This article presents a theory of how the melt region advances as an intrusion layer along the top boundary of a solid phase-change material that is heated from the side. The phase-change material fills the pores of a solid matrix. We show that the thickness of the horizontal melt layer increases as x 3 5, where x is the horizontal distance measured by from the leading edge of the layer. The total length of the intrusion layer increases as t 3 4, and as Tmax 5 4. Finite-difference simulations of convection melting in the Darcy-Rayleigh number range of 200-800 agree with the theoretical results. We also show that in a rectangular porous medium heated from the side, the size of the entire melt region is dominated by the melting contributed by the horizontal intrusion layer, if the time is great enough so that the group (Ste Fo) 3 4 is greater than 1. © 1990.