and heat losses are negligible. Table 3 shows the comparison of computed temperature drop with experimental and analytical value.

Table 3 Temperature drop comparison between energy balance, experimental values with the present computation.
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3.2 Pressure drop and friction factor

Figure 8 illustrates variation of pressure drop (difference between upstream and downstream pressure) with Reynolds number for different cases discussed above. As expected, pressure drop in micro channel pin fin heat sink is high compared to pin fin heat sink and unfinned micro channel heat sink. In case of unfinned micro channel heat sink, when working fluid flows inside confined channel, the viscous shear effect produced due to side walls is highly dominant and contributes to total pressure drop. It can be observed that MCHS-SPF has largest pressure drop compared to other cases. Both form drag and friction drag contribute to total pressure drop. When fluid passes around sharp corners, as in case of HS-SPF and MCHS-SPF, the flow around pin fin leads to form drag, the combined effect of viscous shear and separation around sharp corner contribute to increase in total pressure drop. Whereas due to stream line separation in HS-CPF and MCHS-CPF, pressure drop is slightly less than square pin fin. For all the cases pressure drop is minimum for lower flow velocity and increases with flow velocity. At low velocity, fluid viscosity and pin fin surface are responsible for boundary layer formation around pin fin. Wall effects are highly significant and high wall shear stress is responsible for pressure drop [12].

Figure 8
figure 8

Variation of pressure drop with Reynolds number for different heat sink configurations.

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On the other hand, the wall effects become weaker and insignificant with increases in flow velocity, the force exerted by fluid due to pin fin surface increases, leading to boundary layer separation from pin fin surface and vortex formed are shed into wake resulting in very rapid rise in pressure drop. Pressure drop for MCHS-CPF increases by 63% in comparison with HS-CPF and for MCHS-SPF it increases by 58% in comparison with HS-SPF, respectively. Hence pressure drop increases with Reynolds number for all cases.

Friction factor decreases with Reynolds number, however at certain Reynolds number it reaches a constant value and remain constant thereafter. This trend is observed for all cases and are slightly inconsistent which is mainly due to the influence of different forces. The total forces exerted by fluid around solid surface is sum of forces exerted due to shear stress along flow direction namely frictional resistance and swirl resistance generated due to asymmetrical pressure distribution. At low flow velocity, frictional resistance is more compared to swirl resistance, due to the absence of vortex shedding the resistance offered is mainly due to friction. Due to inverse pressure gradient and end wall effect, separation occurs at high Reynolds number leading to vortex generation which is carried away from wake zone. The effect of swirl resistance increases with Reynolds number and becomes more dominant compared to frictional resistance. Hence frictional factor decreases with Reynolds number and remain constant due to inertia. Circular pin fin is more stream lined leading to delay in boundary layer separation and smaller wake zone compared to square pin fin as shown in figure 9. The effect of larger surface area can be the reason behind the larger pressure drop due to the friction drag [27].

Figure 9
figure 9

Variation of friction factor with Reynolds number for different heat sink configurations.

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3.3 Temperature drop

Figure 10 shows the temperature drop with Reynolds number for different cases discussed above. At low flow velocity fluid travels at slower rate absorbing maximum heat from heat sink resulting in rise in outlet temperature. Whereas at high flow velocity fluid travels at faster rate absorbing minimum heat leading to minimum rise in bulk temperature. At low Reynolds number heat transfer due to diffusion plays a key role for rise in outlet temperature and forced convection heat transfer plays a key role for drop in outlet temperature at high Reynolds number [28]. Flow around HS-CPF and MCHS-CPF is more stream lined, leading to better fluid mixing, which increases bulk temperature at outlet. Whereas in case of square pin fin, fluid flow is accelerated due to separation at sharp corners leading to drop in outlet temperature as seen in HS-SPF and MCHS-SPF. Hence Temperature drop for circular pin fin is slightly on the higher side compared to square pin fin for both pin fin heat sink and micro channel pin fin heat sink.

Figure 10
figure 10

Variation of temperature drop with Reynolds number for different heat sink configurations.

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3.4 Maximum thermal resistance

Figure 11 shows variation of maximum thermal resistance with Reynolds number for different configurations of heat sink. For all cases of heat sink, thermal boundary layer thickness decreases with Reynolds number resulting in maximum heat transfer thereby decrease in thermal resistance. For flow around HS-SPF and MCHS-SPF, fluid separates around sharp corners triggering flow separation and promoting fluid mixing [12]. The wakes formed around square pin fin are large compared to circular pin fin leading to decrease in thermal resistance as shown in figures 14 and 15.

Figure 11
figure 11

Variation of thermal resistance with Reynolds number for different heat sink configurations.

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Maximum thermal resistance for MCHS-SPF and MCHS-CPF are low compared to HS-SPF and HS-CPF. The main reason is that, in case of micro channel heat sink with pin fin the combined effect of axial conduction phenomenon along flow direction and forced convection leads to decrease in thermal resistance; whereas the axial conduction effect is highly negligible for pin fin heat sink leading to increase in thermal resistance. This shows that axial conduction plays a key role in enhancing heat transfer for micro scale [8]. Thermal resistance for MCHS-SPF decreases by 42% in comparison with HS-SPF whereas for MCHS-CPF decreases by 57% compared to HS-CPF.

3.5 Flow pattern

Figures 12 and 13 illustrate temperature distribution and velocity distribution slice taken from the centre line along the symmetry plane for different cases. The temperature at the entry is 293 K everywhere. The temperature rise starts at the upstream point of the flow domain, and the heated fluid layer becomes thicker as it gets closer to the outlet as shown in figure 12. While the temperature for different cases would certainly change along the longitudinal direction. For all cases, temperature distribution is maximum at the corner of heat sink since there is negligible amount of heat dissipation due to convection. The minimum temperature occurs at the entry of heat sink which is mainly due to higher heat transfer coefficient at the entry. The presence of pin fin interrupts the temperature profile and does not allow the boundary layer to grow to fully developed state as shown in figure 12. Due to flow interruption there is a redevelopment in thermal boundary layer resulting in better fluid mixing thereby increasing heat transfer. Along with this heat transfer is further enhanced due to the presence of pin fins.

Figure 12
figure 12

Temperature (K) contour along the symmetric plane passing through central vertical line for different heat sink configurations.

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Figure 13
figure 13

Velocity (m/s) contour along the symmetric plane passing through central vertical line for different heat sink configurations.

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Figure 13 indicates the average flow velocity is high for MCHS-SPF and MCHS-CPF compared to HS-SPF and HS-CPF. Higher flow velocity brings about more heat transfer from hot surface to coolant thereby contributing to enhancement in heat transfer which in turn reduces the surface temperature of heat sink.

The stream line across MCHS-SPF and MCHS-CPF for different Reynolds number is shown in figures 14 and 15. When the flow velocity increases, the force exerted by fluid from, pin fin surface increases leading to flow separation around pin fin and wake formation. Increase in flow velocity promotes flow separation leading to increase in larger wake zone [3]. From the stream line contour it is very clear that secondary vortices are formed for both MCHS-SPF and MCHS-CPF, This may be due to the influence of turbulence promoting flow separation at low Reynolds number. Formation of secondary vortices is delayed for MCHS-CPF compared to MCHS-SPF due to stream line separation. When Reynolds number increases from 100 to 900, length of recirculation zone increases from 0.38*10−3 m to 0.49*10−3 m for MCHS-SPF and 0.3 × 10−3 m to 0.42 × 10−3 m for MCHS-CPF. Recirculation zone is broader for pin fin with sharp corners compared to stream line separation showing pronounced flow separation leading to intense mixing of fluid resulting in heat transfer enhancement.

Figure 14
figure 14

Stream line contour with Reynolds number for MCHS-SPF.

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Figure 15
figure 15

Stream line contour with Reynolds number for MCHS-CPF.

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3.6 Nusselt number

Figure 16 demonstrates nusselt number as a function of Reynolds number for different cases. As expected nusselt number increases with Reynolds number for all the cases. Nusselt number for micro channel pin fin heat sink (MCHS-SPF and MCHS-CPF) and pin fin heat sink (HS-SPF and HS-CPF) are high compared to unfinned-MCHS, which is mainly due to the presence of extended surfaces.

Figure 16
figure 16

Variation of nusselt number with Reynolds number for different heat sink configurations.

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The temperature profile for HS-SPF, HS-CPF, MCHS-SPF and MCHS-CPF is highly disrupted due to the presence of pin fins as shown in figures 12 and 13, thereby not allowing the thermal boundary layer to reach the fully developed state. This disruption is due to the presence of pin fins leads to redevelopment of thermal boundary layer [26], also the presence of pin fin intensifies flow separation absorbing maximum heat from solid pin fins and increasing heat transfer. The collective effect of redevelopment of boundary layer and better fluid mixing is responsible for increase in Nusselt number for heat sink with pins. The Nusselt number trend for pin fin heat sink is similar to the result obtained in numerical study by [3].

The performance of heat sink based on nusselt number form higher to lower value are in the order MCHS-SPF, MCHS-CPF, HS-SPF, HS-CPF and unfinned-MCHS. Pin fins with sharp corners triggers flow separation and has larger surface area compared to circular pin fin, hence heat sink with square pin fin performance is better compared to circular pin fin.

The main objective of the study was to decrease the maximum surface temperature and enhance high heat transfer rate. By employing micro channel with pin fin the conduction heat transfer can be highly enhanced compared to pin fin heat sink resulting in higher heat transfer rate thereby reducing surface temperature. The values of pressure drop and nusselt number for various heat sink configuration are provided in table 4.

Table 4 Comparison of pressure drop and nusselt number for various heat sink configuration.
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3.7 Thermal performance index

The presence of extended surface in pin fin heat sink and micro channel pin fin heat sink has better heat transfer performance compared to unfinned micro channel with rise in pressure drop. Hence a non-dimensional parameter namely thermal performance index (TPI) is defined to study the overall performance of pin fin heat sink and micro channel heat sink by comparing with unfinned micro channel. Thermal performance index is defined as \( \eta = \frac{{{\raise0.7ex\hbox{${Nu}$} \!\mathord{\left/ {\vphantom {{Nu} {Nu_{o} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Nu_{o} }$}}}}{{{{(\Delta P} \mathord{\left/ {\vphantom {{(\Delta P} {\Delta P_{o} }}} \right. \kern-0pt} {\Delta P_{o} }})^{1/3} }} \). Figure 17 shows the variation of thermal performance index with Reynolds number subjected to 10 W/cm2. This clearly shows the overriding rise in overall pressure drop compared to increase in heat transfer. For fluid flow in MCHS-SPF and MCHS-CPF the intensity of velocity fluctuation is more rapid compared to HS-SPF and HS-CPF. Micro channel pin fin heat sink (MCHS-SPF and MCHS-CPF) are highly sensitive to end wall effect the same penetrates to main flow more rapidly compared to pin fin heat sink (HS-SPF and HS-CPF) leading to increase in pressure drop. Hence in terms of TPI, pin fin heat sink are considered to be superior compared to micro channel pin fin heat sink.

Figure 17
figure 17

Thermal performance index with Reynolds number for different heat sink configurations.

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3.8 Local Nusselt number and friction factor for micro channel pin fin heat sink

Figures 18 and 19 illustrate variation of local Nusselt number along the length of micro channel heat sink for MCHS-SPF and MCHS-CPF. Nusselt number is very large at the entry of channel and decreases to a constant value along the flow direction due to thinning boundary layer approaching fully developed flow. As Reynolds number increases thermal developing length shift towards right for both cases whereas developing length is slightly delayed for MCHS-SPF this may be due to wake effect. The thermally entry length ratio [29] (Lthr = Lth/L) increase from 0.17 to 0.78 and 0.15 to 0.65 for MCHS-SPF and MCHS-CPF with rise in Reynolds number from 100 to 900, respectively.

Figure 18
figure 18

Variation of Nusselt number along the length of channel for different Reynolds number for MCHS-SPF.

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Figure 19
figure 19

Variation of Nusselt number along the length of channel for different Reynolds number for MCHS-CPF.

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Due to entrance effect in MCHS-SPF friction factor is very large at entry compared to MCHS-CPF and reaches a constant value at the exit of channel approaching hydrodynamic fully developed flow. For Reynolds number 100 the flow is assumed to be hydro dynamic by a value 0.007 m and 0.0072 m for MCHS-SPF and MCHS-CPF as shown in figures 20 and 21. This shows that the sufficient length of micro channel heat sink is in the entrance region. Hydrodynamic entrance length increases with Reynolds number and implies that the hydrodynamic entrance effect is extended along the channel.

Figure 20
figure 20

Variation of friction factor along the length of channel for different Reynolds number for MCHS-SPF.

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Figure 21
figure 21

Variation of friction factor along the length of channel for different Reynolds number for MCHS-CPF.

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4 Conclusion

In the present work, experimentally tested system were numerically modelled at Reynolds number between 200 and 1600. The numerical results were compared with experimental data to show the credibility of numerical method. Later, thermal hydraulic performance of pin fin heat sink and micro channel pin fin heat sink was compared with unfinned micro channel heat sink based on pressure drop, friction factor, nusselt number, performance index and stream contours.

The novelty of the present work lies in the fact that, the combined effect of micro channel heat sink with different pin fin shapes are examined to show its effect on thermal-hydraulic performance and compared with pin fin heat sink.

Based on the present work the following conclusions were drawn.

  1. 1.

    The combined effect of axial conduction and forced convection plays a key role in decreasing maximum thermal resistance for MCHS-SPF and MCHS-CPF. Maximum thermal resistance for MCHS-SPF decreases by 42% compared to HS-SPF and for MCHS-CPF it decreases by 57% compared to HS-CPF, respectively. MCHS-SPF and MCHS-CPF are observed to be far superior when compared to pin fin heat sink (HS-SPF and HS-CPF) in terms of heat transfer enhancement, indicating that the micro channel pin fin heat sink can be significantly a better alternative for pin fin heat sink.

  2. 2.

    The effective convective heat transfer gives importance to elucidating means for incorporating various pin fin shapes and increase in flow rates. However, the presence of pin fins and high flow rates necessitate higher pressure drop. Thus pressure drop is a major concern during the design of heat sink. Further, more efforts are made to develop better heat sink configurations which significantly enhances heat transfer with minimum pressure drop. Hence a non-dimensional parameter namely, thermal performance index based on unfinned micro channel heat sink increases with Reynolds number and HS-SPF has highest performance index compared to other heat sink configuration, which shows that HS-SPF would be a better alternative when combined effect of heat transfer and pressure drop are considered.

  3. 3.

    The formation of secondary vortices for MCHS-SPF has strong influence on enhancement of heat transfer compared to MCHS-CPF. The Thermal entry length for MCHS-SPF is slightly delayed due to wake formation and study shows that sufficient hydrodynamic length of channel is within the entrance region for both MCHS-SPF and MCHS-CPF. Recirculation zone is broader for pin fin with sharp corners compared to stream line separation showing pronounced flow separation leading to intense mixing of fluid resulting in heat transfer enhancement.

  4. 4.

    At low velocity, the presence of pin fin has little influence on flow and is evident at high velocity. The pressure drop increases with flow velocity and is sufficiently large for fluid flow with sharp separation compared to stream line separation for both micro channel pin fin heat sink and pin fin heat sink. Pressure drop for MCHS-CPF increases by 63% compared to HS-CPF whereas for MCHS-SPF it increases by 58% compared to HS-SPF.

  5. 5.

    The water outlet temperature and temperature with in heat sink for all configurations could be greatly reduced at higher Reynolds numbers with penalty in pressure drop.