Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model

doi:10.1016/j.icheatmasstransfer.2009.08.003

International Communications in Heat and Mass Transfer

Volume 37, Issue 1, January 2010, Pages 91-97

https://doi.org/10.1016/j.icheatmasstransfer.2009.08.003 Get rights and content

Abstract

Laminar convective heat transfer of nanofluids in a circular tube under constant wall temperature condition is studied numerically using a CFD¹ approach. Single-phase and two-phase models have been used for prediction of temperature, flow field, and calculation of heat transfer coefficient. Effects of some important parameters such as nanoparticle sources, nanoparticle volume fraction and nanofluid Peclet number on heat transfer rate have been investigated. The results of CFD simulation based on two-phase model were used for comparison with single-phase model, theoretical models and experimental data. Results have shown that heat transfer coefficient clearly increases with an increase in particle concentration. Also the heat transfer enhancement increases with Peclet number. Two-phase model shows better agreement with experimental measurements. For Cu/Water nanofluid with 0.2% concentration, the average relative error between experimental data and CFD results based on single-phase model was 16% while for two-phase model was 8%. Based on the results of the simulation it was concluded that the two-phase approach gives better predictions for heat transfer rate compared to the single-phase model.

Introduction

Nanofluids are containing nanopowders with dimensions smaller than 100 nm and are suspended in base fluid such as water or ethylene glycol. Nanofluids were first used by Choi et al., at the Argon national laboratory [1]. Nanofluids enhance the heat transfer rate of the base fluids [2], [3], [4]. Addition of small amount of high thermal conductivity solid nanoparticles in base fluid increases the thermal conductivity, thus increasing the heat transfer rate. In fact the reduction of the thermal boundary layer thickness due to the presence of the nanoparticles and the random motion within the base fluid may have important contributions to such heat transfer improvement as well [5], [6]. By increasing the nanofluid concentration, the heat transfer rate increases, because under these conditions the interaction and collision of nanoparticles intensifies. Also diffusion and relative movement of particles near the wall leads to rapid heat transfer from wall to nanofluid.

Use of nanofluids to increase the heat transfer rate has some benefits such as [7], [8]:

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Heat transfer system size reduction
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Heat transfer improvement
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Weight and cost reduction of thermal apparatus
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Minimal clogging and
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Microchannel cooling and miniaturization of systems.

There are several published articles related to investigation of convective heat transfer of nanofluids, most of them are based on experimental works [9], [10], [11], [12], [13], [14].

Li and Xuan presented experimental study to investigate the heat transfer coefficient and friction factor of Cu/Water nanofluid up to 2% volume concentration [9], [10]. The experimental results showed that the Nusselt number of Cu/Water nanofluid with 2% volume concentration was 60% higher than base fluid.

Yang et al., reported experimental investigation of convective heat transfer of graphite/Water nanofluid in a horizontal tube heat exchanger [11]. In this study effect of Reynolds number, volume fraction, temperature and nanoparticle source on heat transfer coefficient have been studied. The results illustrated that heat transfer coefficient increases with the Reynolds number and particle volume fraction.

Experimental studies on convective heat transfer of Cu/Water, CuO/Water and Al₂O₃/Water nanofluids are reported by Zeinali et al. [12], [13].

The experimental set-up consisted of a one-meter annular tube, which was constructed of 6 mm diameter inner cupper tube 0.5 mm thick, and 32 mm diameter outer stainless steel tube. The nanofluid flows inside the inner tube while saturated steam entered the annular section, which created constant wall temperature condition.

The effect of Peclet number and nanoparticle volume fraction on heat transfer of different nanofluids has been studied. The augmentation of heat transfer using nanofluids was found to be much higher than the predictions of existing correlations.

There are a few publications dealing with numerical studies on convective heat transfer of nanofluids [14], [15], [16], [17], [18], [19].

Numerical modeling of heat transfer of nanofluids can be conducted using two-phase or single-phase (homogeneous) approaches. Most of the studies in this area have been made using homogeneous model. In this model it is assumed that the fluid phase and nanoparticles are in thermal equilibrium with zero relative velocity. This assumption is reasonable when the base fluid easily fluidized, thus it can be approximately considered to behave as a single fluid.

In two-phase model, base fluid and nanoparticles are considered as two different liquid and solid phases with different momentums respectively. In this model the eulerian or lagrangian framework can be used. In the eulerian/eulerian framework, each phase is treated as an interpenetrating continuum having separate transport equations.

Maiga et al., proposed a numerical formulation for investigation of forced convective heat transfer of Water/Al₂O₃ and ethylene glycol/Al₂O₃ nanofluids inside a heated tube [14]. The single-phase model has been used for simulation. The results showed that heat transfer increased with increasing particle volume fraction and ethylene glycol/Al₂O₃ gave higher heat transfer enhancement than Water/Al₂O₃ [14].

Praveen K. Namburu et al. presented a single-phase model to study the turbulent flow and heat transfer characteristics of nanofluids in a circular tube. Their results showed that the nanofluid containing smaller diameter nanoparticles showed higher viscosity and Nusselt number [15].

Akbarnia and Behzadmehr reported a CFD model based on single-phase model for investigation of laminar convection of Water/Al₂O₃ nanofluid in a horizontal curved tube. In their study, effects of buoyancy force, centrifugal force and nanoparticle concentration have been discussed [16].

Zeinali et al. proposed a dispersion model to account for the presence of nanoparticles in nanofluid. They showed that the dispersion and random movement of nanoparticles inside the fluid change the structure of flow field and led to heat transfer enhancement [17].

Behzadmehr et al. and Mirmasoumi et al. have used two-phase model for prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux. In their work the mixture model, based on the single fluid two-phase model was employed in the CFD simulation [18], [19].

The aim of this study is to compare two-phase and single-phase models for prediction of laminar heat transfer in a tube with constant wall temperature.

The effects of Peclet number, particle volume fraction and nanoparticle sources on heat transfer rate have been investigated under laminar conditions. The CFD results have been compared to the theoretical models and experimental data reported by Zeinali et al. [12], [13].

Section snippets

Experimental background

Experimental studies on convective heat transfer of Cu/Water, CuO/Water and Al₂O₃/Water nanofluids are reported by Zeinali et al. [12], [13].

The experimental set-up is shown in Fig. 1 and consisted of a one-meter annular tube, which was constructed of 6 mm diameter inner cupper tube with 0.5 mm thickness, and 32 mm diameter outer stainless steel tube. The nanofluid flows inside the inner tube while saturated steam enters the annular section, which created constant wall temperature condition. The

CFD modeling

The CFD approach uses a numerical technique for solving the governing equations for a given flow geometry and boundary conditions. In this paper flow pattern and temperature distribution through a circular pipe were simulated using a commercial CFD package, CFX version 11. The use of CFD reduces the number of necessary experiments and gives results, which would hardly be accessible by measurements [20], [21].

The detailed flow field for the single-phase and two-phase flows in a circular tube

Results and discussions

In order to establish accuracy of the numerical model, the predicted Nusselt number for distilled water inside a tube with constant wall temperature has been compared to the experimental data and Seider–Tate relation (Eq. (14)) for laminar flow.

The relations are as follows: $h_{nf} (exp) = {\frac{C_{p_{nf}} \cdot ρ_{nf} \bar{U} \cdot A \cdot (T_{b 2} - T_{b 1})}{π \cdot D \cdot L \cdot {(T_{w} - T_{b})}_{L M}}}_{}$ $N u_{nf} (exp) = \frac{h_{nf} (exp) \cdot D}{k_{nf}}$ $N u_{nf} (C F D) = \frac{h_{nf}_{(CFD)} \cdot D}{k_{nf}}$ $N u_{nf} (Theory) = 1.86 {({Re}_{nf} \cdot \Pr_{nf} \cdot \frac{D}{L})}^{\frac{1}{3}} {(\frac{μ_{nf}}{μ_{wnf}})}^{0.14}$ $R e_{nf} = \frac{ρ_{nf} \bar{U} D}{μ_{nf}}$ $P r_{nf} = \frac{C_{p_{nf}} \cdot μ_{nf}}{k_{nf}} .$

Fig. 3 shows the comparison between the experimental

Conclusions

In the present work the Computational Fluid Dynamics models have been developed to predict the convective heat transfer coefficient of different nanofluids in a circular tube.

The volume-averaged continuity, momentum, and energy equations were numerically solved using CFX version 11. Single-phase and two-phase models have been used for prediction of temperature and fluid flow distribution and calculation of heat transfer coefficient. It has been shown that the two-phase model is more precise

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^☆: Communicated by W.J. Minkowycz.

¹: Computational Fluid Dynamics.

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Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model☆

Abstract

Introduction

Section snippets

Experimental background

CFD modeling

Results and discussions

Conclusions

International Journal of Heat and Fluid Flow

International Journal of Heat and Mass Transfer

International Journal of Heat and Mass Transfer

Superlattices and Microstructures

Renewable and sustainable energy reviews

International Journal of Heat and Mass Transfer

International Journal of Thermal Science

International Journal of Heat and Mass Transfer

Superlattices and Microstructures

International Journal of Thermal Science

International Journal of Heat and Fluid Flow