Forced Convection Heat Transfer In A Microchannel With Nanofluid Incorporating Different Geometry Saima Aktar Sumaiya, Maahi Muhiuddin Talukder and A. K. M. Monjur Morshed1,a) 1
Bangladesh University of Engineering and Technology, Dhaka a)
Corresponding author:
[email protected]
Abstract. Microchannels are currently of great interest for use in compact heat exchangers and electronic circuits being extensively used where very high heat transfer performance is desired. In this present study, the effect of incorporating fins of different shape, circular and triangular, on fluid flow and heat transfer in microchannel heat sinks have been investigated comprehensively and the results were compared with that of microchannel without fin. Water and water based alumina ( H2 O + Al2 O3 ) nanofluid were used as the working fluid. Performance has been evaluated based on average Nusselt number and pressure drop characteristics. The study was performed numerically using commercially available CFD platform FLUENT. The microchannel with triangular fin was found to have the best thermal performance compared to the other two configurations.
INTRODUCTION Thermal management is pivotal to effective functioning of devices comprising of electronic circuits. The placement of a large number of electronic circuits in a device platform leads to the generation of high heat fluxes. The failure to remove such high heat fluxes is likely to result in malfunction of circuits, which along with increased substrate temperature would eventually lead to the total failure of the device. The contradictory requirements of high heat dissipation and low temperature rise are commonly required for a wide range of applications. The microchannel heat sink can make those two contrasting features converge at one point which can be attributed to its unique construction enabling the designers to bring a heat source and a heat sink into close proximity, thus minimizing thermal resistance. Tuckerman and Pease[1] first performed experiments on silicon based microchannel heat sink. Peng and Peterson[2] presented an analytical and numerical study on the heat transfer characteristics of forced convection across a micro channel heat sink. Judy et. al. [3] did pressure drop experiments on both round and square microchannels. They tested distilled water, methanol and isopropanol over a Reynolds number range of 8 to 2300. Their results showed no distinguishable deviation from laminar flow theory for each case. Steinke et. al. [4] presented an analytical approach for characterizing electronic packages, based on the steady-state solution of the Laplace equation for general rectangular geometries, where boundary conditions are uniformly specified over specific regions of the package. Qu and Mudawar [5] conducted a similar type investigation by developing a fully explicit two - dimensional incompressible laminar Navier-Stokes solver using a Cartesian grid. Developing flow heat transfer in micro-channel was investigated by Lee et. al. [6] and they proposed analytical correlation between Nusselt number and non-dimensional flow length for developing flow in microchannel. Heat transfer rate is very high in the developing zone compared to developed zone. The result of Al - Bakhit et. al. [7] found that entrance region the developing velocity profiles lead to higher values of overall heat transfer coefficient. Gunnasegaran et. al. [8] studied the effects of geometrical parameters on heat transfer and fluid flow in microchannel heat sink. It is found that the temperature distribution is much uniform for the smallest hydraulic diameter of the micro-channel heat sinks, and pressure drop and friction factor are larger. Cho et. al. [9] investigated the cooling performance of microchannel heat sinks with different geometric structures under various heat flux conditions. Chai et. al. [10] studied and optimized the structural parameters of the microchannel with offset fan-shaped re-entrant cavities, triangular re-entrant cavities and aligned fan-shaped re- entrant cavities by numerical simulation of flow and
heat transfer mechanism. The first study on the possibility of increasing thermal conductivity of a solid-liquid mixture by adding more volume fraction of solid particles was done by Maxwell [11]. Several investigations revealed that the thermal conductivity of the nanoparticles suspension could be increased by more than 20% for the case of very low nanoparticles concentrations. In this present study, a measure has been undertaken to examine the opportunities of enhancement of heat transfer by employing nanofuid as the working fluid and also by incorporating different roughness element in a simple straight rectangular microchannel. The numerical analysis has been performed using the commercial CFD package ANSYS FLUENT. The performance of the heat sink with different features has been compared on the basis of Nusselt number.
Model and Formulation The microchannel we have used for our simulation purpose is 10 mm in length, 180 µm in height, and 57 µm in width. The substrate is 10mm in length, 900 µm in height, and 100 µm in width. The microchannel is not placed at the middle of the substrate , rather the centreline of the channel is offset from the centreline of the substrate by 90 µm. In the finned microchannel, the cylindrical fins are 30 µm in diameter and 50 µm in height. They are five such fins along the base of the channel and they are placed in such a way that the centre-to-centre distance between two adjacent fins is 1.5 mm. And in case of the triangular fin, the height of the triangular wedge is 50 µm, the base of the triangle is 30 µm, and the height of the triangle is 800 µm and there are three such fins placed along the base of the channel. Fig. 1 and 2 depict different aspects of our models. Discretization of the computational domain has been done by GAMBIT by creating mesh. In case of simple channel the mesh created is structured in nature. But in case of the finned channels the mesh generated is unstructured and the elements were tetragonal or hybrid. The channel inlet has been chosen to be pressure-inlet and the flow is assumed to be fully developed flow. The pressure at the inlet is varied at 10, 20, 30, 40, 50 KPa (gauge). The channel outlet has been chosen to be pressureoutlet. The pressure at outlet has been kept constant at atmospheric pressure or 0 pascal (gauge). At inner wall surfaces no slip condition prevails i.e. u = v = 0. For thermal boundary conditions, adiabatic boundary condition is applied to all the boundaries of the solid region except at the heater surface i.e. the bottom surface. Heat flux at the bottom surface has been varied as 50, 90 and 150 W/m2 . Governing equations take the following form: Continuity equation: ∂ρ ~ =0 + ∇.(ρV) (1) ∂t Momentum equation: ~ ∂V ~ V ~ = −∇P + ρ~g + ∇.τi j ρ + ρ(V.V) (2) ∂t Energy equations: k∇2 T = 0 (3) Re =
ρV Dh µ
hDh kf q h= Tw − Ti Nu =
For nanofluid:
(4) (5) (6)
ρn f = (1 − ϕ)ρb f + ϕρ p
(7)
C Pn f = (1 − ϕρb f ) + ϕC P p
(8)
µn f = 123ϕ2 + 7.3ϕ + 1
(9)
kn f = 4.97ϕ2 + 2.72ϕ + 1
(10)
FIGURE 1. (a) Simple Microchannel, (b) Front view of the model
Numerical Simulaition In order to perform numerical analysis of the model considered in this study, commercial CFD package ANSYS FLUENT has been used. At first water with constant properties has been used as the heat transfer fluid and silicon as the heat sink material with properties as k = 140 W/m-K, C p = 714 J/kg-K, ρ = 2330 kg/m3 . Later in this study, nanofluid consisting of water with 4% volume fraction of Al2 O3 has been used as the coolant with properties of the particle as k p = 36 W/m-k, C P p = 773 J/kg-k and ρ p = 3880 kg/m3 . Pressure based solver has been employed since incompressible fluid has been used. As the governing equations involved are nonlinear and contain many dependent variable, implicit formulation has been used. Maximum Reynolds number under consideration being 103.4, a laminar model has been used to solve the governing equations. SIMPLE scheme has been used for pressure velocity coupling. To discritize the governing equations second order upwind scheme has been employed. The convergence criteria have been set as 10−8 for energy and 10−4 for all other variables. A mesh independence test has been conducted to claim the reliability of the results obtained. Three different mesh of 59400, 102800 and 113000 cells have been created for the straight channel. For each of the three mesh temperature profile along the channel have been plotted. The mesh with 102800 cells has shown negligible difference of about 0.5% as compared to the mesh of 113000 cells as illustrated by Fig. 3. Hence, the mesh with 102800 cells has been adopted to generate the case study results hereafter.At the very beginning of the study Nu is calculated for the straight channel with water as working fluid from the numerical results obtained from FLUENT. This result is compared with that obtained from Nusselt number correlations proposed by Lee et. al. [6]. Although the numerical results dont match exactly with the analytical results, they tend to follow the same pattern. The maximum discrepancy is about 7%. The reason behind this discrepancy lies with the quality of the mesh. Since the numerical results follow the same trend as that of the analytical one, we get inspiration to proceed for further investigation. The discrepancy between analytical and numerical result is illustrated in Fig. 4.
Results and Discussion Heat transfer performance of microchannel heat sink with different geometry was investigated in this study. At first we studied the simple straight rectangular channel with water as the heat transfer fluid. We determined the temperature profile, heat transfer coefficient, Nu for this geometry. Then cylindrical fins were incorporated in the straight channel to take advantage of the increased surface area and similar investigation was performed. The numerical results obtained for this geometry were compared with those of straight rectangular channel. A higher heat transfer coefficient and higher Nu reveals improvement in heat transfer which validates that greater surface area results in better heat transfer rate. In order to take advantage of increased surface area along with the effect of boundary layer interruption, we incorporated triangular ribs in the straight rectangular channel. Similar investigations were performed as that of straight channel and straight channel with cylindrical fins to obtain the numerical results. The results were compared with the previous ones. Although the heat transfer coefficient and Nu are clearly higher than those of straight rectan-
FIGURE 2. (a) Cylindrical Fin, (b) Top view of the model with cylindrical fins, (c) Triangular ribs, (d) Top view of the model with triangular ribs
315 59400 cells 102800 cells 113000 cells
T (k)
310 305 300 295
0
0.0025
0.005 x(m)
0.0075
0.01
FIGURE 3. Temperature Profile along the Channel for Different Mesh Size
gular channel, they have only slightly been improved than those of cylindrical fins. The slightly better performance is possibly due to the effect of boundary layer interruption introduced by the ribs. Fig. 5 and 6 shows the improvement of incorporating cylindrical fins and triangular ribs. Whether water or nanofluid is used as working fluid, fins and ribs enhance cooling capacity of microchannel heat sink. The results indicate that Nu of microchannels with fins and ribs can 1.25 - 1.31 times of simple straight rectangular channel. These roughness elements disturb the flow and create recirculation flow and decrease the thermal boundary layer thickness, thus enhancing heat transfer rate and hence cooling capacity. Initially water was used as the working fluid in this study which provides quite good results. In quest of further improvement of heat transfer nanofluid was employed as the working fluid. Small solid particles suspended in a fluid
9
From Lee [6] From FLUENT
Nu x
8 7 6 5 4 0
0.05 0.1 0.15 0.2 X ∗ = X/(ReP rDh )
0.25
FIGURE 4. Comparison of Numerical Results with Analytical Solution
10
Nu avg
7.5 5 Straight Channel Cylindrical Fin Triangular Rib
2.5 0 0
50
100
150
Re FIGURE 5. Variation of Average Nusselt Number with Reynolds Number (Water)
8 Nu avg
6 4 2
Straight Channel Cylindrical Fin Triangular Rib
0 0
20
40
60
Re FIGURE 6. Variation of Average Nusselt Number with Reynolds Number (Nanofluid)
are supposed to improve its thermal conductivity since the thermal conductivity of solid metals is higher than that of the fluids. To take advantage of this fact a single phase model of nanofluid with physical and thermal properties-all assumed to be constant with temperature was employed to study the heat transfer performance of the microchannel heat sink. In the single phase model the fluid with the suspended nanoparticles is assumed to be continuous. The advantage of using single phase lies with its simplicity and less computational time required. In this study nanofluid
composed of distilled water and Al2 O3 nanoparticles with volume fraction of 4% was employed. The numerical results reveal higher heat transfer coefficient for nanofluid which in turn means higher Nu. It is due to the higher thermal conductivity of the nanoparticles than the base fluid (water) and also a better energy exchange process resulting from the chaotic movement of nanoparticles. Using nanoparticles has improved the thermal conductivity of the working fluid by 11.67% as compared to the base fluid. Nanoparticles havealso improved the average Nu up to 1.35 times as compared to base fluid. Although the nanofluid actually being a two phase fluid, the results show that it acts as a single phase fluid than a liquid-solid mixture. The results also represent that nanofluid enhances the effectiveness of the microchannel heat sink for all the geometries considered in this study. It is evident from Fig. 7, 8 and 9 that for the same value of Re, nanofluid provides better heat transfer performance. We can further conclude that nanofluid can significantly increase heat transfer rate even for relatively small volume fraction.
6
Nu
4 2 Water Nanofluid
0 0
20
40
60
Re FIGURE 7. Comparison of Nu between Water and Nanofluid for Straight Rectangular Channel
8
Nu
6 4 2 0
Water Nanofluid
0
20
40
60
80
Re FIGURE 8. Comparison of Nu between Water and Nanofluid for Rectangular Channel with Cylindrical Fin
For each case considered in this study including geometry and coolant, three different value of heat flux have been used to heat the Silicon substrate. The values of heat flux were 50 W/cm2 , 90 W/cm2 and 150 W/cm2 . The temperature profile of the heat sink along the length of the channel should be linear theoretically due to constant flux applied. We have also got almost linear profile of temperature in each case. The temperature increases towards outlet. The reason behind this is that at inlet the fluid is capable of extracting more heat. As a result it takes away more heat with it from the inlet region. As it approaches the outlet, its ability of removing heat from the solid decreases. Thats why, the temperature of the Silicon substrate is higher near the outlet region. Again due to increasing value of flux, the temperature of the solid at each section increases. However, heat flux has almost no effect on the local Nu.
8
Nu
6 4 2 0
Water Nanofluid
0
20
40
60
80
Re FIGURE 9. Comparison of Nu between Water and Nanofluid for Rectangular Channel with Triangular Ribs
Reynolds number (Re) has significant effect on convective heat transfer. To get a detailed scheme of the implication of Re on the performance of the microchannel heat sink, computations have been carried out by varying pressure difference between inlet and outlet of the fluid channel. In this current study pressure difference has been varied in the range of P = 10 - 50 KPa (g) with an increment of 10 KPa for all geometry and working fluid. With elevating pressure the velocity of the working fluid increases which in turn increases Re. Higher Re implies that forced convection is dominant over natural convection which means that forced convection governs the flow. When water is used as the working fluid, Re varies in the range of Re = 18.55 - 103.4 including the effect of different geometry. In case of nanofluid Re varies in the range of Re = 9.67 - 54.57 including the effect of different geometry. show that for the same value of Re, nanofluid provides better heat transfer performance. Convective heat transfer phenomena are best described in terms of Nu. The higher the Nu, the higher is the convective heat transfer. In this current study, we have determined both Nu x i.e. Nu along the channel and average Nu. The variation of Nu x along the length of the channel has been determined for various pressure differences between the inlet and outlet. The profiles of local Nu for all the geometries and working fluids considered in this study have almost the same pattern. Nu x is dependent on temperature gradient. Fig. 10 shows proflie of Nu along the channel with triangular ribs with nanofluid as the coolant. As temperature gradient near the inlet zone is higher, Nu is higher in this area. This phenomenon also validates the fact that at the beginning of the channel, fluid is capable of transferring more heat from solid surface and so convective heat transfer is higher in this region. As the fluid proceeds through the channel, its temperature increases and hence heat transfer rate decreases. Therefore, convective heat transfer decreases near the outlet zone.
20 10 20 30 40 50
Nu X
15 10
KPa KPa KPa KPa KPa
5 0
2
4
6 x (mm)
8
10
FIGURE 10. Profile of Nusselt number along the channel in Rectangular Channel with Triangular Ribs with Nanofluid
Conclusions The present study has dealt with conjugate heat transfer in microchannel heat sink including the effect of various geometry and working fluid by means of finite volume based simulations on fluid flow and thermal characteristics. The possibilities of enhancement of heat transfer have been investigated by incorporating cylindrical fins and triangular ribs in the simple straight rectangular channel. Nanofluid has been employed to explore the further improvement of heat transfer capabilities. Incorporating fins and ribs have clearly improved Nu and therefore heat transfer rate. Triangular ribs in the microchannel have slightly better impact than cylindrical fins. Cylindrical fins can improve the average Nu by 1.24 to 1.3 times compared to the straight rectangular channel while triangular ribs can improve up to 1.31 times. It is evident from numerical results that nanofluids can improve heat transfer performance by improving the thermal conductivity of the working fluid. Using nanofluid in the microchannel can improve the thermal conductivity by 11.67% and the average Nu by 1.35 times compared to the base fluid.
ACKNOWLEDGMENTS First of all we would like to express our profound gratitude to almighty Allah for bestowing us with the ability to complete this work properly. Then we would like to express our earnest gratefulness to our esteemed supervisor, Dr. A.K.M. Monjur Morshed, whose continuous and careful supervision has enabled us to complete this whole work.
REFERENCES [1] [2] [3] [4]
[5] [6] [7]
[8]
[9]
[10]
[11]
D. B. Tuckerman, R. Pease, High-performance heat sinking for vlsi, Electron Device Letters, IEEE 2 (1981) 126–129. X. Peng, G. Peterson, The effect of thermofluid and geometrical parameters on convection of liquids through rectangular microchannels, International Journal of Heat and Mass Transfer 38 (1995) 755–758. J. Judy, D. Maynes, B. Webb, Characterization of frictional pressure drop for liquid flows through microchannels, International Journal of heat and mass transfer 45 (2002) 3477–3489. M. E. Steinke, S. G. Kandlikar, Single-phase liquid friction factors in microchannels, in: ASME 3rd International Conference on Microchannels and Minichannels, American Society of Mechanical Engineers, 2005, pp. 291–302. W. Qu, I. Mudawar, Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink, International Journal of Heat and Mass Transfer 45 (2002) 2549–2565. P.-S. Lee, S. V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, International Journal of Heat and Mass Transfer 48 (2005) 1688–1704. H. Al-Bakhit, A. Fakheri, A hybrid approach for full numerical simulation of heat exchangers, in: ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems, American Society of Mechanical Engineers, 2005, pp. 839–846. P. Gunnasegaran, H. Mohammed, N. Shuaib, R. Saidur, The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes, International Communications in Heat and Mass Transfer 37 (2010) 1078–1086. E. S. Cho, J. W. Choi, J. S. Yoon, M. S. Kim, Experimental study on microchannel heat sinks considering mass flow distribution with non-uniform heat flux conditions, International Journal of Heat and Mass Transfer 53 (2010) 2159–2168. 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, International Communications in Heat and Mass Transfer 38 (2011) 577–584. J. C. Maxwell, A treatise on electricity and magnetism, volume 1, Clarendon press, 1881.
