Experimental and numerical investigation of heat transfer in a miniature heat sink utilizing silica nanofluid

Superlattices and Microstructures 51 (2012) 247–264

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Experimental and numerical investigation of heat transfer in a miniature heat sink utilizing silica nanofluid Seyyed Abdolreza Fazeli, Seyyed Mohammad Hosseini Hashemi, Hootan Zirakzadeh ⇑, Mehdi Ashjaee Department of Mechanical Engineering, University of Tehran, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 4 July 2011 Received in revised form 11 November 2011 Accepted 23 November 2011 Available online 1 December 2011 Keywords: Experimental and numerical studies Miniature heat sink Silica nanofluid Artificial neural network

a b s t r a c t In this paper, heat transfer characteristics of a miniature heat sink cooled by SiO2–water nanofluids were investigated both experimentally and numerically. The heat sink was fabricated from aluminum and insulated by plexiglass cover plates. The heat sink consisted of an array of 4 mm diameter circular channels with a length of 40 mm. Tests were performed while inserting a 180 W/ cm2 heat flux to the bottom of heat sink and Reynolds numbers ranged from 400 to 2000. The three-dimensional heat transfer characteristics of the heat sink were analyzed numerically by solving conjugate heat transfer problem of thermally and hydrodynamically developing fluid flow. Experimental results showed that dispersing SiO2 nanoparticles in water significantly increased the overall heat transfer coefficient while thermal resistance of heat sink was decreased up to 10%. Numerical results revealed that channel diameter, as well as heat sink height and number of channels in a heat sink have significant effects on the maximum temperature of heat sink. Finally, an artificial neural network (ANN) was used to simulate the heat sink performance based on these parameters. It was found that the results of ANN are in excellent agreement with the mathematical simulation and cover a wider range for evaluation of heat sink performance. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Along with decreasing of electronic components dimensions and increasing of heat generation by these devices, the problem of removing heat from them and achieving a successful design for ⇑ Corresponding author. E-mail address: [email protected] (H. Zirakzadeh). 0749-6036/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2011.11.017

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Nomenclature Cp heat capacity D channel diameter h heat transfer coefficient H channel height k thermal conductivity L length of Heat Sink n shape factor P pressure q00 heat flux over the bottom surface Q flow rate Re Reynolds number T temperature T in inlet coolant temperature T max maximum temperature of the heat sink base plate inlet uniform velocity um ~ V velocity vector W width of heat sink Greek symbols b thermal expansion l dynamic viscosity q density h thermal resistance / volume fraction Subscripts Avg average f fluid nf nanofluid p particle s solid Acronyms 3D 3 dimensional ANN artificial neural network

maximum cooling has become drastically important. Then, in order to overcome the challenge of keeping electronic equipment at their best performance, finding new ways of thermal load managing and performing optimization processes is inevitable. Incapability of conventional fluids such as water in critical heat flux situations was compensated with the creation of ‘‘Nanofluid’’ conception. The innovative idea of adding metallic and non-metallic nanopowders to a base fluid was proposed first by Choi [1], showing a number of potential advantages, such as increase in heat transfer and reduction of heat transfer system size. Khanafer et al. [2] investigated the heat transfer improvement in a 2D enclosure utilizing nanofluids for a range of volume fractions and Grashof numbers. It was found that the heat transfer across the enclosure increases with enhancement of the volumetric fraction of the copper nanoparticles in water for all given Grashof numbers. Later, Kim et al. [3] assessed the pool boiling characteristics of dilute dispersions of Al2O3, ZrO2 and SiO2 nanoparticles in water. Their study showed that a significant improvement in critical heat flux can be achieved even in the lowest nanoparticle concentration. Ho et al. [4] studied the effects of uncertainties due to adopting different formulas for the effective thermal conductivity and dynamic viscosity of alumina/water nanofluid on the heat transfer characteristics and found that heat transfer efficacy of nanofluid can strongly be dependent on how the dynamic viscosity is estimated. More recently, investigation of heat transfer enhancement with use of TiO2–water nanofluid filled in a rectangular enclosure heated from below was carried out by Wen and Ding [5]. Research conducted by Vasu et al. [6,7] resulted in a series of

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thermophysical correlations to calculate thermal conductivity, viscosity and Nusselt number in both turbulent and laminar flows of different nanofluids (Al2O3 + H2O, Cu + H2O, etc.) and it was concluded that these fluids possess higher thermal properties relative to their pure base fluids. Mohammed et al. [8,9] investigated the effect of using a wide range of different nanofluids on heat transfer and laminar fluid flow characteristics in microchannel heat sinks with various shapes using FVM. They demonstrated that an increase in volume fraction does not necessarily increase the heat transfer coefficient. Gunnasegaran et al. [10] presented a comprehensive analysis of roughness effect and regions that the high and low temperatures occur in a microchannel heat sink. Numerous other theoretical and experimental studies were conducted by different researches [11–14] using nanofluids, and they have shown that these new class of coolants can be considered as a promising replacement for conventional coolants. All analytical and numerical studies pursue a much more important goal than just to report a single analysis of fluid flow and heat transfer characteristics: optimization. In order to design an efficient heat sink which is the objective of multiple studies, simulation of heat and fluid flow in the device is required. Knight et al. [15,16] tried to optimize heat sink in both laminar and turbulent flow regimes. It was shown that in small pressure drops, laminar flow will be the main flow regime leading to lowest thermal resistance. On the other hand, when the pressure drop is high, the optimal resistance is found in the turbulent region. Some other works concerning optimization of heat sinks can be found in literature [17–23]. Data obtained from simulations will then be used to find an optimal design point which optimizes objective functions. Calculation of objective functions and solving heat and fluid flow equations in heat sinks can only be done using very time consuming and costly computational fluid dynamic (CFD) approaches, which cannot be used in an iterative optimization task. As a result, several attempts have been made to predict heat sink behavior without being obliged to completely solve the governing equations of heat sinks. Another goal of this paper is to predict heat and fluid flow characteristics of heat sinks using artificial neural networks (ANNs). Artificial neural network (ANN) technique is based on imitating the structure and mechanisms of the human brain and has proven to be effective tool in dealing with complex systems in recent years. One of its greatest advantages is that, while it has the capability of identifying and modeling complete nonlinear relationships (or behaviors) between the input and the output of a system due to its high learning ability, it can be applied to complex problems where conventional numerical methods have lost their applicability [24–26]. ANN has been used in many engineering application such as predicting the pool boiling critical heat flux [27], modeling multi-blade fan/scroll system [28], simulating convective heat transfer coefficients [29] and heat rate predictions in humid air–water heat exchangers [30]. It was reported in these studies that calculation time was significantly reduced using ANN. To the knowledge of authors few works have been concerned about cooling capability of silicawater nanofluids. Thus, the main objectives of the present paper is to analyze performance of SiO2– water nanofluids for heat dissipating purposes using experimental data and then to investigate the effect of key shape parameters on the performance of cooled heat sink. A neural network is then created and trained in order to evaluate the cycle outputs in the whole acceptable range of pre-defined input parameters.

2. Preparation and properties of nanofluids The silicon dioxide (SiO2) spherical nanoparticles (purchased from Wacker, Germany) with an averaged particle size of 18 nm and 99.9% purity were dispersed in distilled water, as the base fluid, to form the SiO2–water nanofluids. The nanofluids were synthesized by the two-step method, without any surfactant in order to not affect the viscosity and the thermal conductivity of suspensions. Desired volume fraction of silica-water nanofluids were prepared by mixing appropriate quantities of nanoparticles with the base fluid, and then sonicated by an ultrasonic bath (Hielscher UP400S, H40 sonotrode) for at least 90 min. The silica nanofluids used in the current study stayed stable for a period of 72 h without any visible settlement. Four volumetric fractions of the silica–water nanofluid, / = 3.5, 4, 4.5 and 5 vol.%, were prepared for the experiment.

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3. Experimental apparatus Fig. 1 demonstrates the flow loop and components that was designed and constructed for the present study. The main components of the test apparatus are: a closed-loop for circulating the fluid, heat sink test section and data acquisition system. Fluid is sent into the loop from a holding tank and is continuously circulated by a gear pump which can be operated at variable rotation speeds to supply different flow rates. A constant temperature bath (F10-Hc Julabo) was installed upstream of the gear pump to control the heat sink inlet temperature. The loop flow rate is controlled upon exiting the pump by two by-pass lines and using three ball valves for coarse adjustment and a needle valve which allows fine adjustment of the flow rate. Volumetric flow rate passing through the loop was measured using a calibrated flow meter. The test module consists mainly of a miniature channel heat sink, housing, plexiglass cover plates as insulation, and the heater. The miniature channel heat sink was fabricated from a square block of aluminum with dimensions 40 mm  40 mm  10 mm using a wire-cut machine. The channels have circular shape with an internal diameter of 4 mm. Graphical representation of the miniature heat sink and test module is depicted in Figs. 2 and 3. The heat sink assembly was placed inside a plexiglass shroud isolated from the ambient. Because of plexiglass low thermal conductivity, the effect of lateral heat transfer from the sides of the test section is eliminated. All the thermocouples used in this study were calibrated and the uncertainty of the temperature measurement was estimated to be less than 5%. Two K-type thermocouples, coated with a compound of copper powder and thermal paste, were embedded in the heat sink for measuring the base plate temperature. Also located in the inlet and outlet of manifold were two K-type thermocouples inserted to measure the inlet and exit temperatures of the fluid. In order to provide a constant heat flux surface for simulating an electronic chip, a heater block of the shape shown in Fig. 3 [31–33], was fabricated from the same material used in constructing the heat sink. Six holes were drilled in the upper cylindrical part of the heater block for embedding K-type thermocouples, three of which have a depth of 3 cm and the other three have a depth of 1.5 cm. These

Fig. 1. Schematic of the experimental setup.

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Fig. 2. Geometric configuration miniature heat sink.

thermocouples will later be used for extrapolating of heat sink base plate temperature. Isolation of heater block from surrounding is done by placing it in a thick fiberboard box filled with slag wool, so that heat transfer interaction could only take place at the interface of the heater block and the heat sink. To improve the thermal transfer efficiency, a layer of highly thermally conductive thermal grease was located at the contact surface between heat sink and heater block. The set of thermocouples were connected to a Testo 177-T4 data logger through an eight channel selector, and all the temperatures required for the analysis of heat sink and heater were recorded simultaneously into the computer by means of a USB port. Uncertainty of the experimental data may origin from the measuring errors of quantities such as heat flux or temperature. The uncertainties of the measurements in the present study are reported in Table 1. 4. Experimental results and discussion The particle volume fraction of the nanofluid used in this study was in the range of 3–5%. Flow rate and inlet temperature for both pure water and nanofluids were the same. Flow rates chosen for this study were 4.46, 12.28, 21.76 and 25.8 cc/s. Inlet temperature was fixed at 27 °C. The comparison between the performances of water and silica-nanofluids as coolants is demonstrated as below. Fig. 4 depicts the effect of nanoparticles concentration on temperature difference between two ends of heat sink base plate when flow rate was adjusted to 4.46 cc/s. It was found that there is a linear relation between heat transfer enhancement and volume fraction of particles. Fig. 5 shows the convective heat transfer coefficient as a function of Reynolds number of the pure water and the SiO2–water nanofluids at different particle volume factions in laminar flow. As the Reynolds number varied from 400 to 2000, the heat transfer coefficients of the nanofluids with the volume fractions of 3.5%, 4%, 4.5% and 5% increased by 3–8%, 8–8.5%, 10.5–13% and 9–15% as compared with

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Fig. 3. Geometric configuration of heater block.

Table 1 Uncertainty of measurements. Quantity

Uncertainty

Heat flux (W/m2) Temperature (°C) Heat transfer coefficient (W/m2 K)

±5.3% ±0.1 ±4.2%

that of pure water, respectively. Also, at different Reynolds numbers with an increase in the volume flow rate, the heat transfer coefficient didn’t follow a constant behavior. At some Reynolds numbers, an increase of the volume flow rate resulted in the elevation of heat transfer enhancement and in other Reynolds numbers a declination was observed. Another result which can be derived from Fig. 5 is that higher particle concentration leads to more heat transfer enhancement. While heat transfer

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Fig. 4. Base plate temperature variation.

Fig. 5. Heat transfer coefficient enhancement of using SiO2–water nanofluid.

enhancement when using nanoparticles depends on flow conditions (such as Reynolds number), it can be attributed to different issues, such as Brownian motion, high thermal conductivity of nanofluid suspensions due to the role of interfacial layers, near wall particles interaction effects, reduction of boundary layer thickness, and delay in boundary layer development [34–38]. The cooling performance of a heat sink with nanofluids can be stated as the thermal resistance defined as:

h¼

ðT max  T in Þ q00

ð1Þ

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Fig. 6. Thermal resistance as a function of flow rate.

where q00 , T in and T max are heat flux, inlet coolant temperature and the maximum temperature of the heat sink base plate, respectively. In our study the base plate temperatures measured near the outlet of flow were treated as the maximum temperatures. The thermal resistances of pure water and 5% volume fraction nanofluid for a 180 W/cm2 heat flux input and different flow rates are illustrated in Fig. 6. It shows that in the investigated range of flow rates the thermal resistance defined by Eq. (1) is reduced when nanofluid is applied as coolant. This enhancement in heat transfer of heat sinks indicates that nanofluids could be a promising replacement for pure water in systems where there is need to more efficient heat transfer. 5. Numerical simulation of the flow and convection heat transfer 5.1. Numerical analysis In this section, three-dimensional fluid flow and conjugate heat transfer in the liquid cooled heat sink are first analyzed numerically and then compared to the experimental data. Finally an artificial neural network (ANN) is used to simulate the heat sink performance based on key parameters affecting maximum temperature of electronic components, i.e., channel diameter, as well as heat sink height and number of channels. Heat sink considered here has the same dimensions as the one used in the experiments (Fig. 2). The electronic component is simulated as a constant heat flux generator q00 below the heat sink and all other surfaces of the heat sink are assumed to be insulated. Nanofluid enters the tubes at uniform velocity and temperature of um and T in , respectively. The flow is assumed to be laminar, steady and incompressible. Viscous dissipation and natural convection are neglected and thermophysical properties of the nanofluid are assumed to be constant. Considering the nanofluid as a continuous media with thermal equilibrium between the base fluid and the solid nanoparticles, the governing equations for nanofluid phase can be stated as below,

VÞ ¼ rP þ lnf r2 ~ V qnf ð~ V:r~

ð2Þ

qnf C p;nf ð~ V:rTÞ ¼ knf r2 T

ð3Þ

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For solid, the momentum and energy equations are simply,

~ V ¼~ 0

ð4Þ

ks r2 T ¼ 0

ð5Þ

Thermophysical properties of nanofluids are calculated using the formulas summarized by Buongiorno [39],

qnf ¼ ð1  /Þqf þ /qp

ð6Þ

It should be noted that for calculating the specific heat of nanofluid some of prior researchers have used the following correlation,

C nf ¼ ð1  /ÞC f þ /C p

ð7Þ

It is modified and presented by Buongiorno [39] which is more accurate,

  C nf ¼ ð1  /Þqf C f þ /qp C p =qnf

ð8Þ

The most commonly used thermal conductivity equation was proposed by Hamilton and Crosser [40] for the mixtures containing micrometer size particles; it is assumed that this equation is applicable for the nanofluids,

knf kp þ ðn  1Þkf  ðn  1Þ/ðkf  kp Þ ¼ kf kp þ ðn  1Þkf þ /ðkf  kp Þ

ð9Þ

In the above equation n represents shape factor and is equal to 3 for spherical nanoparticles. Zhang et al. [41] has shown that this correlation can be used to accurately predict the thermal conductivity of nanofluids. The Einstein equation was then used to estimate the viscosity of nanofluids because very dilute suspensions were used in this work,

lnf ¼ ð1 þ 2:5/Þlf

ð10Þ

where lf is the viscosity of the base liquid, and / is the volume fraction of nanoparticles. Eq. (10) applies to suspensions of low particle concentrations usually / <4%, where particle–particle interactions are negligible. Properties of the base fluid and nanofluids are calculated at 298 K and are shown in Table 2. The thermophysical properties of the materials used for the heat sink for simulation are considered at 298 K and are shown in Table 3. 5.2. Method of solution and validation The SIMPLE algorithm [42] is applied to solve the governing differential equations. The Gauss–Seidal iterative technique is used to solve the resulting system of equations. Successive over-relaxation is applied to improve the convergence time. When the criterion of max jðviþ1  vi Þ=viþ1 j 6 106 is satisfied, the solution is regarded as convergent; where v represents any dependent variable, namely u, v, w and T, and i is the number of iterations. The momentum equation is solved by assigning the true value to the viscosity in the fluid and a very large value to the viscosity in the solid. The energy

Table 2 Thermophysical properties of different phases. Property

Fluid phase (water)

Solid phase (SiO2)

Cp (J/kgK) q (kg/m3) k (W/mK) b  105 (K1) l  104 (kg/ms)

4179 997.1 0.6 21 8.9

765 2220 1.38 0.056 –

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Table 3 Thermophysical properties of material used. Materials

Density (kg/m3)

Specific heat (J/kg K)

Thermal conductivity (W/mK)

Aluminium

2719

871

202.4

equation can be solved after defining the thermal conductivity for both solid and fluid, Right after the velocity field is determined. Several grids with different structures were tested to ensure independence of final results from the grid and a grid scheme with tri elements was found to show the best results and was used for the numerical simulation as shown in Fig. 7. Furthermore, in order to check the independency of results from grid size, a sample heat sink was simulated with several grid sizes and the results for various parameters such as average Nusselt number, pressure drop were compared as a function of grid size, as shown in Fig. 8. It is clear that in a model with more than 4  105 tri elements, the rate of change of average Nusselt number with respect to grid size is quite negligible (less than 1%) and results can be considered to be independent of grid size. In this study a grid scheme with about 6  105 tri elements was used for simulation of fluid flow and heat transfer in heat sink to ensure grid independency of results. In order to demonstrate the validity of numerical results, heat transfer coefficient of pure water and 3.5% nanofluid derived from numerical investigation is compared to the experimental data as depicted in Fig. 9. Fig. 9a compares the experimental values for average heat transfer coefficient of heat sink with numerical results for pure water, while Fig. 9b shows the results for 3.5% nanofluid. Good agreement between the numerical and experimental results was observed at different Reynolds numbers. Therefore the numerical scheme is reliable and can be used effectively for the next step of this study which is optimization of the miniature heat sink. 5.3. Artificial neural network modeling An artificial neural network tries to recognize an approximate pattern between inputs and their desired outputs by imitating the brain functions. Their ability of learning by examples makes the ANNs

Fig. 7. Mesh scheme of a channel wall used for numerical simulation.

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Fig. 8. Variation of average Nusselt number as a function of grid size.

more flexible and powerful than the parametric approaches. Thus, ANNs can be used to find patterns and detect trends that are too complex to be noticed by either humans or other computer techniques. An ANN compromises interconnected groups of artificial neurons and their respective weight building blocks; the behavior of the network depends largely on the interaction between these building blocks which are used in training the network in order to perform a particular function. Each neuron accepts a weighted set of inputs and responds with an output or activation function, which can be hard limit threshold function, log–Sigmoid function, or hyperbolic tangent function.

Hard limit : f ðxÞ ¼



0;

x<0

ð11Þ

1; x P 0

Log—sigmoid function : f ðxÞ ¼

1 1 þ ex

Hyperbolic tangent sigmoid : f ðxÞ ¼

ex  ex ex þ ex

ð12Þ

ð13Þ

A typical ANN consists of three layers, an input layer which takes the input variables from the problem, a hidden layer(s) made up of artificial neurons that transform the inputs, and an output layer that stores the results. ANNs are trained to get specific target output from a particular input, using a suitable learning method; therefore, the error between the output of the network and the desired output should be minimized by modifying the weights and biases. Afterwards, this trained network can be applied to the simulated system to predict the system outputs for the inputs which have not been introduced to the network during the training phase. The training rule used in the current study is the back-propagation (BP) training algorithm. This algorithm is a gradient descent algorithm, in which the network weights are changed along the negative of the gradient of the performance function. For feed-forward networks, performance functions are usually considered as the average squared error between the network and the target outputs. This method is called back-propagation because of the way in which the gradient is computed for nonlinear multilayer networks. Recently, the basic algorithm has undergone some modifications that are based on other standard optimization techniques, such as conjugate gradient and Newton methods. Properly trained back-propagation networks can achieve reasonable answers when presented with

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Fig. 9. Average heat transfer coefficient for: (a) pure water, (b) 3.5 vol.% nanofluid.

inputs that they did not see. This property makes it possible to train a network on a predefined set of input/target pairs and get acceptable results without training the network on all possible input/output pairs. In modeling heat sinks maximum temperature of electronic component and pressure drop in the heat sinks are two of the most important factors that indicate the performance of device, and hence to model the relationship between heat sink parameters and these objectives, several feed-forward neural networks with different hidden layers are employed and compared in the study. 5.4. Numerical results and discussion The parametric analysis is performed to evaluate the effects of three major parameters on the combined cycle performance: channel diameter (D), heat sink height (H) and number of channels in a heat

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Table 4 Conditions assigned to the heat sink parameters. Nanofluid inlet temperature (K) Nanofluid flow rate (l/min) Heat generated in electronic component (W) Width of heat sink (mm) Length of heat sink (mm) Diameter of channels (mm) Heat sink height (mm)

300 0.9 160 40 40 3–8 4–10

Fig. 10. Effect of number of circular channels on maximum temperature of electronic components for different values for diameters of circular channels.

sink. When one specific parameter is studied, other parameters are kept constant. The values of the constant parameters and the range in which three substantial variables are altered are shown in Table 4. As mentioned previously, several feed-forward neural networks with one, two and three hidden layers are employed in the study in order to model the heat sink performance based on the above input variables. Furthermore, in order to achieve accurate results while decreasing the calculation time as much as possible, networks respective errors and training calculation time were compared and an optimum network with 24 neurons in the first layer and 17 neurons in the second layer was used to simulate the performance of heat sink. Fig. 10 shows the effect of number of circular channels on maximum temperature of electronic component. The curves correspond to a heat sink with channel number range of 1–8 circular channels, and three different channel diameters, while heat sink height is kept constant at H = 10 mm. It can be observed that in general, maximum temperature of electronic component decreases as number of circular channels is increased. This is because a heat sink with more circular channels will have a higher overall heat transfer coefficient and as a result the electronic component temperature will decrease with increasing the number of channels. Moreover, it can be seen that the maximum temperature of electronic component decreases with increasing the diameter of circular channels. This is because a larger circular channel will increase the ratio of fluid to solid phase in the heat sink which in turn improves the thermal performance of heat sink and decreases overall thermal resistance. Hence, maximum temperature of electronic component will decrease while increasing the diameter of channels.

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Fig. 11. Effect of number of circular channels on pressure drop in heat sink for different values for diameters of circular channels.

In all three curves, the results predicted by ANN show excellent agreement with the ones obtained from mathematical simulation, which are depicted by markers. In addition, for more than seven channels in heat sinks, simulation process for modeling heat transfer and fluid flow in the heat sink using the mathematical modeling would be very time consuming because of the complexity of generated mesh. However, the neural network can provide interesting solutions in this range of input parameters, which follow a reasonable trend based on previous values. Fig. 11 shows the effect of number of circular channels on pressure drop in heat sink for the same diameters of circular channels as the previous diagram. As it is observed, the pressure drop in the heat sink tends to decrease as the number of channels is elevated. This is mainly because the total fluid flow in the heat sink is constant and increasing the number of channels will result in decreasing the flow in each channel and consequently the pressure drop in the heat sink will be decreased. It is also evident that the pressure drop increases with decreasing the diameter of channels. This fact is rather obvious, as increasing channel diameter in heat sink will decrease the speed of flow in each channel which has a reverse effect on pressure drop in channel and as a result the overall pressure drop will decrease. The effect of diameters of circular channels on maximum temperature of electronic components for different number of circular channels is shown in Fig. 12, when heat sink height is set to 9 mm. As it was stated in previous sections, increasing the diameter of channels will increase the ratio of fluid phase to solid phase and improve heat transfer characteristics of heat sinks which lead to a lower temperature in electronic component. This is mainly because fluid phase can remove heat using both convection and conduction while in solid phase heat transfer is just due to conduction; therefore, increasing the fluid to solid ratio in heat sinks will improve the performance of heat sink. However, it should be noted that increasing the diameter of channels will not always have a significant effect on the performance of heat sink. As shown in Fig. 12 increasing the diameter of channels while there are three channels in heat sink does not have a great effect on the maximum temperature of electronic components and might even have an adverse effect on performance of heat sink. Fig. 13 shows the effect of diameters of circular channels on pressure drop in heat sink for different number of circular channels. It can be observed that the pressure drop decreases with increasing the diameter of channels which is mainly because the velocity in the channels reduced as a result of increasing the diameter of channels. It is clear from Fig. 13 that the reduction in the pressure drop

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Fig. 12. Effect of diameters of circular channels on maximum temperature of electronic components for different number of circular channels.

Fig. 13. Effect of diameters of circular channels on pressure drop in heat sink for different number of circular channels.

because of increasing the diameter of channels will gradually reach an asymptotic value, which is because fluid flow became laminar and pressure drop in this field is rather constant. The effect of heat sink height on maximum temperature of electronic components and pressure drop in heat sink is shown in Figs. 14 and 15. It can be seen that while it has no sensible effect on the pressure drop in heat sink, increasing it will affect the maximum temperature of electronic components. It can be seen from Fig. 14 that by increasing the height of heat sink an optimum point in the maximum temperature of electronic components will be found. Finally, it should be noted that the results obtained for maximum temperature of electronic components and pressure drop in heat sink from the neural network are completely consistent with the

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Fig. 14. Effect of heat sink height on maximum temperature of electronic components for different number of circular channels.

Fig. 15. Effect of heat sink height on pressure drop in heat sink for different number of circular channels.

data obtained from mathematical simulation. The maximum error associated with estimating the parameters in the whole range of consideration was observed to be less than 0.07%. 6. Conclusion In this study, heat transfer characteristics of a mini-channel heat sink cooled by silica-water nanofluid were investigated both experimentally and numerically. Tests were performed for volume fractions in the range of 3.5–5%. The obtained temperature distributions are then used to evaluate the thermal resistance that characterizes the heat sink performance. Also a neural network was cre-

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ated and trained in order to evaluate the cycle outputs in the whole acceptable range of pre-defined input parameters. Key findings from the study are as follows, (1) SiO2 nanoparticles dispersed into the water increased heat transfer coefficient of the heat sink significantly. This outperformance can be mainly attributed to higher thermal conductivity of the nanofluids and Brownian motion of particles. (2) Amount of augmentation in heat transfer coefficient increased with increasing particle concentrations and the amount of heat transfer enhancement did not decrease at higher Reynolds numbers. (3) Thermal resistance of the miniature heat sink was decreased to as low as 0.325 K/W and by about 10% due to the decreased temperature of base plate when using SiO2–water nanofluids. (4) An optimum neural network with 24 neurons on its first layer, and 17 neurons on its second layer was used to model the performance of heat sink when numerical simulations cannot be applied or are too costly to perform. Excellent agreement was found with the result of neural network model and numerical simulation and the network was then used to predict heat sink performance while changing its parameter.

References [1] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, Developments and Applications of NonNewtonian Flows, FED-vol. 231/MDvol. 66 (1995) 99–105. [2] K. Khanafer, K. Vafai, M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Trans. 46 (2003) 3639–3653. [3] S.J. Kim, I.C. Bang, J. Buongiorno, L.W. Hu, Surface wettability change during pool boiling of nanofluids and its effect on critical heat flux, Int. J. Heat Mass Trans. 50 (2007) 4105–4116. [4] C.J. Ho, M.W. Chen, Z.W. Li, Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity, Int. J. Heat Mass Trans. 51 (2008) 4506–4516. [5] D. Wen, Y. Ding, Formulation of nanofluids for natural convective heat transfer applications, Int. J. Heat Fluid Flow 26 (6) (2005) 855–864. [6] V. Vasu, K. RamaKrishna, A.C.S. Kumar, Exploitation of thermal properties of fluids embedded with nanostructured materials, Int. Energy J. 8 (2007) 181–190. [7] V. Vasu, K.K. Rama, A.C.S. Kumar, Empirical correlations to predict thermophysical and heat transfer characteristics of nanofluids, Thermal Sci. J. 12 (3) (2008). [8] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, Heat transfer in rectangular microchannels heat sink using nanofluids, Int. Commun. Heat Mass Trans. 37 (10) (2010) 1496–1503. [9] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, Influence of various base nanofluids and substrate materials on heat transfer in trapezoidal microchannel heat sinks, Int. Commun. Heat Mass Trans. 38 (2) (2010) 194–201. [10] P. Gunnasegaran, H.A. Mohammed, N.H. Shuaib, R. Saidur, The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes, Inter. Commun. Heat Mass Trans. 37 (8) (2010) 1078– 1086. [11] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, The impact of various nanofluid types on triangular microchannels heat sink cooling performance, Int. Commun. Heat Mass Trans. 38 (6) (2011) 767–773. [12] P. Ravi, P. Bhattacharya, P.E. Phelan, Thermal conductivity of nanoscale colloidal solutions Nanofluids, Phys. Rev. Lett. 94 (2005) 25901–25914. [13] S.E.B. Maiga, S.E.B. Nguyen, C.T. Galanis, N. Roy, G. Mare, T. Coqueux, Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension, Int. J. Numerical Methods Heat Fluid Flow 16 (3) (2006) 275–292. [14] J.A. Eastman, S.U.S. Choi, Anomalously increased effective thermal conductivities of Ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78 (6) (2001) 718–720. [15] R.W. Knight, J.S. Goodling, D.J. Hall, Optimal thermal design of forced convection heat sinks-Analytical, ASME J. Electron Pack 113 (1991) 313–321. [16] R.W. Knight, D.J. Hall, J.S. Goodling, R.C. Jeager, Heat sink optimization with application to microchannels, J. IEEE Trans Components Hydbrids Manuf Technol. 15 (1992) 832–842. [17] S. Sasaki, T. Kishmoto, Optimal structure for micro-grooved cooling fin for high-powered LSI Devices, Electron Lett. 22 (1986) 1332–1334. [18] L.J. Missagia, J.N. Walpole, Z.L. Liau, R.J. Phillips, Microchannel heat sinks for two-dimensional high power density diode laser arrays, IEEE J Quantum Electron 25 (9) (1989) 1988–1992. [19] C. Salandram, Computational model for optimizing longitudinal fin heat transfer in laminar integral flows, Heat Transfer in Electronic Equipment, ASME HTD (1991) 171. [20] S.F. Choquette, M. Faghri, Optimum design of microchannel heat sink. Micro-Electro-Mechanical-Systems (MEMS), ASME DSC 59 (1996) 115–126. [21] K. Foli, T. Okabe, M. Olhafer, Y. Jin, B. Sendho, Optimization of micro heat exchanger, CFD, analytical approach and multiobjective evolutionary algorithms, J. Heat Mass Trans. 49 (2006) 1090–1099. [22] Z.H. Wang, X.D. Wang, W.M. Yan, Y.Y. Duan, D.J. Lee, J.L. Xu, Multi-parameters optimization for microchannel heat sink using inverse problem method, Int. J. Heat Mass Trans. 54 (13–14) (2011) 2811–2819.

264

S.A. Fazeli et al. / Superlattices and Microstructures 51 (2012) 247–264

[23] N. Hansen, I. Catton, F. Zhou, Heat Sink Optimization: A Multi-Parameter Optimization Problem, ASME Conf. Proc. (2010) 649–655. [24] D.E. Rumelhart, G.E. Hinton, R.J. Williams, Learning representation by backpropagaion error, Nature 323 (9) (1986) 533–536. [25] S. Chen, S.A. Billings, P.M. Grant, Non-linear system identification using neural network, Int. J. Control 1 (6) (1990) 1191–1214. [26] J. Ilonen, J.K. Kamarainen, J. Lampinen, Differential evolution training algorithm for feed-forward neural networks, Neural Process. Lett. 17 (1) (2003) 93–105. [27] H.M. Ertunc, Prediction of the pool boiling critical heat flux using artificial neural network, IEEE Trans. Comp. Packaging Technol. 29 (2006) 770–777. [28] S.Y. Han, J.S. Maeng, Shape optimization of cut-off in a multi-blade fan/scroll system using neural network, Int. J. Heat Mass Trans. 46 (5) (2003) 2833–2839. [29] K. Jambunathan, S.L. Hartle, S.A. Frost, V.N. Fontama, Evaluating convective heat transfer coefficients using neural networks, Int. J. Heat Mass Trans. 39 (11) (1996) 2329–2332. [30] A.P. Vega, G. Diaz, M. Sen, K.T. Yang, R.L. McClain, Heat rate predictions in humid air-water heat exchangers using correlations and neural networks, ASME J. Heat Trans. 123 (2) (2001) 348–354. [31] X. Wei, Stacked microchannel heat sinks for liquid cooling of microelectronics devices, Ph.D. thesis, Academic Faculty, Georgia Institute of Technology, (2004). [32] B. Dang, Integrated Input/Output Interconnection and Packaging for GSI, Ph.D. thesis, Georgia Institute of Technology, (2006). [33] M. Determan, Thermally activated miniaturized cooling system. Ph. D. thesis, Georgia, Institute of Technology, (2008). [34] Y. Ding, H. Alias, D. Wen, R.A. Williams, Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids), Int. J. Heat Mass Trans. 49 (1–2) (2006) 240–250. [35] H.S. Chen, W. Yang, Y.R. He, Y.L. Ding, L.L. Zhang, C.Q. Tan, A.A. Lapkin, D.V. Bavykin, Heat transfer and flow behavior of aqueous suspensions of titanate nanotubes (nanofluids), Powder Technol. 183 (2008) 63–72. [36] B. Pak, Y. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Trans. 11 (2) (1998) 151–170. [37] Y. Xuan, Q. Li, Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer, 125 (1) (2003), 151–155. [38] Y. Yang, Z.G. Zhang, E.A. Grulke, W.B. Anderson, G. Wu, Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow, Int. J. Heat Mass Trans. 48 (6) (2005) 1107–1116. [39] J. Buongiorno, Convective transport in nanofluids, J. Heat Trans. 128 (2006) 240–250. [40] R.L. Hamilton, O.K. Crosser, Thermal conductivity of heterogeneous two component system, I and EC Fundamentals 1 (1962) 187–191. [41] X. Zhang, H. Gu, M. Fujii, Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles, J. Appl. Phys. 100 (4) (2006) 1–5. [42] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington DC, 1980.