Mixed convection with heating effects in a vertical porous annulus with a radially varying magnetic field

Fully developed parallel flow in an annular region filled with a porous medium surrounding an electric cable is investigated. The effects of buoyancy and MHD force as well as the heat generation due to Joule heating and viscous dissipation are taken into account. The mixed convection seepage flow is analyzed according to Darcy law and to Boussinesq approximation. Buoyancy effect is modelled by setting the isoflux wall temperature as the reference temperature. As a consequence of this choice, the local momentum and energy balance equations and the boundary conditions can be written in a dimensionless form that defines an initial value problem instead of a boundary value problem. The initial value problem is solved both by an analytical series method and by numerical integration. The effect of the radially varying magnetic field on the fluid velocity and temperature distributions is analyzed. It is shown that a significantly strong magnetic force tends to inhibit the flow even for a high hydrodynamic pressure gradient.