Effect of radial magnetic field on natural convection flow in alternate conducting vertical concentric annuli with ramped temperature

In this article, a numerical analysis has been performed to study the effect of radial magnetic field on natural convection of a viscous incompressible and electrically conducting fluid within the concentric vertical annuli containing a ramped type temperature profile at the surface of inner cylinder taking into account the induced magnetic field. Two cases are considered which are case 1, when inner cylinder is perfectly conducting and outer cylinder is non-conducting and case 2, has opposite configuration. The governing partial differential equations have been solved by using Matlab software. The influence of Hartmann number and magnetic Prandtl number on different profiles has been presented graphically. It is found that the effect of Hartmann number and magnetic Prandtl number is to decrease the velocity profile in both the cases. This study suggest that the heat transfer can be controlled by using ramped temperature and conductivity of the cylinder.