Magnetohydrodynamic mixed convection flow in vertical concentric annuli with time periodic boundary condition: Steady periodic regime

This work reports an analytical solution for fully developed mixed convection flow of viscous, incompressible, electrically conducting fluid in vertical concentric annuli under the influence of a transverse magnetic field, where the outer surface of inner cylinder is heated sinusoidally and the inner surface of outer cylinder is kept at a constant temperature. The analysis is carried out for fully developed parallel flow and steady-periodic regime. The governing dimensionless momentum and energy equations are separated into steady and periodic parts and solved analytically. Closed form solutions are expressed in terms of modified Bessel function of first and second kind. The influence of each governing parameters such as magnetic field parameter, Prandtl number and the dimensionless frequency of heating on flow formation and thermal behaviour are discussed with the aid of graphs. During the course of investigation, it is found that the oscillation amplitude of the friction factor is maximized at a resonance frequency near the surface of the concentric annuli where there is periodic heating. Furthermore, increasing transverse magnetic field decreases the oscillation amplitude of the friction factor.