Free convection between vertical concentric annuli with induced magnetic field when inner cylinder is electrically conducting

Abstract

An analysis is made for the fully developed laminar free convective flow in an open ended vertical concentric annuli with constant heat flux and constant temperature on the inner and outer walls, in the presence of a radial magnetic field. The length of the cylinder is assumed to be infinite and radiation heat transfer from the hot surface is assumed to be negligible. The inner cylinder is taken to be magnetic conducting while the outer cylinder is non-conducting. Buoyancy effect is also considered along with Boussinesq approximation. The induced magnetic field is taken into account arising due to the motion of an electrically conducting fluid. The governing linear simultaneous ordinary differential equations are first obtained in the non dimensional form and solved analytically for the velocity, induced magnetic field, temperature field and  then skin-friction and induced current density are obtained. The expressions for the fluid flux and induced current flux in non-dimensional form have been also obtained. The effects of governing physical parameters occurring in the model are shown on the graphs and tables.