Relation between aspect ratio of heated body and squeezing force in close-contact melting

The problem of close-contact melting of a cylindrical solid body of a phase-change material is studied analytically. Relative orders of magnitude for various terms are examined using the dimensionless governing equation, taking into account the temperature distribution in the cylindrical heated body. It is found that the unsteady terms can be neglected. The governing equation approximated is solved using a Fourier series. The relationship between the squeezing force due to the weight of the phase-change material and the melting velocity is determined as a function of the aspect ratio of the heated body. The critical condition above which a steady melting phenomenon exists is shown in the plane of aspect ratio and dimensionless applied temperature difference. If the aspect ratio is very small, this relationship tends to that derived by Moallemi in which the temperature in the heated body is assumed to be constant. In the case that the aspect ratio is comparatively small, its effect on the melting velocity is very strong. Convection in the melting fluid layer makes the range of steady melting narrow.