Close-contact melting of phase change materials with a non-Newtonian power-law fluid liquid phase—Modeling and analysis

In the current study, we model and analyze close-contact melting of a vertical cylinder on an isothermal surface, where the molten liquid phase rheological properties correspond to the non-Newtonian power-law fluid model. Under the assumptions of thin layer approximation and quasi-steady conditions, we derive analytical solutions for the initial molten layer thickness and maximum pressure as well as the time-dependent melt fraction, molten layer thickness, and pressure and velocity distributions in the thin molten layer. Dimensional analysis of the various derived analytical expressions reveals the governing dimensionless groups and their fundamental scaling laws. We show that the derived scaling laws generalize the classical and well-established Newtonian close-contact melting scaling laws. Moreover, the new model provides quantitative estimations that are extensively compared against the Newtonian case. It is shown that for typical values of the flow behavior index, the dimensionless pressure and hydraulic resistance in the molten layer decrease monotonically as the flow behavior index decreases. As a result, the dimensionless molten layer thickness decreases. Thus, we demonstrate that non-Newtonian effects can significantly impact the melting dynamics. As such, in comparison with the Newtonian fluid case, the melting rate is enhanced for shear-thinning fluids, whereas the melting rate is reduced for shear-thickening fluids.