Non-monotonic phase change front propagation during one-dimensional melting/solidification in the conduction-dominated regime

Development of theoretical techniques to model melting/solidification is important for a number of engineering problems. Using an approximate analytical technique, this work considers melting/solidification of a one-dimensional phase change material (PCM) with convective heat transfer boundary conditions at the two ends. Good agreement with past work under special conditions is shown. Assuming negligible buoyancy-driven convective heat transfer, it is shown that, under certain conditions, the phase change front may grow non-monotonically, i.e., beyond a peak value of the phase change front, there may be a reversal in the direction of the front propagation, before steady state is reached. It is shown that this retraction phenomenon is governed by the Stefan number, ratio of applied temperature differences, ratios of thermophysical properties, and Biot numbers associated with boundary conditions. The retraction phenomenon is explained on the basis of the competition between phase change front propagation and solid phase thermal diffusion. Retraction is shown to occur when the rate of propagation is much greater than the rate of diffusion. The retraction phenomenon investigated here is novel because most one-dimensional phase change problems proceed monotonically, and a reversal in the phase change direction does not commonly occur. In addition to the theoretical interest in non-monotonic phase change propagation, results from this work may also be helpful in improving the thermal performance of PCMs in practical engineering devices.