Mechanical Engineering Technologies and Applications: Volume 3

Three-Dimensional Mixed Convection in a Cubical Cavity with Nanofluid

Bellout Saliha¹, *, Bessaïh Rachid¹

¹ LEAP Laboratory, Department of Mechanical Engineering, Faculty of Sciences Technology, University of Brothers Mentouri-Constantine 1, Route de Ain El. Bey, Constantine, Algeria

Abstract

The present study reports numerical simulations of three-dimensional laminar mixed convection heat transfer of water-based-Al2O3 nanofluid in an open cubic cavity with a heated block. Ansys-Fluent 14.5 was used to simulate 3D flows with heat transfer. Streamlines, isotherms, vertical velocity profile, and local Nusselt numbers are presented for Reynolds numbers in the range (300

Keywords: Cubical cavity, Heated block, Mixed convection, Nanofluid.

* Corresponding author Bellout Saliha: LEAP Laboratory, Department of Mechanical Engineering, Faculty of Sciences Technology, University of Brothers Mentouri-Constantine 1, Route de Ain El. Bey, Constantine, Algeria;

E-mail: [email protected].

INTRODUCTION

The improvement of heat transfer by mixed convection is the main object of several works. There is a real demand in the industrial world for new strategies allowing improving the thermal behaviour of fluids in the cooling system. This new fluid concept is called nanofluid. The idea is then to insert solid particles of nanometric size into liquids to improve the mixture's thermal performance. Their syntheses meet the needs of improving thermal properties and is the most promising solution in heat transfer improvement.

This interest in nanofluids was reflected in numerous technological and industrial applications; since 1995, numerous experimental and numerical studies were carried out on convection with nanofluids [1-7].

The objective of the present study is to numerically simulate the heat transfer properties by mixed convection of a nanofluid (Al2O3-water) in an open cubic cavity, heated by a heat source; the effects of Reynolds number, the volume fraction and the position of the heat source are studied to improve heat exchange.

Mathematical Formulation

Problem Description

The physical model considered is a cubic cavity of L = 5cm, shown schematically in Fig. (1). The volumetric heat source (qv) is placed on the lower wall of the cavity; the other walls are adiabatic. The nanofluid enters at a speed of U0 and a temperature T0.

Fig. (1))

Cubical cavity filled with nanofluid (Al2O3 / Water).

The equations governing the flow and heat transfer are written as follows:

Continuity:

x-momentum:

y-momentum:

z-momentum:

Energy:

In the fluid region:

In the Solid Region (Heat Source):

The thermophysical properties of the nanofluid are defined as follows [8-10]:

Boundary Conditions:

The boundary conditions are described as follows:

• Heat source: u=v=w=0, qv=2 × 10⁶ W/m³.

• At the inlet (x =0cm, 0.7L < y < L, 0 < z < L) : u =U0 , v=w=0, T = T0.

• At the outlet (x=5cm, 0

and

otherwise

The thermophysical properties of pure water and nanoparticle at 25oC are shown in Table 1.

Table 1 Thermophysical properties of pure water and Al2O3 nanoparticles at 25oC.

Numerical Method and Code Validation

We describe the computational procedure to simulate our study case numerically. For this numerical simulation, we used the commercial software Ansys-Fluent 14.5 based on the finite volume method by choosing the SIMPLE algorithm. Fig. (2) shows the mesh of the computational domain.

Five meshes were tested (12×50×12, 14×61×14, 16×72×16, 18×83×18 and 20×94×20) nodes for Re = 300, Grashof Gr = 9,14×105 and volume fraction ϕ = 0%. The test of the mesh was made on Tmax and Nuavg with the size of the grid (Table 2).

Table 2 Mesh test results, for ϕ=0% Re = 300, Gr = 9,14×105.

Fig. (2))

Mesh of the computational domain.

From Table 2, Tmax and Nuavgbecome insensitive to the number of nodes from the grid (18 × 83 × 18 and 20 × 94 × 20). Therefore, the (18 × 83 × 18) node grid was chosen for our numerical simulations.

In order to confirm the accuracy of the results, it is essential to assess the reliability of the Ansys Fluent 14.5 calculation code; the validation was made by comparison with the numerical results of Sourtiji et al. [7]. From Fig. (3), a good agreement is obtained.

Fig. (3))

Validation of this calculation code with the numerical results of E. Sourtijis et al. [7].

Results and Discussion

To study the phenomenon of mixed convection of a nanofluid (Al2O3-water) flow in an open cubic cavity, we will examine three parameters on dynamic and thermal fields:

• The effect of the Reynolds number (300

• The effect of the volume fraction (0 <ϕ <0.08) at Re =