0
Research Papers

# Two-Phase Analysis on the Conjugate Heat Transfer Performance of Microchannel With Cu, Al, SWCNT, and Hybrid NanofluidsOPEN ACCESS

[+] Author and Article Information

Department of Mechanical
& Aerospace Engineering,
e-mail: me12p1006@iith.ac.in

K. Venkatasubbaiah

Department of Mechanical
& Aerospace Engineering,
e-mail: kvenkat@iith.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received November 19, 2016; final manuscript received March 23, 2017; published online June 13, 2017. Assoc. Editor: Ranganathan Kumar.

J. Thermal Sci. Eng. Appl 9(4), 041011 (Jun 13, 2017) (10 pages) Paper No: TSEA-16-1335; doi: 10.1115/1.4036804 History: Received November 19, 2016; Revised March 23, 2017

## Abstract

This numerical study has been carried out by developing two-phase mixture model with conjugate heat transfer. Pure and hybrid nanofluids (HyNF) with particle as well as base fluid hybridization are used in analyzing the performance of microchannel under forced convection laminar flow. The flow as well as heat transfer characteristics of pure water, copper (Cu), aluminum (Al), single-walled carbon nanotube (SWCNT), and hybrid (Cu + Al, water + methanol) nanofluids with various nanoparticle volume concentrations at different Reynolds numbers are reported. Sphericity-based effective thermal conductivity evaluation is considered in the case of SWCNT nanofluids by using volume and surface area of nanotubes. A significant enhancement in the average Nusselt number is observed numerically for both pure and hybrid nanofluids. Pure nanofluids such as Al, Cu, and SWCNT with 3 vol % nanoparticle concentration enhanced the average Nusselt number by 21.09%, 32.46%, and 71.25% in comparison with pure water at Re = 600. Whereas, in the case of hybrid nanofluids such as 3 vol % HyNF (0.6% Cu + 2.4% Al) and 3 vol % SWCNT (20% Me + 80% PW), the enhancement in average Nusselt number is observed to be 23.38% and 46.43% in comparison with pure water at Re = 600. The study presents three equivalent combinations of nanofluids (1 vol % Cu and 0.5 vol % SWCNT), (2 vol % Cu, 1 vol % SWCNT and 3 vol % HyNF (0.6% Cu + 2.4% Al)) as well as (2 vol % SWCNT and 3 vol % SWCNT (20% Me + 80% PW)) that provides a better switching option in choosing efficient working fluid with minimum cost based on cooling requirement. The study also shows that by dispersing SWCNT nanoparticles, one can enhance the heat transfer characteristics of base fluid containing methanol as antifreeze. The conduction phenomena of solid region cause the interface temperature between solid as well as fluid regions to increase along the length of the microchannel. The developed numerical model is validated with the numerical and experimental results available in the literature.

<>

## Introduction

Heat fluxes generated by high power integrated circuits in next-generation computers and electronic devices require innovative cooling techniques [1]. Microchannel heat sinks with liquid coolants will extract enormous amount of high heat fluxes due to high surface to volume ratio [2,3]. Ordinary heat transfer fluids like pure water, methanol, and ethylene glycol possess limited heat transport capabilities due to poor thermal properties [4]. This limitation in the heat transfer performance of ordinary working fluids can be compensated by suspending high thermal conductive nanoparticles within the base fluid. Such a new class of heat transfer fluids with nanoparticles are referred to as nanofluids [5,6].

Beck et al. [7,8] investigated the thermal conductivity of alumina nanofluid with the use of liquid metal transient hot wire apparatus. The investigations show that nanofluids with ethylene glycol and 20 nm alumina particles enhance the thermal conductivity with respect to volume fraction. Garg et al. [9] investigated the thermal conductivity and viscosity of Cu nanoparticles dispersed in ethylene glycol. The study shows that the measured thermal conductivity enhances for volume loadings of nanoparticles up to 2%. The thermophysical properties of SWCNT nanofluids are experimentally studied by Xing et al. [10] with a mass fraction of 0.1–1 wt % in the temperature range of 10–60 °C. The observations conclude that for a concentration of 1 wt % at 60 °C, the maximum thermal conductivity and viscosity enhancements increase by up to 16.2% and 35.9%. Moreover, the evaluated results indicate that SWCNT nanofluids have good heat transfer performance in laminar flow regime.

Heat transfer performance of alumina nanofluid was experimentally studied by Vafaei and Wen [11] as well as Anoop et al. [12]. The observations conclude that the heat transfer coefficient of nanofluid depends on mass flow rate and nanoparticle diameter along with volume concentration. It is observed that nanofluid with a concentration of 4 wt % and a particle diameter of 45 nm enhances the heat transfer coefficient by 25% at Re = 1550. Whereas in the case of nanofluid with a particle diameter of 150 nm, the enhancement is found to be around 11%. Experimental studies on convective heat transfer performance of copper nanofluid were conducted by Li and Xuan [13] and Azizi et al. [14]. The results conclude that the entrance Nusselt number of nanofluids is enhanced up to 43%. Ding et al. [15] studied the thermal behavior of multi-walled carbon nanotube (MWCNT) nanofluids in a horizontal tube. The results reported an enhancement of 350% in heat transfer coefficient for 0.5 wt % nanoparticles at a Reynolds number of 800. Experimental study on the enhancement of heat transfer performance in a shell and tube heat exchanger using MWCNT nanofluid was carried by Lotfi et al. [16]. The study showed that the maximum enhancement in heat transfer coefficient is found to be 6.66% at 630 W for 0.015 wt %.

Numerical study on the forced convection heat transfer of alumina and zirconia nanofluids in a vertical tube was carried out by Saberi et al. [17]. The study concluded that nanofluids exhibit higher convective heat transfer coefficient in comparison with water similar to the experimental data. Moreover, it is also observed that the relative error for mixture model was 8% and 5% for alumina and zirconia nanofluids, and it is the better model in comparison with single-phase approach. Meng and Li [18] numerically investigated the natural convection of water-based Al2O3 nanofluids ($ϕ=0.01$ and 0.04) inside a horizontal cylinder. Experimental and numerical study was carried out by Bhadouriya et al. [19] in order to analyze the friction factor as well as heat transfer characteristics of fluid flow in a twisted square duct. The results showed that a maximum enhancement factor of 10.5 is obtained with twist ratio of 2.5, Prandtl number of 20, and Reynolds number of 3000. It is also observed that in laminar flow regime (Re < 3000), a twist ratio of 11.5 has a maximum friction factor ratio and Nusselt number ratio value of 2.1 and 2.6, respectively, at critical Reynolds number. Hasan [20] investigated the flow as well as heat transfer characteristics of Al2O3 and diamond nanofluids in micropin fin heat sink. It is observed that the use of nanofluid as coolant instead of pure water will increase the amount of heat dissipation and enhances the heat transfer performance. The study showed an increment of 9.9%, 9.78%, and 9.12% in terms of heat transfer rate when compared with water. Hasan et al. [21] conducted numerical investigation on the performance of counter flow microchannel heat exchanger. The study is carried out with water-based Cu and Al2O3 nanofluids. It is observed that the heat transfer rate for Cu nanofluid is between 0.764 and 0.772. Whereas for Al2O3 nanofluid, the value is between 0.730 and 0.739. Single-phase forced convection flow inside microchannels with carbon nanotubes (CNTs) was investigated by Dietz and Joshi [22]. The study concluded that the increase in thermal performance gained by increasing the surface area is overshadowed by the decrease in mass flow rate.

Numerical investigations as in Refs. [23] and [24] were carried out by using single-phase and two-phase models with Al2O3 as well as Cu nanofluids in a square cavity and microchannel. The results conclude that the average Nusselt number increases with increase in Reynolds number and volume concentration of nanoparticles. The observations conclude that the average Nusselt number is enhanced by 67.77% at Re = 500. Experimental and numerical study on the flow as well as heat transfer performance of nanofluids in microchannels is carried out by Singh et al. [25,26] using discrete phase model and homogeneous heat transfer model. The study showed that nanofluids do not show any significant difference in hydrodynamic behavior at low concentrations. However, their heat transfer behavior depends on channel size. Nimmagadda and Venkatasubbaiah [27] as well as Labib et al. [28] numerically studied the effect of Al2O3, silver, and carbon nanofluids in a microchannel and in long horizontal tube. The studies used homogeneous and mixture models. The observations conclude that nanofluid hybridization is a cost-effective solution. Hybrid (0.6% Al2O3 + 2.4% Ag) nanofluid enhanced the heat transfer coefficient by 126–148% than that of pure water. In the case of CNT hybrid (0.05% CNT + 1.6% Al2O3) nanofluid, the heat transfer coefficient is enhanced by 59.86%. Derakhshan and Akhavan-Behabadi [29] as well as Halelfadl et al. [30] used MWCNT nanofluid in their experimental and analytical studies within a microchannel heat sink. The results conclude that the use of nanofluid significantly enhances the thermal performance. The studies showed that the Nusselt number is enhanced by 22% and 18% for horizontal plain and microfin tubes. Moreover, the convective heat transfer is enhanced by 13% at 40 °C.

From the existing numerical and experimental investigations, it is observed that the research is limited to pure metallic or oxide nanofluids with few experimental studies on thermal performance of nanofluids containing multiwalled carbon nanotubes. The amount of research carried out with copper (Cu), aluminum (Al), and SWCNT nanofluids is limited. Further, no numerical investigation has been reported on the combined heat transfer characteristics of Cu, Al, and SWCNT nanofluids in microchannel along with particle as well as base fluid hybridization. An approach to find equivalent combinations of nanofluids that provides a better switching option in choosing efficient working fluid with minimum cost based on the comparative nature of flow as well as heat transfer characteristics by considering the combined effect of particle volume concentration and hybridization has not been presented in the literature. Moreover, the presence of solid region under the flowing zone of the microchannel will impose conduction effect that influences the real-time heat transfer performance. These points are the motivation for this numerical investigation. A two-dimensional two-phase mixture model with conjugate heat transfer has been developed and the flow as well as heat transfer characteristics of Cu, Al, and SWCNT nanofluids with particle and base fluid hybridization at different Reynolds numbers and particle volume concentrations are presented.

## Geometry Description

Figure 1 shows the schematic diagram of microchannel considered for the numerical investigation. The length, width, and height of the channel are 58.5 mm, 10,000 μm, and 200 μm, respectively. It is reasonable to consider a two-dimensional flow through the channel since its height is substantially smaller than its width. Pure water is used as base fluid and nanofluids with different nanoparticles such as Cu, Al, and SWCNT are used in this study. Methanol is also added to the base fluid in order to study the effect of base fluid hybridization on the flow and heat transfer characteristics. The diameter of the metallic nanoparticles is chosen to be 100 nm. For SWCNT nanoparticles, the length and diameter are considered to be 3 μm and 2 nm, respectively. The length to diameter ratio of SWCNT nanoparticles in this study is 1500. For carbon nanotube, the length to diameter ratio exceeds 1000 [31]. The length of CNT will be in micrometer [31] and the maximum length can reach up to 2 mm [32]. This high aspect ratio of CNTs is one of the reason for large enhancement of the convective heat transfer coefficient [15]. SWCNT nanoparticles with average diameter ranging from 2 to 14 nm and length ranging from 3 to 12 μm are used in Ref. [33]. As per the literature [15,3133], the dimensions of SWCNT nanoparticles used in this investigation are realistic in nature. The bottom side of the microchannel is considered with solid region of finite thickness made up of silicon. The height (hs) of the solid region is chosen to be 175 μm and heat flux is uniformly applied to its bottom as shown in Fig. 1.

## Thermophysical Properties

Pure water is considered as base fluid and nanofluids used in the numerical investigation are obtained with different nanoparticles such as SWCNT, Cu, and Al. Methanol is also added to the base fluid in order to study the effect of base fluid hybridization on the flow and heat transfer characteristics. The nanofluid effective thermophysical properties are calculated based on the equations reported by Xuan and Roetzel [34], Pak and Cho [35], and Brinkman [36] as given below: Display Formula

(1)$(ρCp)nf=(1−ϕ)(ρCp)bf+ϕ(ρCp)p$
Display Formula
(2)$ρnf=(1−ϕ)ρbf+ϕρp$
Display Formula
(3)$μnf=μbf(1−ϕ)2.5$

where (ρCp) and $ϕ$ are the fluid heat capacity and volume fraction of the nanoparticles. Subscripts bf, nf, and p indicate base fluid, nanofluid, as well as nanoparticles, respectively.

Heat transfer characteristics of base fluid and nanofluid will have dominating dependency on thermal conductivity. Hence, appropriate standard models are needed for evaluating the effective thermal conductivity of metallic and carbon nanofluids. The effective thermal conductivity of SWCNT nanofluid with cylindrical particles is calculated using the model developed by Hamilton and Crosser [37] as given below Display Formula

(4)$knfkbf=kp+(n−1)kbf+(n−1)ϕ(kp−kbf)kp+(n−1)kbf−ϕ(kp−kbf)$

Here, n is the empirical shape factor and its value is obtained as $3/ψ$. ψ represents the sphericity of nanoparticles and its value is obtained by $(π1/3(6Vp)2/3)/Ap$.

In the case of metallic nanofluids with spherical particles, the thermal conductivity model developed by Patel et al. [38] is used. This model considers the Brownian motion of ultrafine particles due to the chaotic movement within the matrix of base fluid Display Formula

(5)$knf−kbfkbf=kpkbf(1+cupdpαbf)dbfdpϕ1−ϕ$

Here, c is a constant which is obtained from large range of experimental data and its value is equivalent to 25,000. up represents the Brownian velocity of nanoparticles and its value is obtained by $2kBT/πμbf dp2$. The thermophysical properties of base fluids and nanofluids used in this study are given in Table 1.

## Governing Equations and Boundary Conditions

As shown in Fig. 1, Ui and Ti represent the inlet velocity as well as temperature of the fluid in a wide rectangular microchannel under laminar two-dimensional forced convection flow. This study has been carried out by developing two-phase mixture model with conjugate heat transfer. Moraveji and Ardehali [39] concluded that mixture model is most precise and requires less central processing unit (CPU) usage as well as less run time in comparison with other two-phase models (VOF and Eulerian). This conclusion made them to choose mixture model in developing Nusselt number and friction factor correlations for Al2O3/water nanofluid in mini-channel heat sink. Hejazian et al. [40] observed that two-phase models (mixture and Eulerian) almost showed the same results for turbulent flow of Al2O3 nanofluid inside a horizontal tube. But the mixture model was slightly more accurate in predicting the Nusselt number. These advantages are the reasons for selecting two-phase mixture model in this numerical study. This model considers strong coupling between primary and secondary phases based on single-fluid two-phase approach with particles following the flow direction [28,41,42]. The base fluid is treated as continuous or primary phase and nanoparticles as dispersed or secondary phase. Moreover, these two phases will interpenetrate in the flow domain, which means that within any control volume, there will be volume fraction of continuous phase as well as volume fraction of dispersed phase [28]. The continuity and momentum equations are written for the mixture of primary and secondary phases. In addition, particle concentration is solved from continuity equation of secondary phase. Complete details about mixture model are given in Manninen et al. [43] for further idea.

Continuity equationDisplay Formula

(6)$∇·(ρmUm)=0$

where $Um=(ϕpρpUp+ϕcρcUc)/ρm$ and $ρm=ϕpρp+ϕcρc$ are the mass-average velocity and mixture density.

Momentum equationDisplay Formula

(7)$∂(ρmUm)∂t+∇⋅(ρmUmUm)=−∇p+∇⋅[μm(∇Um+∇UmT)]−∇⋅(ϕpρpUdr,pUdr,p)$

where $Udr,p=Up−Um$ is the drift velocity for particulate phase [41,43].

The normal and shear stresses acting on the fluid particle are responsible for the viscous term and is given as the second term on the right-hand side of Eq. (7). The phase slip due to the relative motion between the phases is responsible for diffusion stress term and is given as the third term on the right-hand side [41,43]. This diffusion stress term represents the momentum diffusion.

Energy equationDisplay Formula

(8)$∂(ρmCpmTm)∂t+∇⋅(ρmCpmTmUm)=∇⋅[kf(∇Tm)]$

Volume fraction equationDisplay Formula

(9)$∂(ϕp)∂t+∇⋅(ϕpUm)=−∇⋅(ϕpUdr,p)$

Slip velocity and drift velocity

The velocity of dispersed phase (p) relative to the velocity of continuous phase (c) is represented as relative or slip velocity Display Formula

(10)$Ucp=Up−Uc$

The drift velocity is related to the relative velocity as Display Formula

(11)$Udr,p=(1−ϕpρpρm)Ucp$

Algebraic slip formulation

The slip velocity is of the form Display Formula

(12)$Ucp=τpfdrag(ρp−ρm)ρpa$

where $τp=ρpdp2/18μcϕc−2.65$ is the particle relaxation time. The function fdrag is taken from Schiller and Naumann [44] Display Formula

(13)$fdrag=1+0.15 Rep0.687 Rep≤1000 and fdrag=0.0183 Rep Rep>1000$

where $Rep=(ρc|Ucp|dp/μc) and a=−(Um.∇)Um$ is acceleration.

The nondimensional equations are obtained by using various scaling factors such as time ($Dh/Ui$), length (Dh), velocity (Ui), pressure ($ρfUi2$), and temperature ($ΔT=q0Dh/kf$). The nondimensional parameters used in Figs. 24 are as follows: axial length $x*=x/Dh$, normal length $y*=y/Dh$, velocity $U*=U/Ui$, and temperature $T*=(T−Tmeanfluid)/(q0Dh/kf)$.

The bottom side of the microchannel is considered with solid region of finite thickness and heat flux is uniformly applied to it as shown in Fig. 1. A two-dimensional unsteady heat conduction equation as given below represents the governing equation for solid region Display Formula

(14)$∂Ts∂t=αs(∂2Ts∂x2+∂2Ts∂y2)$

where αs is thermal diffusivity of the solid; Ts is the dimensional temperature in the solid region.

###### Boundary and Initial Conditions.

The fluid is flowing with uniform velocity and temperature at inlet of the microchannel. Fully developed flow condition is applied for both velocity and temperature fields near the outlet section. No slip velocity boundary condition is applied to both bottom and top walls of the channel. The top wall is considered as adiabatic in order to prevent the heat loss to surroundings and heat flux of q0 = 150,000 W/m2 is uniformly applied to the bottom side of the solid region. The initial condition is considered as inviscid solution for velocity and temperature fields. Heat fluxes and temperatures at the interface between solid and fluid regions are equal and are given by Display Formula

(15)$Ts=Tf;−ks∂Ts∂y=−kf∂Tf∂y$

###### Nusselt Number.

The heat transfer performance of microchannel incorporated with pure water and different nanofluids is evaluated in terms of Nusselt number (Nu). The local Nusselt number is calculated using the following equation: Display Formula

(16)$Nulocal=hDhkf=q0Dhkf(Tinterface−Tmeanfluid)=−∂Tf*∂y*(Tinterface*−Tmeanfluid*)$

where h is the convective heat transfer coefficient of the fluid, and Tinterface and $Tinterface*$ are dimensional and nondimensional interface temperatures.

The local Nusselt number values are integrated along the interface of the microchannel in order to obtain the average Nusselt number (Nuavg) values.

## Numerical Methods

This study is carried out by developing two-phase mixture model with conjugate heat transfer. Finite volume method is used to discretize the set of nonlinear differential equations in both solid and fluid regions. The obtained discretized equations are then solved by using simplified marker and cell (SMAC) algorithm on collocated grid [45,46]. First, the pressure field is excluded in order to obtain the predicted velocity fields explicitly. These obtained predicted velocity fields are used to find the pressure field by satisfying conservation of mass. The convergence criterion in solving the pressure Poisson equation set to ≤ 10−6 and Gauss–Seidel iteration method is used for solving. The corrected velocity field is then obtained by using the predicted velocity field and pressure field. This corrected velocity field is used in obtaining the temperature distribution within the channel. The decoupling nature of velocity and pressure on nonstaggered grid is avoided by implementing Rhie–Chow momentum interpolation technique in the algorithm [47,48]. The convection terms are discretized using second-order upwind method. The heat flux equation as given in Eq. (15) is discretized at the interface by using forward finite difference scheme for fluid region and backward finite difference scheme in solid region. The interface temperature as given in Eq. (17) is obtained from the discretized heat flux equation with the imposition of equal temperatures between solid and fluid regions. The interface temperature equation in dimensional form is represented in terms of solid and fluid temperatures near the interface as given below: Display Formula

(17)$Tsi,j=Tfi,j=Tinterface=ksTsi,j−1Δysolid+kfTfi,j+1ΔyfluidksΔysolid+kfΔyfluid$

At each time step, the temperature field within the solid region is obtained from two-dimensional unsteady heat conduction equation as given in Eq. (14). Whereas, the temperature field within the fluid region of the microchannel is obtained from energy equation as given in Eq. (8). However, at the interface between solid and fluid regions, the temperature is calculated by using Eq. (17). The solution is marched with time integration for fluid and solid regions. Numerical stability is maintained by using small time step in explicit first-order Euler time integration.

## Grid Independence and Validation

Grid independence study has been conducted at a Reynolds number of 600 with pure water and 3 vol % SWCNT nanofluid. Four different grids 175 × 40, 200 × 48, 225 × 56, and 300 × 72 have been chosen to find the dependency of obtained solution on grid size. Figure 2 shows the velocity and temperature profiles at exit of the microchannel for different grids. The corresponding average Nusselt number values are given in Table 2. From Fig. 2 and Table 2, it is found that the solution for grid size of 200 × 48 is grid independent. Hence, all simulations in this study are presented with this grid size.

The accuracy of this two-phase model and solution methodology is validated with the experimental and numerical results available in the literature. The results are validated with oxide and metallic nanofluids against Eulerian–Eulerian multiphase approach. As shown in Figs. 5(a) and 5(b), the average Nusselt number values of 0.1 vol % Al2O3 and 3 vol % Cu nanofluids at different Reynolds numbers are compared against the experimental and numerical results of Kalteh et al. [24,49]. The geometry dimensions as well as the boundary conditions given by Kalteh et al. [24,49] are used in this numerical model for validation. The geometry used in Ref. [24] is isothermally heated parallel plate microchannel without conjugate heat transfer. For validating this numerical model, the same boundary condition is applied to the walls of microchannel with similar geometry. The obtained results with the present numerical model are then plotted as shown in Fig. 5(b) against the numerical results given by Kalteh et al. [24]. In the case of Ref. [49], the microchannel consists of solid region under the flow domain and this results in conjugate heat transfer. A constant heat flux of 20.5 kW/m2 is applied to the bottom of the solid region as given in Ref. [49]. Similar geometry with same boundary condition as per Ref. [49] is incorporated in this numerical model for testing its validity and the obtained results are shown in Fig. 5(a) against the experimental and numerical results of Kalteh et al. [49]. However, at the interface between solid and fluid region, the heat fluxes as well as temperatures will be equal as given in Eq. (15) for the case of conjugate heat transfer problem. Thus, numerical simulations are performed as per the parameters given in Refs. [24] and [49] and obtained results are then plotted in comparison with the cited results as shown in Figs. 5(a) and 5(b). From Fig. 5, present results are in good agreement with the numerical and experimental results available in the literature. The validated numerical model is then used to study the conjugate heat transfer performance of microchannel with Cu, Al, SWCNT, and hybrid nanofluids using a constant heat flux of q0 = 150,000 W/m2.

## Results and Discussion

Numerical study has been carried out to analyze the performance of microchannel under forced convection laminar flow. Pure and hybrid nanofluids with particle as well as base fluid hybridization are used in the investigation. The flow as well as heat transfer characteristics of pure water, Cu, Al, SWCNT, and hybrid (Cu + Al, water + methanol) nanofluids with various nanoparticle volume concentrations at different Reynolds numbers are discussed and reported.

The steady-state velocity and temperature contours of pure water and 3 vol % SWCNT nanofluid in a rectangular microchannel are shown in Fig. 3 at Re = 600. From Fig. 3(a), it is observed that the velocity field of pure water and 3 vol % SWCNT nanofluid do not overlap with each other. This is because of the effect of diffusion momentum for 3 vol % SWCNT nanofluid, which is due to the relative motion between continuous and particle phases. However, in the case of pure water, the diffusion stress term on the right-hand side of the momentum equation becomes zero due to the absence of particle phase. From Fig. 3(b), the temperature field of pure water and 3 vol % SWCNT nanofluid shows a deviation due to the difference in effective thermal conductivities of the two fluids.

###### Effect of Reynolds Number and Concentration.

The effect of Reynolds number on the dimensional velocity and temperature profiles of 3 vol % SWCNT nanofluid at exit of the microchannel is shown in Fig. 6. From Fig. 6(a), it is observed that the velocity of nanofluid increases as Re increases from 200 to 600. This is due to increase in the inlet velocity of the flowing fluid with respect to Re. This increment in the inlet velocity reduces the temperature as shown in Fig. 6(b). The maximum velocity of the fluid increases from 0.642 m/s to 1.926 m/s and the maximum temperature decreases from 330.8 K to 315.4 K with increase in Re from 200 to 600.

The variation in the interface temperature between the solid and fluid region along the length of the microchannel is shown in Fig. 4(a) for different Reynolds number. From Fig. 4(a), it is observed that for a particular Re, the interface temperature of 3 vol % SWCNT nanofluid increases along the length of the channel. This is because the fluid gains more amount of heat as it flows through the channel. The interface temperature decreases with the increase in Re. This is due to increase in the velocity of the nanofluid. The effect of Reynolds number and volume concentration on the local Nusselt number is shown in Figs. 4(b) and 4(c). From Fig. 4(b), it is observed that the local Nusselt number of 3 vol % SWCNT nanofluid along the length of the microchannel increases with increase in Re. This is due to the increase in the velocity of the flowing fluid with respect to Reynolds number. The variation in local Nusselt number along the length of the microchannel with respect to volume concentration is shown in Fig. 4(c) at Re = 600. From Fig. 4(c), it is observed that the local Nusselt number increases with increase in SWCNT nanoparticle volume concentration. This is due to the increase in the effective thermal conductivity of nanofluid with respect to volume concentration.

###### Effect of Concentration on Velocity.

The effect of volume concentration and hybridization on the dimensional velocity profiles at exit of the microchannel is shown in Fig. 7 at Re = 600. From Figs. 7(a) and 7(b), it is observed that the velocity of 3 vol % Cu is lower than that of pure water and other nanofluids. This is due to a decrease in the kinematic viscosity, which in turn is due to increase in the density of nanofluid. The densities of pure water, 3 vol % SWCNT, and 3 vol % Cu nanofluids are 996.512 kg/m3, 1023.617 kg/m3, and 1235.417 kg/m3. However, the velocity of 3 vol % SWCNT nanofluid is slightly higher than that of pure water even though the density slightly increases. This is due to the significant increase in the dynamic viscosity of 3 vol % SWCNT nanofluid in comparison to density. The effect of particle and base fluid hybridization on the dimensional velocity is shown in Figs. 7(c) and 7(d). The density of 3 vol % HyNF (1.5% Cu + 1.5% Al) is 1141.512 kg/m3, which is lower than 3 vol % Cu and higher than 3 vol % Al nanofluids. This is the reason for its velocity profile to fall between those two nanofluids as shown in Fig. 7(c). From Fig. 7(d), it is observed that the velocity drops as the percentage of methanol increases. This is due to a decrease in the dynamic viscosity of the nanofluid. However, for 3 vol % SWCNT nanofluid (20% Me + 80% PW), the dynamic viscosity is close to pure water and as a result their velocities almost overlap with each other. The variations in velocities are mainly due to its dependent nature on kinematic viscosity, which, in turn, is dependent on particle concentration and density.

###### Effect of Concentration on Temperature and Average Nusselt Number.

The effect of volume concentration and hybridization on the dimensional temperature profiles at exit of the microchannel as well as the average Nusselt numbers of various working fluids at different Reynolds numbers are shown in Figs. 8 and 9. From Fig. 8(a), the dimensional temperature of 3 vol % SWCNT nanofluid is lower than that of pure water and all other working fluids. This is due to its higher effective thermal conductivity and input velocity as shown in Fig. 7(a). The effective thermal conductivities of pure water, 3 vol % Al, 3 vol % Cu, and 3 vol % SWCNT nanofluids are 0.615 W/m K, 0.741 W/m K, 0.828 W/m K, and 1.112 W/m K, respectively. For a particular concentration, this increment in the effective thermal conductivities will reduce the corresponding Prandtl numbers and enhances the average Nusselt number as shown in Fig. 9(a) by lowering the temperature as observed in Fig. 8(b). It is observed that Al, Cu, and SWCNT nanofluids with 3 vol % nanoparticle concentration enhanced the average Nusselt number by 21.09%, 32.46%, and 71.25% in comparison with pure water at Re = 600.

###### Effect of Hybridization.

The effect of nanoparticle hybridization is shown in Figs. 8(c) and 9(b). The effective thermal conductivity increases with increase in the percentage of copper nanoparticles within the hybrid nanofluid. This increase in effective thermal conductivity lowers the temperature and enhances the average Nusselt number of 3 vol % HyNF (1.5% Cu + 1.5% Al) in comparison with pure water and 3 vol % pure Al nanofluid. The effect of methanol-based base fluid hybridization on the dimensional temperature profiles as well as on the average Nusselt numbers is shown in Figs. 8(d) and 9(c). The effective thermal conductivity of nanofluid varies depending on methanol proportion. The thermal conductivity values of 3 vol % SWCNT nanofluid with 80%, 50%, and 20% methanol are 0.518 W/m K, 0.741 W/m K, and 0.963 W/m K. This enhancement in thermal conductivity is responsible for less dimensional temperature of 3 vol % SWCNT nanofluid with 20% methanol as shown in Fig. 8(d). The same will enhance the average Nusselt number of 3 vol % SWCNT (20% Me + 80% PW) nanofluid as shown in Figs. 9(c) and 9(d). From Figs. 8(d) and 9(c), it is observed that the fluid with 80% methanol exhibits higher temperature and lower average Nusselt number than pure water due to its poor effective thermal conductivity. The average Nusselt number of 3 vol % SWCNT (80% Me + 20% PW) nanofluid is 5.751 at Re = 600, which is lower than that of 7.632 in the case of pure water. It is observed that 3 vol % HyNF (0.6% Cu + 2.4% Al) and 3 vol % SWCNT (20% Me + 80% PW) nanofluids exhibit 23.38% and 46.43% enhancement in average Nusselt number in comparison with pure water at Re = 600.

###### Equivalent Combinations of Nanofluids.

Moreover, From Fig. 9(d), it is observed that 1 vol % Cu and 0.5 vol % SWCNT exhibit almost similar heat transfer characteristics as they have almost equivalent effective thermal conductivity values. The slight enhancement of 0.5 vol % SWCNT nanofluid is due to its higher velocity in comparison to 1 vol % Cu nanofluid. It is also observed that 2 vol % Cu, 3 vol % HyNF (0.6% Cu + 2.4% Al), and 1 vol % SWCNT exhibit almost similar heat transfer characteristics due to their equivalent nature of effective thermal conductivities. Similar observation is also identified in the case of 2 vol % SWCNT and 3 vol % SWCNT (20% Me + 80% PW) nanofluids. The effective thermal conductivity of base fluid (20% Me + 80% PW) is lower than that of pure water due to low thermal conductivity of methanol. The lower effective thermal conductivity of methanol-based base fluid is enhanced by dispersing SWCNT nanoparticles. This results in higher heat transfer characteristics of 3 vol % SWCNT (20% Me + 80% PW) nanofluid in comparison with pure water as shown in Fig. 9(d). However, 2 vol % SWCNT and 3 vol % SWCNT (20% Me + 80% PW) nanofluids exhibit almost similar average Nusselt number values due to their equivalent thermal conductivities. The effective thermal conductivity values of 2 vol % SWCNT and 3 vol % SWCNT (20% Me + 80% PW) nanofluids are 0.943 W/m K and 0.963 W/m K, respectively. The average Nusselt number of 3 vol % SWCNT nanofluid ranges from 11.619 to 13.070 for Re = 200–600. Whereas, for pure water, the value ranges from 6.322 to 7.632. The average Nusselt number values of various working fluids at different Re are shown in Table 3.

## Conclusions

Numerical study has been carried out by developing two-phase mixture model with conjugate heat transfer. Pure and hybrid nanofluids (HyNF) with particle as well as base fluid hybridization are used in analyzing the performance of microchannel under forced convection laminar flow. The flow as well as heat transfer characteristics of pure water, copper (Cu), aluminum (Al), SWCNT and hybrid (Cu + Al, water + methanol) nanofluids with various nanoparticle volume concentrations at different Reynolds numbers are reported. The following conclusions are obtained from this study.

• The inlet velocity of flowing fluid increases with increase in Reynolds number. This results in the increment of average Nusselt number.

• The effective thermal conductivity of nanofluid increases with increase in the particle volume concentration. This results in the increment of average Nusselt number. The average Nusselt number value of 3 vol % SWCNT nanofluid is enhanced by 71.25% in comparison with pure water at Re = 600.

• The effect of base fluid hybridization on the heat transfer performance of nanofluid is significant by using methanol in different proportions. 3 vol % SWCNT nanofluid with 20% methanol enhances the Nusselt number by 46.43% in comparison with pure water. This shows that by dispersing SWCNT nanoparticles, one can enhance the heat transfer characteristics of working fluid containing methanol as antifreeze.

• 3 vol % hybrid nanofluid with two different particle hybridization ((0.6% Cu + 2.4% Al) as well as (1.5% Cu + 1.5% Al)) enhances the average Nusselt number in comparison with pure water and 3 vol % pure Al nanofluid. This shows that hybrid nanofluids obtained by mixing Cu and Al nanoparticles in different proportions based on the cooling requirement will be a new class of working fluids with minimum cost and optimized heat transfer characteristics.

• 1 vol % Cu and 0.5 vol % SWCNT nanofluids are found to have almost equivalent heat transfer characteristics. This provides a good switching option to choose effective nanofluid with minimum cost for achieving same heat transfer performance. Similarly, 2 vol % Cu, 1 vol % SWCNT, and 3 vol % HyNF (0.6% Cu + 2.4% Al) as well as 2 vol % SWCNT and 3 vol % SWCNT (20% Me + 80% PW) nanofluids also exhibit equivalent heat transfer characteristics.

The present flow and heat transfer characteristics of Cu, Al, and SWCNT nanofluids in microchannel would be useful for providing guidance toward the design of efficient thermal systems in electronic cooling.

## Nomenclature

• A =

surface area of the particle (m2)

• Cp =

specific heat (J/kg K)

• d =

nanoparticle diameter (nm)

• Dh =

hydraulic diameter (m)

• kf =

fluid thermal conductivity (W/m K)

• ks =

solid thermal conductivity (W/m K)

• KB =

Boltzmann constant (J/K)

• Nu =

Nusselt number

• q0 =

heat flux (W/m2)

• Re =

Reynolds number

• T =

dimensional temperature (K)

• $U$ =

dimensional velocity vector (m/s)

• U =

dimensional axial velocity (m/s)

• Vp =

volume of the particle (m3)

• x =

axial length (m)

• y =

normal length (m)

• μ =

dynamic viscosity (kg/m s)

• ρ =

density (kg/m3)

• $ϕ$ =

volume concentration

Subscripts
• avg =

average

• bf =

base fluid

• c =

continuous phase

• f =

fluid

• i, j =

current grid point

• m =

mixture

• nf =

nanofluid

• p =

particle

• s =

solid

Superscript
• * =

nondimensional or dimensionless quantity

## References

Hassan, I. , Phutthavong, P. , and Abdelgawad, M. , 2004, “ Microchannel Heat Sinks: An Overview of the State-of-the-Art,” Microscale Thermophys. Eng., 8(3), pp. 183–205.
Tuckerman, D. B. , and Pease, F. R. , 1983, “ Microcapillary Thermal Interface Technology for VLSI Packaging,” Digest of Technical Papers—Symposium on VLSI Technology, Maui, HI, Sept. 13–15, pp. 60–61.
Tuckerman, D. B. , 1984, “ Heat Transfer Microstructures for Integrated Circuits,” Ph.D. thesis, Stanford University, Stanford, CA.
Wang, X.-Q. , and Mujumdar, A. S. , 2007, “ Heat Transfer Characteristics of Nanofluids: A Review,” Int. J. Therm. Sci., 46(1), pp. 1–19.
Rafati, M. , Hamidi, A. A. , and Shariati Niaser, M. , 2012, “ Application of Nanofluids in Computer Cooling Systems (Heat Transfer Performance of Nanofluids),” Appl. Therm. Eng., 45–46, pp. 9–14.
Azmi, W. H. , Abdul Hamid, K. , Usri, N. A. , Mamat, R. , and Sharma, K. V. , 2016, “ Heat Transfer Augmentation of Ethylene Glycol: Water Nanofluids and Applications: A Review,” Int. Commun. Heat Mass Transfer, 75, pp. 13–23.
Beck, M. P. , Sun, T. , and Teja, A. S. , 2007, “ The Thermal Conductivity of Alumina Nanoparticles Dispersed in Ethylene Glycol,” Fluid Phase Equilib., 260(2), pp. 275–278.
Beck, M. P. , Yuan, Y. , Warrier, P. , and Teja, A. S. , 2010, “ The Thermal Conductivity of Alumina Nanofluids in Water, Ethylene Glycol, and Ethylene Glycol + Water Mixtures,” J. Nanopart. Res., 12(4), pp. 1469–1477.
Garg, J. , Poudel, B. , Chiesa, M. , Gordon, J. B. , Ma, J. J. , Wang, J. B. , Ren, Z. F. , Kang, Y. T. , Ohtani, H. , Nanda, J. , McKinley, G. H. , and Chen, G. , 2008, “ Enhanced Thermal Conductivity and Viscosity of Copper Nanoparticles in Ethylene Glycol Nanofluid,” J. Appl. Phys., 103(7), p. 074301.
Xing, M. , Yu, J. , and Wang, R. , 2015, “ Thermo-Physical Properties of Water-Based Single Walled Carbon Nanotube Nanofluid as Advanced Coolant,” Appl. Therm. Eng., 87, pp. 344–351.
Vafaei, S. , and Wen, D. , 2010, “ Convective Heat Transfer of Alumina Nanofluids in a Microchannel,” ASME Paper No. IHTC14-22206.
Anoop, K. B. , Sundararajan, T. , and Das, S. K. , 2009, “ Effect of Particle Size on the Convective Heat Transfer in Nanofluid in the Developing Region,” Int. J. Heat Mass Transfer, 52(9), pp. 2189–2195.
Li, Q. , and Xuan, Y. , 2004, “ Flow and Heat Transfer Performances of NANOFLUIDS Inside Small Hydraulic Diameter Flat Tube,” J. Eng. Thermophys., 25(2), pp. 305–307.
Azizi, Z. , Alamdari, A. , and Malayeri, M. R. , 2016, “ Thermal Performance and Friction Factor of a Cylindrical Microchannel Heat Sink Cooled by Cu-Water Nanofluid,” Appl. Therm. Eng., 99, pp. 970–978.
Ding, Y. , Alias, H. , Wen, D. , and Williams, R. A. , 2006, “ Heat Transfer of Aqueous Suspensions of Carbon Nanotubes (CNT Nanofluids),” Int. J. Heat Mass Transfer, 49(2), pp. 240–250.
Lotfi, R. , Rashidi, A. M. , and Amrollahi, A. , 2012, “ Experimental Study on the Heat Transfer Enhancement of MWNT-Water Nanofluid in a Shell and Tube Heat Exchanger,” Int. Commun. Heat Mass Transfer, 39(1), pp. 108–111.
Saberi, M. , Kalbasi, M. , and Alipourzade, A. , 2013, “ Numerical Study of Forced Convective Heat Transfer of Nanofluids Inside a Vertical Tube,” Int. J. Therm. Technol., 3(1), pp. 10–15.
Meng, X. , and Li, Y. , 2015, “ Numerical Study of Natural Convection in a Horizontal Cylinder Filled With Water-Based Alumina Nanofluid,” Nanoscale Res. Lett., 10, pp. 1–10. [PubMed]
Bhadouriya, R. , Agrawal, A. , and Prabhu, S. V. , 2015, “ Experimental and Numerical Study of Fluid Flow and Heat Transfer in a Twisted Square Duct,” Int. J. Heat Mass Transfer, 82, pp. 143–158.
Hasan, M. I. , 2014, “ Investigation of Flow and Heat Transfer Characteristics in Micro Pin Fin Heat Sink With Nanofluid,” Appl. Therm. Eng., 63(2), pp. 598–607.
Hasan, M. I. , Rageb, A. M. A. , and Yaghoubi, M. , 2012, “ Investigation of a Counter Flow Microchannel Heat Exchanger Performance With Using Nanofluid as a Coolant,” J. Electron. Cool. Therm. Control, 2(3), pp. 35–43.
Dietz, C. R. , and Joshi, Y. K. , 2008, “ Single-Phase Forced Convection in Microchannels With Carbon Nanotubes for Electronics Cooling Applications,” Nanoscale Microscale Thermophys. Eng., 12(3), pp. 251–271.
Saghir, M. Z. , Ahadi, A. , Yousefi, T. , and Farahbakhsh, B. , 2016, “ Two-Phase and Single Phase Models of Flow of Nanofluid in a Square Cavity: Comparison With Experimental Results,” Int. J. Therm. Sci., 100, pp. 372–380.
Kalteh, M. , Abbassi, A. , Saffar-Avval, M. , and Harting, J. , 2011, “ Eulerian–Eulerian Two-Phase Numerical Simulation of Nanofluid Laminar Forced Convection in a Microchannel,” Int. J. Heat Fluid Flow, 32(1), pp. 107–116.
Singh, P. K. , Harikrishna, P. V. , Sundararajan, T. , and Das, S. K. , 2010, “ Experimental and Numerical Investigation of Flow of Nanofluids in Microchannels,” ASME Paper No. IHTC14-22474.
Singh, P. K. , Harikrishna, P. V. , Sundararajan, T. , and Das, S. K. , 2011, “ Experimental and Numerical Investigation Into the Heat Transfer Study of Nanofluids in Microchannel,” ASME J. Heat Transfer, 133(12), p. 121701.
Nimmagadda, R. , and Venkatasubbaiah, K. , 2015, “ Conjugate Heat Transfer Analysis of Micro-Channel Using Novel Hybrid Nanofluids (Al2O3 + Ag/Water),” Eur. J. Mech. B, 52, pp. 19–27.
Labib, M. N. , Nine, M. J. , Afrianto, H. , Chung, H. , and Jeong, H. , 2013, “ Numerical Investigation on Effect of Base Fluids and Hybrid Nanofluid in Forced Convective Heat Transfer,” Int. J. Therm. Sci., 71, pp. 163–171.
Derakhshan, M. M. , and Akhavan-Behabadi, M. A. , 2016, “ Mixed Convection of MWCNT-Heat Transfer Oil Nanofluid Inside Inclined Plain and Microfin Tubes Under Laminar Assisted Flow,” Int. J. Therm. Sci., 99, pp. 1–8.
Halelfadl, S. , Adham, A. M. , Mohd-Ghazali, N. , Mare, T. , Estelle, P. , and Ahmad, R. , 2014, “ Optimization of Thermal Performances and Pressure Drop of Rectangular Microchannel Heat Sink Using Aqueous Carbon Nanotubes Based Nanofluid,” Appl. Therm. Eng., 62(2), pp. 492–499.
Aqel, A. , Abou El-Nour, K. M. M. , Ammar, R. A. A. , and Al-Warthan, A. , 2012, “ Carbon Nanotubes, Science and Technology—Part I: Structure, Synthesis and Characterisation,” Arabian J. Chem., 5(1), pp. 1–23.
Pan, Z. W. , Xie, S. S. , Chang, B. H. , Wang, C. Y. , Lu, L. , Liu, W. , Zhou, W. Y. , Li, W. Z. , and Qian, L. X. , 1998, “ Very Long Carbon Nanotubes,” Nature, 394(6694), pp. 631–632.
Nimmagadda, R. , and Venkatasubbaiah, K. , 2016, “ Numerical Investigation on Conjugate Heat Transfer Performance of Micro-Channel Using Sphericity Based Gold and Carbon Nanoparticles,” Heat Transfer Eng., 38(1), pp. 87–102.
Xuan, Y. , and Roetzel, W. , 2000, “ Conceptions for Heat Transfer Correlation of Nanofluids,” Int. J. Heat Mass Transfer, 43(19), pp. 3701–3707.
Pak, B. C. , and Cho, Y. I. , 1998, “ Hydrodynamic and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles,” Exp. Heat Transfer, 11(2), pp. 151–170.
Brinkman, H. C. , 1952, “ The Viscosity of Concentrated Suspensions and Solutions,” J. Chem. Phys., 20(4), p. 571.
Hamilton, R. L. , and Crosser, O. K. , 1962, “ Thermal Conductivity of Heterogeneous Two-Component Systems,” Ind. Eng. Chem. Fundam., 1(3), pp. 187–191.
Patel, H. E. , Sundararajan, T. , Pradeep, T. , Dasgupta, A. , Dasgupta, N. , and Das, S. K. , 2005, “ A Micro-Convection Model for Thermal Conductivity of Nanofluids,” Pramana, 65(5), pp. 863–869.
Moraveji, M. K. , and Ardehali, R. M. , 2013, “ CFD Modeling (Comparing Single and Two-Phase Approaches) on Thermal Performance of Al2O3/Water Nanofluid in Mini-Channel Heat Sink,” Int. Commun. Heat Mass Transfer, 44(1), pp. 157–164.
Hejazian, M. , Moraveji, M. K. , and Beheshti, A. , 2014, “ Comparative Study of Euler and Mixture Models for Turbulent Flow of Al2O3 Nanofluid Inside a Horizontal Tube,” Int. Commun. Heat Mass Transfer, 52(3), pp. 152–158.
Behzadmehr, A. , Saffar Avval, M. , and Galanis, N. , 2007, “ Prediction of Turbulent Forced Convection of a Nanofluid in a Tube With Uniform Heat Flux Using a Two Phase Approach,” Int. J. Heat Fluid Flow, 28(2), pp. 211–219.
Sarhan Musa, M. , 2014, Nanoscale Flow: Advances, Modeling, and Applications, Taylor & Francis, Boca Raton, FL.
Manninen, M. , Taivassalo, V. , and Kallio, S. , 1996, On the Mixture Model for Multiphase Flow, Vol. 288, VTT Publications, Espoo, Finland, pp. 3–67.
Schiller, L. , and Naumann, A. , 1935, “ A Drag Coefficient Correlation,” Z. Ver. Deutsch. Ing., 77, pp. 318–320.
Cheng, L. , and Armfield, S. , 1995, “ A Simplified Marker and Cell Method for Unsteady Flows on Non-Staggered Grids,” Int. J. Numer. Methods Fluids, 21(1), pp. 15–34.
Harish, R. , and Venkatasubbaiah, K. , 2014, “ Numerical Investigation of Instability Patterns and Nonlinear Buoyant Exchange Flow Between Enclosures by Variable Density Approach,” Comput. Fluids, 96(1), pp. 276–287.
Rhie, C. M. , and Chow, W. L. , 1983, “ Numerical Study of the Turbulent Flow Past an Airfoil With Trailing Edge Separation,” AIAA J., 21(11), pp. 1525–1532.
Yu, B. , Tao, W.-Q. , and Wei, J.-J. , 2002, “ Discussion on Momentum Interpolation Method for Collocated Grids of Incompressible Flow,” Numer. Heat Transfer, Part B, 42(2), pp. 141–166.
Kalteh, M. , Abbassi, A. , Saffar-Avval, M. , Frijns, A. , Darhuber, A. , and Harting, J. , 2012, “ Experimental and Numerical Investigation of Nanofluid Forced Convection Inside a Wide Microchannel Heat Sink,” Appl. Therm. Eng., 36, pp. 260–268.
View article in PDF format.

## References

Hassan, I. , Phutthavong, P. , and Abdelgawad, M. , 2004, “ Microchannel Heat Sinks: An Overview of the State-of-the-Art,” Microscale Thermophys. Eng., 8(3), pp. 183–205.
Tuckerman, D. B. , and Pease, F. R. , 1983, “ Microcapillary Thermal Interface Technology for VLSI Packaging,” Digest of Technical Papers—Symposium on VLSI Technology, Maui, HI, Sept. 13–15, pp. 60–61.
Tuckerman, D. B. , 1984, “ Heat Transfer Microstructures for Integrated Circuits,” Ph.D. thesis, Stanford University, Stanford, CA.
Wang, X.-Q. , and Mujumdar, A. S. , 2007, “ Heat Transfer Characteristics of Nanofluids: A Review,” Int. J. Therm. Sci., 46(1), pp. 1–19.
Rafati, M. , Hamidi, A. A. , and Shariati Niaser, M. , 2012, “ Application of Nanofluids in Computer Cooling Systems (Heat Transfer Performance of Nanofluids),” Appl. Therm. Eng., 45–46, pp. 9–14.
Azmi, W. H. , Abdul Hamid, K. , Usri, N. A. , Mamat, R. , and Sharma, K. V. , 2016, “ Heat Transfer Augmentation of Ethylene Glycol: Water Nanofluids and Applications: A Review,” Int. Commun. Heat Mass Transfer, 75, pp. 13–23.
Beck, M. P. , Sun, T. , and Teja, A. S. , 2007, “ The Thermal Conductivity of Alumina Nanoparticles Dispersed in Ethylene Glycol,” Fluid Phase Equilib., 260(2), pp. 275–278.
Beck, M. P. , Yuan, Y. , Warrier, P. , and Teja, A. S. , 2010, “ The Thermal Conductivity of Alumina Nanofluids in Water, Ethylene Glycol, and Ethylene Glycol + Water Mixtures,” J. Nanopart. Res., 12(4), pp. 1469–1477.
Garg, J. , Poudel, B. , Chiesa, M. , Gordon, J. B. , Ma, J. J. , Wang, J. B. , Ren, Z. F. , Kang, Y. T. , Ohtani, H. , Nanda, J. , McKinley, G. H. , and Chen, G. , 2008, “ Enhanced Thermal Conductivity and Viscosity of Copper Nanoparticles in Ethylene Glycol Nanofluid,” J. Appl. Phys., 103(7), p. 074301.
Xing, M. , Yu, J. , and Wang, R. , 2015, “ Thermo-Physical Properties of Water-Based Single Walled Carbon Nanotube Nanofluid as Advanced Coolant,” Appl. Therm. Eng., 87, pp. 344–351.
Vafaei, S. , and Wen, D. , 2010, “ Convective Heat Transfer of Alumina Nanofluids in a Microchannel,” ASME Paper No. IHTC14-22206.
Anoop, K. B. , Sundararajan, T. , and Das, S. K. , 2009, “ Effect of Particle Size on the Convective Heat Transfer in Nanofluid in the Developing Region,” Int. J. Heat Mass Transfer, 52(9), pp. 2189–2195.
Li, Q. , and Xuan, Y. , 2004, “ Flow and Heat Transfer Performances of NANOFLUIDS Inside Small Hydraulic Diameter Flat Tube,” J. Eng. Thermophys., 25(2), pp. 305–307.
Azizi, Z. , Alamdari, A. , and Malayeri, M. R. , 2016, “ Thermal Performance and Friction Factor of a Cylindrical Microchannel Heat Sink Cooled by Cu-Water Nanofluid,” Appl. Therm. Eng., 99, pp. 970–978.
Ding, Y. , Alias, H. , Wen, D. , and Williams, R. A. , 2006, “ Heat Transfer of Aqueous Suspensions of Carbon Nanotubes (CNT Nanofluids),” Int. J. Heat Mass Transfer, 49(2), pp. 240–250.
Lotfi, R. , Rashidi, A. M. , and Amrollahi, A. , 2012, “ Experimental Study on the Heat Transfer Enhancement of MWNT-Water Nanofluid in a Shell and Tube Heat Exchanger,” Int. Commun. Heat Mass Transfer, 39(1), pp. 108–111.
Saberi, M. , Kalbasi, M. , and Alipourzade, A. , 2013, “ Numerical Study of Forced Convective Heat Transfer of Nanofluids Inside a Vertical Tube,” Int. J. Therm. Technol., 3(1), pp. 10–15.
Meng, X. , and Li, Y. , 2015, “ Numerical Study of Natural Convection in a Horizontal Cylinder Filled With Water-Based Alumina Nanofluid,” Nanoscale Res. Lett., 10, pp. 1–10. [PubMed]
Bhadouriya, R. , Agrawal, A. , and Prabhu, S. V. , 2015, “ Experimental and Numerical Study of Fluid Flow and Heat Transfer in a Twisted Square Duct,” Int. J. Heat Mass Transfer, 82, pp. 143–158.
Hasan, M. I. , 2014, “ Investigation of Flow and Heat Transfer Characteristics in Micro Pin Fin Heat Sink With Nanofluid,” Appl. Therm. Eng., 63(2), pp. 598–607.
Hasan, M. I. , Rageb, A. M. A. , and Yaghoubi, M. , 2012, “ Investigation of a Counter Flow Microchannel Heat Exchanger Performance With Using Nanofluid as a Coolant,” J. Electron. Cool. Therm. Control, 2(3), pp. 35–43.
Dietz, C. R. , and Joshi, Y. K. , 2008, “ Single-Phase Forced Convection in Microchannels With Carbon Nanotubes for Electronics Cooling Applications,” Nanoscale Microscale Thermophys. Eng., 12(3), pp. 251–271.
Saghir, M. Z. , Ahadi, A. , Yousefi, T. , and Farahbakhsh, B. , 2016, “ Two-Phase and Single Phase Models of Flow of Nanofluid in a Square Cavity: Comparison With Experimental Results,” Int. J. Therm. Sci., 100, pp. 372–380.
Kalteh, M. , Abbassi, A. , Saffar-Avval, M. , and Harting, J. , 2011, “ Eulerian–Eulerian Two-Phase Numerical Simulation of Nanofluid Laminar Forced Convection in a Microchannel,” Int. J. Heat Fluid Flow, 32(1), pp. 107–116.
Singh, P. K. , Harikrishna, P. V. , Sundararajan, T. , and Das, S. K. , 2010, “ Experimental and Numerical Investigation of Flow of Nanofluids in Microchannels,” ASME Paper No. IHTC14-22474.
Singh, P. K. , Harikrishna, P. V. , Sundararajan, T. , and Das, S. K. , 2011, “ Experimental and Numerical Investigation Into the Heat Transfer Study of Nanofluids in Microchannel,” ASME J. Heat Transfer, 133(12), p. 121701.
Nimmagadda, R. , and Venkatasubbaiah, K. , 2015, “ Conjugate Heat Transfer Analysis of Micro-Channel Using Novel Hybrid Nanofluids (Al2O3 + Ag/Water),” Eur. J. Mech. B, 52, pp. 19–27.
Labib, M. N. , Nine, M. J. , Afrianto, H. , Chung, H. , and Jeong, H. , 2013, “ Numerical Investigation on Effect of Base Fluids and Hybrid Nanofluid in Forced Convective Heat Transfer,” Int. J. Therm. Sci., 71, pp. 163–171.
Derakhshan, M. M. , and Akhavan-Behabadi, M. A. , 2016, “ Mixed Convection of MWCNT-Heat Transfer Oil Nanofluid Inside Inclined Plain and Microfin Tubes Under Laminar Assisted Flow,” Int. J. Therm. Sci., 99, pp. 1–8.
Halelfadl, S. , Adham, A. M. , Mohd-Ghazali, N. , Mare, T. , Estelle, P. , and Ahmad, R. , 2014, “ Optimization of Thermal Performances and Pressure Drop of Rectangular Microchannel Heat Sink Using Aqueous Carbon Nanotubes Based Nanofluid,” Appl. Therm. Eng., 62(2), pp. 492–499.
Aqel, A. , Abou El-Nour, K. M. M. , Ammar, R. A. A. , and Al-Warthan, A. , 2012, “ Carbon Nanotubes, Science and Technology—Part I: Structure, Synthesis and Characterisation,” Arabian J. Chem., 5(1), pp. 1–23.
Pan, Z. W. , Xie, S. S. , Chang, B. H. , Wang, C. Y. , Lu, L. , Liu, W. , Zhou, W. Y. , Li, W. Z. , and Qian, L. X. , 1998, “ Very Long Carbon Nanotubes,” Nature, 394(6694), pp. 631–632.
Nimmagadda, R. , and Venkatasubbaiah, K. , 2016, “ Numerical Investigation on Conjugate Heat Transfer Performance of Micro-Channel Using Sphericity Based Gold and Carbon Nanoparticles,” Heat Transfer Eng., 38(1), pp. 87–102.
Xuan, Y. , and Roetzel, W. , 2000, “ Conceptions for Heat Transfer Correlation of Nanofluids,” Int. J. Heat Mass Transfer, 43(19), pp. 3701–3707.
Pak, B. C. , and Cho, Y. I. , 1998, “ Hydrodynamic and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles,” Exp. Heat Transfer, 11(2), pp. 151–170.
Brinkman, H. C. , 1952, “ The Viscosity of Concentrated Suspensions and Solutions,” J. Chem. Phys., 20(4), p. 571.
Hamilton, R. L. , and Crosser, O. K. , 1962, “ Thermal Conductivity of Heterogeneous Two-Component Systems,” Ind. Eng. Chem. Fundam., 1(3), pp. 187–191.
Patel, H. E. , Sundararajan, T. , Pradeep, T. , Dasgupta, A. , Dasgupta, N. , and Das, S. K. , 2005, “ A Micro-Convection Model for Thermal Conductivity of Nanofluids,” Pramana, 65(5), pp. 863–869.
Moraveji, M. K. , and Ardehali, R. M. , 2013, “ CFD Modeling (Comparing Single and Two-Phase Approaches) on Thermal Performance of Al2O3/Water Nanofluid in Mini-Channel Heat Sink,” Int. Commun. Heat Mass Transfer, 44(1), pp. 157–164.
Hejazian, M. , Moraveji, M. K. , and Beheshti, A. , 2014, “ Comparative Study of Euler and Mixture Models for Turbulent Flow of Al2O3 Nanofluid Inside a Horizontal Tube,” Int. Commun. Heat Mass Transfer, 52(3), pp. 152–158.
Behzadmehr, A. , Saffar Avval, M. , and Galanis, N. , 2007, “ Prediction of Turbulent Forced Convection of a Nanofluid in a Tube With Uniform Heat Flux Using a Two Phase Approach,” Int. J. Heat Fluid Flow, 28(2), pp. 211–219.
Sarhan Musa, M. , 2014, Nanoscale Flow: Advances, Modeling, and Applications, Taylor & Francis, Boca Raton, FL.
Manninen, M. , Taivassalo, V. , and Kallio, S. , 1996, On the Mixture Model for Multiphase Flow, Vol. 288, VTT Publications, Espoo, Finland, pp. 3–67.
Schiller, L. , and Naumann, A. , 1935, “ A Drag Coefficient Correlation,” Z. Ver. Deutsch. Ing., 77, pp. 318–320.
Cheng, L. , and Armfield, S. , 1995, “ A Simplified Marker and Cell Method for Unsteady Flows on Non-Staggered Grids,” Int. J. Numer. Methods Fluids, 21(1), pp. 15–34.
Harish, R. , and Venkatasubbaiah, K. , 2014, “ Numerical Investigation of Instability Patterns and Nonlinear Buoyant Exchange Flow Between Enclosures by Variable Density Approach,” Comput. Fluids, 96(1), pp. 276–287.
Rhie, C. M. , and Chow, W. L. , 1983, “ Numerical Study of the Turbulent Flow Past an Airfoil With Trailing Edge Separation,” AIAA J., 21(11), pp. 1525–1532.
Yu, B. , Tao, W.-Q. , and Wei, J.-J. , 2002, “ Discussion on Momentum Interpolation Method for Collocated Grids of Incompressible Flow,” Numer. Heat Transfer, Part B, 42(2), pp. 141–166.
Kalteh, M. , Abbassi, A. , Saffar-Avval, M. , Frijns, A. , Darhuber, A. , and Harting, J. , 2012, “ Experimental and Numerical Investigation of Nanofluid Forced Convection Inside a Wide Microchannel Heat Sink,” Appl. Therm. Eng., 36, pp. 260–268.

## Figures

Fig. 1

Schematic diagram of microchannel

Fig. 2

Grid independence study at Re = 600: ((a) and (c)) velocity and ((b) and (d)) temperature

Fig. 3

Pure water (solid lines) and 3 vol % SWCNT nanofluid (dashed lines) for Re = 600: (a) velocity contours and (b) temperature contours

Fig. 4

Effect of Re and volume concentration: (a) interface temperature along the channel length and ((b) and (c)) local Nusselt number along the channel length

Fig. 5

Validation with experimental and numerical results in terms of average Nusselt number

Fig. 6

Dimensional profiles of 3 vol % SWCNT nanofluid for different Re: (a) velocity at exit and (b) temperature at exit

Fig. 7

Dimensional profiles of velocity at exit of the microchannel for pure water and different nanofluids at Re = 600

Fig. 8

Dimensional profiles of temperature at exit of the microchannel for pure water and different nanofluids at Re = 600

Fig. 9

Average Nusselt numbers of pure water and different nanofluids at different Re

## Tables

Table 1 Thermophysical properties of base fluids and nanofluids
Table 2 Grid independence study at Re = 600
Table 3 Average Nusselt number values of pure water and nanofluids with respect to volume concentration and Reynolds numbers

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections