Abstract
An analytical investigation is conducted to study the effect of magnetic field on convection heat transfer through packed porous beds which consists of a horizontal fluid layer (river bed) and a porous zone with anisotropic permeability and underlined by a surface heated by a constant temperature T1. The free surface of the fluid layer overlying the horizontal porous layer receives solar rays to length of day and is then considered heated isothermally at temperature T2 such as T1 T2. Flow in porous medium is assumed to be governed by the generalized Brinkman-extended Darcy law and in the fluid layer by the Navier-Stokes model. The Beavers-Joseph condition is applied at the interface between the two layers. The influence of Hartmann number and hydrodynamic anisotropy on the convective phenomenon is investigated analytically. It is found that the magnetic field, the anisotropic permeability and the thickness of the porous lining, ε, have a strong influence of the geothermal convective flow and the heat transfer rate.
Highlights
The first study concerning the effect of a magnetic field on the natural convection heat transfer in a rectangular porous cavity seems to be due to [1]
An analytical investigation is conducted to study the effect of magnetic field on convection heat transfer through packed porous beds which consists of a horizontal fluid layer and a porous zone with anisotropic permeability and underlined by a surface heated by a constant temperature T1
It is found that the magnetic field, the anisotropic permeability and the thickness of the porous lining, ε, have a strong influence of the geothermal convective flow and the heat transfer rate
Summary
The first study concerning the effect of a magnetic field on the natural convection heat transfer in a rectangular porous cavity seems to be due to [1]. The effect of a magnetic field on the convective heat transfer was investigated analytically using matched asymptotic expansions. We consider the convective heat transfer through a parallel-plate horizontal system consisting of a homogeneous porous bed underlying a single-component fluid layer whose upper surface is free and isothermally heated. On the basis of the generalized Brinkman-extended Darcy model, of Navier-Stokes equations and of energy equation which takes into account the viscous dissipation, the effects of magnetic field, of anisotropic parameters of the porous matrix and of the influence of the depth ratio on velocity and temperature fields and heat transfer rate are investigated in detail
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