Numerical investigation of heat transfer enhancement using carbon nanotube-based non-Newtonian nanofluids

International Communications in Heat and Mass Transfer 37 (2010) 1153–1157

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International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t

Numerical investigation of heat transfer enhancement using carbon nanotube-based non-Newtonian nanofluids☆ R. Kamali ⁎, A.R. Binesh Department of Mechanical Engineering, Shiraz University, Shiraz, 71348-51154, Iran

a r t i c l e

i n f o

Available online 3 July 2010 Keywords: Carbon nanotube (CNT) Nanofluids Non-Newtonian fluid CFD

a b s t r a c t In this study convective heat transfer of multi-wall carbon nanotube (MWCNT)-based nanofluids in a straight tube under constant wall heat flux condition is numerically investigated. To achieve this goal Navier–Stokes equations are solved using the finite volume technique with considering CNT-based nanofluids as non-Newtonian fluids of shear-thinning character using the non-Newtonian power law model. The objectives of this research are to provide detailed information of non-Newtonian behavior of CNT nanofluids, comparison of the numerical simulation predictions to the experimental measurements and investigation of non-Newtonian effects on the local heat transfer of the CNT nanofluid and compare the thermal performance of the CNT nanofluids and conventional fluids. As a result the heat transfer coefficient is dominated by the wall region due to non-Newtonian behavior of CNT nanofluid. The results reported in this paper illustrate that the numerical simulation can be one of the most powerful and beneficial tools for the CNT nanofluids optimization and performance analysis. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Due to the rapid development of modern technology, recent micro electromechanical systems (MEMS) generate an enormous amount of heat, which disturbs the normal performance of the devices and reduces reliability [13]. Therefore, an efficient cooling system is one of the most important problems in designing MEMS components. In the recent years the considerable amount of research and development on MEMS cooling performance and improvements in cooling capabilities have been performed. However a large amount of these researches have been lacking because conventional fluids have poor heat transfer properties. Therefore industrial cooling devices using nanofluids as coolants are increasingly important in current and future heat removal applications. The concept of nanofluids refers to a new kind of heat transport fluid that is a mixture of suspending nanoscale metallic or nonmetallic particles and a base heat transfer liquid. The use of nanofluids in the place of conventional heat transfer fluids offers great potential to increase the performance of liquid cooling systems without increasing the complexity of cooling system. The nanofluids can be classified by kinds of nanoparticle materials. Metallic nanoparticles, such as Cu and Fe are the first kind of materials. The second kind and prevalent materials are metal oxide nanoparticles such as Al2O3 and CuO. The third type is carbon nanotubes (CNTs). Single-wall carbon nanotubes (SWCNTs) and ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (R. Kamali). 0735-1933/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2010.06.001

multi-walled carbon nanotubes (MWCNTs) are cylindrical allotropes of carbon. SWCNTs consist of a single cylinder of graphene, while MWCNTs are tubular structures which are composed of multilayered concentric cylinders of single graphene sheets and are many microns in length but with nanometer-sized diameters. It would appear that carbon nanotubes would be the ideal fibers for heat transport because of their high aspect ratios and also because their thermal conductivity is higher than metallic and metal oxide nanoparticles. Many experimental and numerical investigations have been carried out to determine convective heat transfer characteristics for nanofluids based on metallic and metal oxide nanoparticles. Parameters involved in such studies are size of nanoparticles [2,6,12], concentration of nanoparticles (Hwan [7,8,16]), thermal conductivity [5,14,15,17] and etc. A few studies have been reported to date on convective heat transfer of aqueous CNT nanofluids and more research works must be carried out to investigate the characteristics of CNT nanofluids and the mechanism of the forced convective heat transfer of CNT nanofluids. Faulkner et al. [3] illustrated the force convection heat transfer enhancement of aqueous CNT nanofluids through a microchannel on the extremely low Reynolds number flow condition and 1.1–4.4% CNT volume concentrations. Y. Ding et al. [1] investigated the convective heat transfer of CNT-based nanofluids through a horizontal tube. They have shown that the maximum convective heat transfer coefficient enhancement reaches over 350% at laminar flow and constant wall heat flux conditions and they illustrated that the convective heat transfer enhancement depends on the flow condition and CNT concentration. Also they experimentally analyzed the CNT–water

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Nomenclature C K P q″ Re T V

heat capacity thermal conductivity pressure heat flux Reynolds number temperature velocity vector

Greek symbols μ viscosity ρ density η non-Newtonian viscosity γ̇ shear rate ϕ volume fraction

Subscripts nf nanofluid bf base fluid

nanofluids viscosity and they have shown that the viscosity of CNT nanofluids increased with decreasing temperature and increasing CNT concentration. P. Garg et al. [4] have experimentally investigated viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids in a straight cooper tube. They reported thermal conductivity and heat transfer coefficient enhancement in the tube at different Reynolds number and 1% CNT volume concentration and they found that CNT nanofluids exhibit a shearthinning non-Newtonian behavior. In this study the heat transfer characteristics of the aqueous MWCNTs nanofluids and non-Newtonian behavior of CNT nanofluids and effects of shear-thinning non-Newtonian behavior of CNT nanofluids on the heat transfer characteristics are numerically investigated. 2. Computational model 2.1. Geometry and grid

state conservation of mass, momentum and energy equations are as follows: Continuity equation: → ∇⋅ V = 0

ð1Þ

Momentum equation: →  →  → ρnf V⋅∇ V = −∇p + ∇⋅ μnf ∇ V

ð2Þ

Energy equation: → ρnf Cnf V⋅∇T = ∇⋅½knf ∇T

ð3Þ

where, ρnf, μnf, Cnf and knf are density, viscosity, heat capacity and → thermal conductivity of nanofluid, respectively, V is the velocity vector, p is the pressure and T is the nanofluid temperature. 2.3. Thermophysical and rheological properties of CNT nanofluid The density and specific heat have been described by classical formulas developed for conventional solid–liquid mixtures with the assumption that the carbon nanotubes are well dispersed within the base fluid: ρnf = ð1−ϕÞρbf + ϕρp

ð4Þ

Cpnf = ð1−ϕÞCpbf + ϕCpp

ð5Þ

where ϕ is the volume fraction of the CNTs, ρ and Cp are density and specific heat and the subscripts nf, bf, p refer to nanofluid, base fluid and CNTs respectively. Most of experimental studies on the viscosity of aqueous nanofluids have been limited to metal oxide nanofluids such as Al2O3 [11], CuO [10] and only a few researchers have studied viscosity of aqueous CNT nanofluids [1,4,9]. These research works show that the viscosity of CNT nanofluids is a function of shear rate and the nonNewtonian shear-thinning behavior was observed for aqueous MWCNT nanofluids. The current study correlates empirical data of MWCNT nanofluids reported by P. Garg et al. [4] with a theoretical non-Newtonian viscosity model. Several models have been developed to describe the viscosity behavior of non-Newtonian fluids based on

The computational domain used in the numerical simulations is shown in Fig. 1. It is the same as P. Garg et al.'s experimental work in (2009). The tube length is 914.4 mm and the tube diameter is 1.55 mm. A constant heat flux is applied around the tube wall. The computational domain is effectively reduced by exploiting axisymmetric boundary along the centerline of the tube. For all cases investigated in this study, a structured grid is used for the CFD simulations. 2.2. Governing equations The single phase model is used for numerical investigation of twodimensional axisymmetric steady, forced laminar convection flow of nanofluid inside a straight circular tube. Moreover nanofluid is assumed to be incompressible and non-Newtonian. Therefore, steady

Fig. 1. Schematic view of two-dimensional computational domain for a straight tube.

Fig. 2. 1% MWCNT nanofluid viscosity experimental data and the power law model fitting curve.

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Fig. 3. 1% MWCNT nanofluid thermal conductivity experimental data and third order polynomial fitting curve.

Fig. 4. Comparison of predicted and measured heat transfer coefficient at Re = 600 for 1% CNT nanofluid and water.

experimental and theoretical studies. For shear thinning (Pseudo plastics) and shear thickening (dilutant materials) non-Newtonian fluid, the apparent viscosity is generally expressed by the power law non-Newtonian model:

carbon nanotube (MWCNT)-based nanofluids in a tube with 914.4 mm length and 1.55 mm diameter under constant wall heat flux condition (q″ = 0.6 W/cm2). Numerical simulations were carried out for both water base fluid and aqueous 1% CNT nanofluid. Initial numerical simulations were carried out for water base fluid to check the accuracy of simulations and comparison of base fluid heat transfer characteristics with the aqueous 1% CNT nanofluid. The present study is validated by comparing the results with experimental data reported in the literature [4]. Figs. 4–6 show the predicted heat transfer coefficient for three Reynolds numbers Re = 600, Re = 900 and Re = 1200 in comparison with experimental data for both 1% CNT nanofluid and water base fluid. As seen in these figures, the computed heat transfer coefficient is in good agreement with the experimental data at different Reynolds numbers. This good agreement between numerical results and experimental data could be due to considering suitable models for thermophysical and rheological properties of CNT nanofluid. Also the results clearly show that CNT nanofluids considerably exhibit improved convective heat transfer coefficient and the percentage convective heat transfer coefficient enhancement increases continuously with the axial distance. The maximum percentage enhancement in heat transfer coefficient is about 30% and is observed at Re = 600. In Fig. 7 the radial profiles of CNT nanofluid viscosity in different locations of entrance region at Re = 900 are illustrated. The viscosity of non-Newtonian CNT nanofluid at the center of the tube is at its maximum value and decreases to its minimum value at the tube wall because the shear rate close to the wall is big; also the average viscosity in the tube inlet is higher than other locations because the shear rate is small, while the heat transfer coefficient is dominated by the wall region. Therefore the nonNewtonian behavior of CNT nanofluid is one of the important heat transfer characteristics. Fig. 8 shows the radial profiles of CNT nanofluid thermal conductivity in different axial sections at Re = 900. The thermal conductivity increases gradually along the radial direction from the tube center to the wall and along the axial direction of the tube

n−1

η = kγ˙

ð6Þ

where η, k, γ̇ and n are non-Newtonian viscosity, flow consistency index, shear rate and flow behavior index, respectively. Fig. 2 shows the measured viscosity of 1% MWCNT nanofluid data and the power law model fitting curve. According to this figure, the MWCNT nanofluid viscosity fitted well with the power law viscosity model. For thermal conductivity of aqueous CNT nanofluids the temperature dependency is considered. Fig. 3 illustrated the 1% MWCNT nanofluid thermal conductivity experimental data and the third order polynomial fitting curve that are used in the simulations. Parameters used in viscosity and thermal conductivity equations of non-Newtonian CNT nanofluid are summarized in Table 1. 2.4. Numerical model A segregated solution algorithm with a finite volume-based technique is used as the numerical method. This technique consists of an integration of the governing equations of mass, momentum, and energy on the individual cells within the computational domain to construct algebraic equations for each unknown dependent variable. The pressure and velocity are coupled using the SIMPLE (semiimplicit method for pressure linked equations) algorithm which uses a guess-and-correct procedure for the calculation of pressure on the staggered grid arrangement. The second order upwind scheme is employed for the discretization of the model equations as it is always bounded and provides stability for the pressure-correction equation. 3. Validation and results In this work a number of numerical simulations have been performed to study force convective heat transfer of multi-wall

Table 1 Viscosity and thermal conductivity equation parameters used in simulations. Viscosity

Thermal conductivity

Equation

k

n

Equation

a

b

c

d

η = kγ˙ n−1

0.00135

0.963

K = a + bT + cT2 + dT3

−287.6

3.022

−0.010557

1.22885e−05

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Fig. 5. Comparison of predicted and measured heat transfer coefficient at Re = 900 for 1% CNT nanofluid and water.

Fig. 8. Thermal conductivity radial profiles of CNT nanofluid in different locations at Re = 900.

Fig. 9 shows the average Nusselt number at different Reynolds numbers for 1% CNT nanofluid and water. In this figure the heat transfer performance of the 1% CNT nanofluid was compared to water base fluid. Form this figure; it was observed that the Nusselt numbers for CNT nanofluid are higher than those of water and CNT nanofluid has better heat transfer properties compared to the base fluid. 4. Conclusion

Fig. 6. Comparison of predicted and measured heat transfer coefficient at Re = 1200 for 1% CNT nanofluid and water.

because the bulk temperature of the CNT nanofluid increases along the axial and radial directions, which results in the increase of CNT nanofluid thermal conductivity.

Fig. 7. Viscosity radial profiles of CNT nanofluid in different locations at Re = 900.

In this paper, the study of non-Newtonian CNT nanofluids heat transfer performance analysis through a straight tube under laminar flow and constant heat flux conditions was performed. For the simulation of nanofluid flow field, the incompressible Navier–Stokes equations coupled with energy equation were solved numerically using the finite volume method. The shear-thinning behavior of nonNewtonian CNT nanofluid is investigated using the non-Newtonian power law. The results show that the numerical method coupled with this non-Newtonian model is capable of modeling the action of CNT nanofluid flows passing the tube and the heat transfer coefficient is dominated by the wall region due to non-Newtonian behavior of CNT nanofluid. The characteristics of nanofluid flow such as heat transfer coefficient, thermal conductivity and viscosity are investigated in the computational domain. Results were validated and compared with available experimental data for CNT nanofluid and base fluid. A good

Fig. 9. Average Nusselt number at different Reynolds numbers for 1% CNT nanofluid and water.

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agreement between the predicted and experimental values ensures the accuracy of the numerical predictions collected with the present work.

[8] [9]

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