This paper reports a complete theory of the melting that occurs in a confined porous medium saturated with phase-change material and heated from the side. Darcy flow characteristics are assumed for the liquid phase. The solid phase is isothermal and at the melting point. The first part of the paper reports a matched boundary layer solution for natural convection dominated melting in the quasi-steady regime. The second part reports a solution for the heat transfer during the two earlier regimes, pure conduction followed by mixed conduction and convection. Together, the two solutions cover the entire history of transient heating administered from the side. This theory shows that the liquid-side Stefan number has a profound effect on the heat transfer and melting rates.

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