Effect of Constant Magnetic Field on Convective Heat Transfer through Anisotropic River Beds

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 permea- bility 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 tem- perature T 2 such as T 1 < T 2 . Flow in porous medium is assumed to be go- verned 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 hy- drodynamic anisotropy on the convective phenomenon is investigated analyt- ically. 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.