Analysis of Direct-Contact Melting Under Rotation

In this paper the phenomenon of direct melting under rotation and external pressure is considered. Rotation may be added to direct-contact melting for several purposes, including keeping the melting surface uniform or creating a centrifugal field to assist the removal of the melt. An exact analysis is presented here, which resembles that of the condensation on a rotating surface or the problem of a rotating disk in a large body of fluid. A similarity transformation is applied to reduce the full Navier–Stokes and energy equations to ordinary differential equations. A dimensionless parameter σ has emerged from the analysis, which is the ratio of the external force to the centrifugal force. As σ becomes large (σ→∞, no rotation), the problem becomes that of pure direct-contact melting under external force, and hence resulting in the exact formulation for such a problem. For σ = 0 (pure rotation, no external force), the formulation becomes similar to that of condensation on a rotating disk or a rotating disk in a large body of fluid. It is noted that different scaling of the problem with respect to σ is needed to obtain the solution for the wide range of σ = 0 → ∞. A closed-form solution is obtained for the case where the film is approximated to be thin. A criterion for the validity of this approximation is given. Finally, the numerical results for the general problem are presented in terms of the Prandtl number, the Stefan number, and the force ratio σ.