Hydromagnetic natural convection flow in a fluid-saturated porous medium with nonuniform heat generation

Convective flows can develop naturally within the porous materials if they are subject to external heating with/without internal heat source. In this work, the heat is assumed to be generated internally within the porous enclosure at a rate proportional to a power of the temperature difference. This relation is an approximation of the state of some exothermic chemical reaction. An inclined magnetic field is imposed to the porous enclosure. Darcy, model is used to formulate the porous layer and finite difference method is applied to solve the governing equations. The obtained results indicate that strong internal heating can generate significant maximum fluid temperatures above the heated wall temperature, and location of the maximum fluid temperature moves towards the center of the top wall by strengthening the magnetic field. Local heating exponent does not have a major effect on the flow and temperature distributions as well as the heat transfer performance within the porous medium. The large magnetic fields, regardless of direction, are effective to suppress the convective flows and reduce the rate of heat transfer.