MHD Transient Free Convection Flow in Vertical Concentric Annulus with Isothermal and Adiabatic Boundaries

Abstract

This paper presents MHD transient flow in an infinite vertical concentric annulus when the fluid is set in motion by free convection current occurring in the annulus as a result of application of isothermal heating on the inner surface of the outer cylinder while the outer surface of the inner cylinder is thermally insulated. The solution of the governing equations are obtained using the well-known Laplace transform technique while the Riemann-sum approximation method has been used to invert the solution from Laplace domain to time domain. The numerical values obtained using Riemann-sum approximation approach is validated by presenting a comparison with the values obtained using the implicit finite difference method as well as the steady-state solution. These comparisons with the steady state solution shows a remarkable agreement at large value of time. The effect of the governing parameters on the velocity field, temperature field, mass flow rate as well as the skin-friction on both surfaces of the annulus have been analysed and presented with the aid of line graph. Generally, we observed that the mass flow rate and skin friction at the isothermally heated surface increases with increase in radius ratio. However, the reverse is seen at the thermally insulated surface as the skin-friction decreases with increase in radius ratio.