Conjugate natural convection in a square enclosure under horizontal magnetic field effect

Abdennacer Belazizia,Said Abboudi,Smail Benissaad

doi:10.1051/meca/2015011

Abstract

Steady, laminar, conjugate natural convection flow in a square enclosure is considered. Both effects: conduction in a vertical wall and the presence of a magnetic field are taken together. The enclosure is filled with liquid gallium and subjected to horizontal temperature gradient. The main focus of the study is examining the effect of Hartmann number on fluid flow and heat transfer. The effect of Rayleigh number and conduction in the left wall is also considered. The obtained result show in the absence of a magnetic field that natural convection can be strengthed by the increase of both Rayleigh number and conductivity ratio, because of the increase of the effective temperature difference driving the flow. For poor conducting wall, where the solid part is an insulated material and the thermal resistance is more important the average Nusselt number is approximately constant and having low values comparing with equal and high conducting wall, indicating that most of heat transfer is by heat conduction. In the presence of a magnetic field the results show that for a given Rayleigh number, as the value of Hartmann number increases, convection is suppressed progressively and the rate of heat transfer is reduced in the enclosure.

Highlights

Natural convection in enclosures is a topic of considerable engineering interest
The problem of natural convection flow in a square and rectangular enclosure with uniform temperature at vertical walls and insulated top and bottom walls has been the subject of many studies
In the absence of a magnetic field (Ha = 0), Table 3 shows the effect of both Rayleigh number and thermal conductivity ratio on fluid motion and thermal field in the enclosure for poorly conducting wall (Kr = 0.1), equal wall/fluid conductivity (Kr = 1) and high conducting wall (Kr = 10)

Summary

Introduction

Natural convection in enclosures is a topic of considerable engineering interest. Applications range from thermal design of buildings, to cryogenic storage, furnace design, nuclear reactor design, and others. The problem of natural convection flow in a square and rectangular enclosure with uniform temperature at vertical walls and insulated top and bottom walls has been the subject of many studies. In many practical situations, especially those concerned with the design of thermal insulation, conduction in the walls can have an important effect on the natural convection flow in the enclosure [1,2,3]. According to the above studies, we conclude that fluid flow and heat transfer in enclosures are strongly influenced by both effects: the presence of magnetic field and thermal conduction in walls presenting a thickness. The present work aims to study the effect of wall thickness in a square enclosure on natural convection of conducting fluid in the presence of magnetic field. Greek symbols α∗ Thermal diffusivity ratio αw/αf β Thermal expansion coefficient K−1 θ Non-dimensional temperature (T − Tc)/(Th − Tc) υ Kinematic viscosity m2.s−1 σ Electrical conductivity of the medium Ω−1.m−1 ψ Dimensionless stream function ω Dimensionless vorticity

Problem geometry and governing equations

Results and discussions

Conclusion