Free convection in a saturated porous medium adjacent to a vertical impermeable wall subjected to a non-uniform heat flux

Boundary layer analysis is performed for free convection in a fluid-saturated porous medium adjacent to a vertical impermeable wall subjected to a non-uniform heat flux. The wall heat flux is assumed to be an arbitrary function of the distance along the surface. The solutions are obtained in the form of perturbations to the uniform heat flux case. Using the differentials of the wall heat flux, which are functions of the distance along the surface, as perturbation elements, universal functions are obtained. These universal functions can be used to estimate the heat transfer for any type of wall heat flux variation. For the wall heat flux variation as a power function of the distance from the origin, the solutions obtained by using these universal functions have been compared with those obtained by similarity analysis and the agreement is found to be good. Further, solutions are presented for wall heat flux varying exponentially and sinusoidally but comparison could not be drawn due to non-availability of solutions in the literature.