A similarity solution to unidirectional solidification of nano-enhanced phase change materials (NePCM) considering the mushy region effect

In this Technical Note, we report on the similarity solution to a one-dimensional, two-phase, three-region Stefan problem, with application to unidirectional solidification of nano-enhanced phase change materials (NePCM) in a semi-infinite domain accounting for the presence of a mushy region. The NePCM were considered as homogeneous mixtures with effective thermophysical properties by neglecting diffusion of the nano-additives. As an example, NePCM consisting of dodecanol and graphene nanoplatelets, as the base PCM and nano-additives respectively, were studied. Instead of using predicted values from existing models/correlations, the effective thermophysical properties of the model NePCM at various loadings were measured experimentally, which were substituted directly into the similarity solution. It was shown that a mushy region appears and gradually develops as solidification proceeds with its thickness being non-monotonously changed with increasing the loading, in consistent with the variations of the measured solidus and liquidus temperatures. The relative solidification rate was compared quantitatively, showing that solidification is greatly accelerated up to a factor of 34% at the highest loading of 1.0 wt%. Based on the similarity solution, thermal conductivity enhancement of the NePCM was interpreted to be the major cause leading to expedited solidification.