Transient development of MHD natural convection flow in vertical concentric annulus

Abstract

This paper examines the role of magnetic field on fully developed natural convection flow in an annulus due to symmetric of surfaces. The transport equations concerned with the model under consideration are rendered non-dimensional and transformed into the ordinary differential equation using Laplace transform technique. The solution obtained is then transformed to time domain using the Riemann-sum approximation approach. The governing equations are also solved using implicit finite difference method so as to establish the accuracy of the Riemann-sum approximation approach at transient as well as at steady state solution. The solutions obtained are graphically represented and the effects of pertinent parameters on the flow formation are investigated in detail. The Hartmann number (M), is seen to have a retarding effect on the velocity, skin-frictions and the mass flow rate. Also, skin-friction at both surfaces and the mass flow rate within the annulus are found to be directly proportional to the radii ratio (λ).