Heat transfer in an unsteady MHD flow through an infinite annulus with radiation

An analytical study of a laminar unsteady magnetohydrodynamic flow of a viscous incompressible and electrically conducting Newtonian non-Gray optically thin fluid between two infinite concentric vertical cylinders influenced by time dependent periodic pressure gradient subjected to a magnetic field applied in azimuthal direction and in the presence of appreciable thermal radiation and periodic wall temperature is presented. The governing equations of motion and energy are transformed into ordinary differential equations which are solved in closed form in terms of the modified Bessel functions (of first and second kind) of order zero. The induced magnetic field is neglected, assuming the magnetic Reynolds number to be considerably small. A parametric study accounting for the effects of various physical parameters on the velocity and temperature fields and on the coefficient of skin friction, the rate of heat transfer at the surface of the cylinders, and mass flux across a normal section of the annulus is conducted and the results are discussed graphically.