Buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces

The paper studies free convection in a saturated porous medium above a heated horizontal impermeable surface above or below a cooled horizontal impermeable surface where wall temperature is a power function of distance from the origin. The governing equations are obtained by the Boussinesq approximation, and are transformed by invoking boundary layer approximations valid for large Rayleigh numbers and by introduction of dimensionless variable enabling the finding of similarity solutions. Analytical expressions are obtained for boundary-layer thickness, and local and overall surface heat flux. The problem has applications to convective flow above heated bedrock or below cooled caprock in a liquid-dominated geothermal reservoir.