Abstract
The solution of two-dimensional heat conduction problem on a coated sinusoidal mould of finite thickness is determined using a linear perturbation method. Heat flux at the bottom of the mould is assumed to be constant and the molten metal perfectly wets the mould surface before the beginning of the solidification process. This causes undulatory structure at the moving interface between the solid and liquid phases. Thermal diffusivities of the solidified shell, coating layer and mould materials are assumed to be infinitely large. The physical meaning of this assumption is that thermal capacities of these materials are equal to zero. This simplification allows the entire problem to be solved. The effects of process parameters such as the thermal conductivity of shell, coating and mould materials, thermal contact resistance between each layer and thickness of the coating material on the growth of solidified shell thickness are investigated in detail. The present work can form the thermal part of a subsequent investigation of the related thermo-elastic stress problems.