# CFD simulation of the effect of particle size on the nanofluids convective heat transfer in the developed region in a circular tube

- Reza Davarnejad
^{1}Email author, - Sara Barati
^{1}and - Maryam Kooshki
^{2}

**2**:192

**DOI: **10.1186/2193-1801-2-192

© Davarnejad et al.; licensee Springer. 2013

**Received: **7 January 2013

**Accepted: **15 March 2013

**Published: **30 April 2013

## Abstract

The CFD simulation of heat transfer characteristics of a nanofluid in a circular tube under constant heat flux was considered using Fluent software (version 6.3.26) in the laminar flow. Al_{2}O_{3} nanoparticles in water with concentrations of 0.5%, 1.0%, 1.5%, 2% and 2.5% were used in this simulation. All of the thermo-physical properties of nanofluids were assumed to be temperature independent. Two particle sizes with average size of 20 and 50 nm were used in this research. It was concluded that heat transfer coefficient increased by increasing the Reynolds number and the concentration of nanoparticles. The maximum convective heat transfer coefficient was observed at the highest concentration of nano-particles in water (2.5%). Furthermore, the two nanofluids showed higher heat transfer than the base fluid (water) although the nanofluid with particles size of 20 nm had the highest heat transfer coefficient.

### Keywords

Nanofluid Heat transfer Simulation Laminar flow## Introduction

Fluid heating and cooling play the significant roles in a lot of industrial processes such as power stations, production processes, transportation and electronics. Most of the methods for heat transfer are based on the structure variation, vibration of the heated surface, injection or suction of fluid and applying electrical or magnetic fields (Ahuja 1975; Bergles & Webb 1970; Bergles 1973). These techniques meet a great enhancement in heat flux. Heat transfer in the traditional fluids such as water, ethyleneglycol and oil inherently has low thermal conductivity compared with the metals and metal oxides. Therefore, fluids with suspended solid particles are expected to have better heat transfer properties (Eastman et al. 2001). Due to the associated technological problems, the majority of studies on heat transfer of suspension of metal oxides in fluids were limited to suspensions with millimeter or micron-sized particles. The large particles may cause severe problems in the heat transfer equipments. In particular, large particles quickly tend to settle out. So, pressure drop can occur in the micro-channels (Khanafer et al. 2003). Furthermore, the abrasive actions of the particles cause the erosion phenomenon in pipe lines. Small particles and their little volume fractions prevent particles clogging and pressure drop increment in the nanofluids (Khanafer et al. 2003; Zhou 2004). Moreover, large surface area of nanoparticles increases the stability and reduces the sedimentation of nanoparticles. A more dramatic improvement in heat transfer efficiency is expected as a result of the particle size reduction in a suspension because heat transfer takes place at the particles surface (ZeinaliHeris et al. 2007).

Choi employed the particles in nanometer dimensions as a suspended solution (Choi & Eastman 1995). He showed that the nanofluid thermal conductivity considerably increased. Lee et al. showed that the suspension of 4.0% with 35 nm Cuo particles in ethylene glycol had 20% increment in the thermal conductivity (Lee et al. 1999). Choi et al. observed 60% enhancement in the thermal conductivity of engine oil with 1.0% carbon nanotube (Choi et al. 2001). Das et al. investigated the temperature dependency of thermal conductivity in the nanofluids (Das et al. 2003). It was observed that a 2–4 fold increase in the thermal conductivity of nanofluid can take place over a temperature range of 21–51°C.

According to the literature, alumina and copper oxide are the most ordinary and cheap nanoparticles which are used in the applied processes (Rezaee & Tayebi 2010). Xuan and Li experimentally studied the convective heat transfer and friction coefficient for the nanofluid in both laminar and turbulent flows (Xuan & Li 2000; Xuan & Li 2003). According to these researches, the flow velocity and volume fraction of nanoparticles affected the heat transfer coefficient. Wen and Ding investigated the convective heat transfer characteristics in Al_{2}O_{3}-water nanofluid along a tube (Wen & Ding 2004). It was observed that heat transfer increased by increasing the Reynolds number and volumetric ratio of particles.

Abu-Nada investigated the effects of variable viscosity and thermal conductivity of a nanofluid (Al_{2}O_{3}-water) on the natural convective heat transfer (Abu-Nada 2009). Sharma et al. experimentally studied the convective heat transfer coefficient and pressure drop in the transient region for Al_{2}O_{3}-water nanofluid under a constant heat flux (Sharma et al. 2009). They found that convective heat transfer increased by adding Al_{2}O_{3} nanoparticles in water.

Mirmasoumi et al. numerically studied the convective heat transfer in a fully developed flow for Al_{2}O_{3}-water nanofluid (Mirmasoumi & Behzadmehr 2008). They applied two-phase mixture model in their simulation. They found that the convective heat transfer coefficient significantly increased by decreasing the nanoparticles mean diameter. Since the theoretical models such as Maxwell and Hamilton-Crosser (Keblinski et al. 2002; Xue & Xu 2005; Eastman et al. 2001) predict the thermal conductivity of nanofluids, the mechanisms of thermal conductivity enhancement in the nanofluids should be studied.

Moraveji et al. simulated water-Al_{2}O_{3} nanofluid through a tube under constant heat flux (Moraveji et al. 2011). They found that the heat transfer coefficient increased by increasing the nanoparticle concentration and Reynolds number. Furthermore, the heat transfer coefficient increased by decreasing particle diameter.

In this research, the convective heat transfer in the developed region of the tube flow containing water and Al_{2}O_{3} nanofluid under constant heat flux was simulated using the Computational Fluid Dynamics (CFD) tools. Al_{2}O_{3} nanoparticles with two average diameters of 20 nm and 50 nm were dispersed in water. The nanofluids with five different Al_{2}O_{3} nanoparticle concentrations (0.2%, 1.0%, 1.5%, 2.0% and 2.5% volume fraction) were used. Effects of nanoparticle size and their concentrations on the convective heat transfer coefficient were also investigated.

## Mathematical modeling

The nanofluid as a single phase fluid with different physical properties (density, thermal conductivity and viscosity) was applied for the simulation. Heat transfer and flow are considered by the continuity, momentum and energy equations (Izadi et al. 2009):

Where, β is the ratio of the nano-layer thickness to the original particle radius (β = 0.1) (Yu & Choi 2003). The rheological and physical properties of the nanofluid were calculated at the average bulk temperature.

^{2}) as a boundary condition at the pipe wall was applied.

### CFD simulation procedure

^{2}) as a boundary condition at the pipe wall was applied.

## Results and discussion

Where, D, *q*, *h*
_{
nf
}, k, *T*
_{
w
} and *T*
_{
nf
} are pipe diameter, heat flux, nanofluid heat transfer coefficient, thermal conductivity of the fluid, tube wall temperature and nanofluid temperature, respectively.

Figure 2b demonstrates the meshes generation in this research. Figure 2c and d show temperature distribution at the end of pipe for velocity of 0.0706 and0.1664 (m/s) (or Re = 420 and 991.6) for nanofluid (with the particle diameter of 20 nm and volume fraction of 2.5). The nanofluid was heated by the pipe wall and its temperature increased along the pipe. The temperature of nanofluid along the pipe at Reynolds number of 420 varied sharper than that of Reynolds number of 991.6.Its reason was due to magnifying the heat transfer coefficient (He et al. 2009).

*h*) and Nusselt (

*Nu*) number in the tube versus velocity at particle concentrations of 2.5 and 2% for both particle sizes. As shown in these figures, heat transfer coefficients increased by increasing velocity and decreasing particle diameter. Furthermore, the nanofluid with average particle size of 20 nm showed the maximum heat transfer (Anoop et al. 2009).

## Conclusions

In this article, the heat transfer coefficient in the developed region of pipe flow containing Al_{2}O_{3}-water nanofluid during the constant heat flux was simulated using CFD. The focal point of investigation was to evaluate the effect of particle size on convective heat transfer characteristics in the developed region of the tube flow containing water-Al_{2}O_{3} nanofluid. It was observed that both nanofluids (with 20 and 50 nm particles size) showed higher heat transfer characteristics than that of the base fluid (water). Furthermore, the nanofluid with 20 nm particles size showed the highest heat transfer coefficient. The average heat transfer coefficient and Nusselt number increased by increasing the particle concentration and flow rate. The average temperature of nanofluid decreased by increasing the particles size.

## Nomenclature

D diameter of the tube [m]

k thermal conductivity [W/m.K]

Nu Nusselt number

Re Reynolds number

T Temperature [K]

C specific heat (*J/*
_{
kg.K
})

q heat flux [W/]

x distance a long axis [m]

## Subscripts

w wall

nf nanofluid

In inlet

p particle

Out outlet

bf base fluid

f fluid

## Greek letters

*μ* viscosity (Pa.s)

ф volume fraction

## Declarations

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.