Influence of Temperature-Dependent Internal Heating on Magnoteconvention in a Rotating Darcy Porous Layer

The commencement of conventions which are the stationary and oscillatory in the study of the influence of temperature-dependent internal heating on magnetoconvection in a rotating Darcy porous layer was systematically examined. The linear stability analysis was scrutinized with the boundary condition of the problem being free-free. A modified Boussinesq approximation is included in the momentum equation and the Coriolis force was taken into consideration. The given non-dimensional equations were linearized and the normal mode technique was used to obtain marginal stationary and the marginal oscillatory convection. The criteria for the onset of convection in the system are derived analytically. The effects of the parameters: heat source, , magnetic field, , rotation, and ratio of viscosities, on the onset of convection are presented and analyzed graphically in details. The investigation showed that the result of raising magnetic field, rotation and ratio of viscosity slowed down the commencement of the convections, that is both the stationary and oscillatory convections, hence making the system steady. In the other hand, increasing heat source parameter, catalyzes the commencement of convection and destabilizes the mechanism. Prandtl number was found to slow the onset of oscillatory convection. Hence we can infer that magnetic field parameter, Ha, rotation parameter, T D , and the Prandtl number, Pr, are balancing factors, while the heat source parameter, ℽ, speeds up the commencement of convection.