Melting of a long cylinder due to an axisymmetric hot spot (Q1109615)

By employing a new embedding technique, a short-time analytical solution for the melting of a long cylinder due to an axisymmetric hot spot is presented in this paper. The melt is removed as soon as it is formed. The initial propagation of the melt along the interior of the cylinder exhibits a well-known behaviour. However, the melt propagation along the surface of the cylinder is of a new type and depending on the applied flux whether it is the continuation of the pre-melting flux or different, the initial propagation of the melt along the surface is proportional to \(t^{1/2}\) or \(t^{1/4}\), where t is the dimensionless time. The melt propagation is much faster along the surface of the cylinder than towards the interior.