Nonlinear instability analysis of internally heated convection in a porous layer with the impact of magnetic field and variable gravity

The impact of the magnetic field, heat source, and variable gravity field on the stability of convective phenomena in a porous layer are investigated numerically. Three types of gravity variations, such as linear, parabolic, and cubic functions are considered. For linear and nonlinear theories, the method of normal modes has been employed to solve governing dimensionless equations. It is found that the onset of convection is delayed by increasing the Hartmann number and gravity variation parameter and enhancement of the internal heat source makes the system stable. The subcritical instability region increases as the Hartmann number and gravity variation parameter increase.