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Boundary layer analysis is performed for free convection in a saturated porous medium adjacent to non-isothermal vertical impermeable surfaces. The impermeable surface temperature is assumed to be an arbitrary function of the distance along the surface. The solutions are obtained in the form of perturbations to the isothermal case. Using the differentials of the wall temperature, which are functions of distance along the surface, as perturbation elements, universal functions are derived. These universal functions can be used to estimate the heat transfer to any type of wall temperature variation. Solutions for some specialized wall temperature variations are derived using these universal functions and are compared with the solutions that are available in the literature. The agreement is found to be good. The case of uniform wall heat flux turns out to be a special case of non-isothermal wall solution. ? 1990 Springer-Verlag.