This study considers a small Rayleigh number thermal convection in a fluid-saturated porous medium between two infinite-horizontal walls. The lower and upper walls have sinusoidal temperature distributions with a wave number and a phase difference, and the effect of the parameters on the flow and heat transfer characteristics is investigated. For a given wave number, an out-of-phase configuration yields minimum heat transfer at the walls. Maximum heat transfer occurs at the wave number of 2.286 with an in-phase configuration. (C) 2003 Elsevier Ltd. All rights reserved.