NATURAL CONVECTION FLOW IN A VERTICAL CONCENTRIC ANNULI FILLED WITH POROUS MATERIAL HAVING VARIABLE POROSITY UNDER RADIAL MAGNETIC FIELD: AN EXACT SOLUTION

The present paper investigates the influences of radial magnetic field on steady fully developed free convective flow of a viscous, incompressible, electrically conducting fluid in a vertical concentric annuli formed by two infinite vertical concentric cylinders, filled with porous material having variable porosity. A unified exact solution is derived by taking into consideration of isothermal or isoflux thermal boundary condition at the outer surface of inner cylinder. The solution obtained is graphically represented and the effects of various controlling parameters such as Hartmann number, Darcy number, ratio of viscosity and the gap between the cylinders on the flow formation is discussed. During the course of numerical computations, it is noticed that velocity of the fluid is higher in case of isothermal heating of outer surface of inner cylinder compared with constant heat flux heating when the gap between cylinders is less or equal to radius of inner cylinders while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder.