The inward solidification of a liquid cylinder with periodic axial perturbation of the boundary geometry, and constant boundary temperature or heat flux

In a cognate paper, Kharche and Howarth [1] considered the inward solidification of liquid cylinders (initially at fusion temperature), whose boundary values vary slightly with position axially and periodically along the cylinder. Cases of varying boundary temperature and varying boundary heat flux were both considered. In this paper, we consider a related problem, where the boundary temperature (or heat flux) is constant, but where the boundary profile of the cylinder geometry itself varies slightly and periodically with the axial coordinate (i.e. a slightly corrugated cylinder). The problems are solved analytically in the large Stefan number approximation, and in terms of linearised perturbations of the slight axial variation. As in [1], this work can form the core of an investigation of related thermo-elastic problems, as in [7].