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

This paper considers the inward solidification of liquid cylinders (initially at fusion temperature) whose boundary values vary slightly with position axially and periodically along the cylinder. It is therefore analogous to the work of Gammon and Howarth [1] who considered similar problems, but with angular variation around the cylinder. As in [1] the problems are solved analytically in the large Stefan number approximation, and in terms of linearised perturbations of the slight axial variation. This preliminary investigation will form the thermal element of a subsequent investigation into the thermo-elastic stresses and contact pressure in a solidifying cylindrical ingot, following the methods of Hector et al. [5]