Close-contact melting of a vertical cylinder on an isothermal surface: Modeling and investigation for a non-Newtonian Herschel-Bulkley fluid liquid-phase

The present study deals with close-contact melting of a solid vertical cylinder on an isothermal surface. In particular, we develop a new numerical model designated for phase change materials with a non-Newtonian liquid-phase that behaves according to the Herschel-Bulkley fluid model. We reveal the dimensionless groups that govern the problem, and show that the new model provides a generalization for known and new limiting cases that yield simpler analytical or semi-analytical solutions. Then, we extensively validate the new model against experimental results from the literature. We show that our new model can accurately predict the molten layer thickness and the temporal evolution of the cylinder's height for phase change material with non-Newtonian liquid-phase rheological properties. Furthermore, we investigate the influence of the Herschel-Bulkely model parameters on the dimensionless thin molten layer thickness and the melting rate. We demonstrate that as the dimensionless yield stress and flow behavior index increase, the molten layer thickness increases, whereas the melting rate decreases. We also compare our numerical results against analytical solutions for two limiting cases - power-law fluid model and plug flow in the thin molten layer. Our results determine the accuracy of the two analytical solutions, and show that for sufficiently high values of the dimensionless yield stress, both the dimensionless molten layer thickness and the melt fraction are independent of the flow behavior index. Finally, we develop an approximate model for quick estimations of the exact numerical model results. We prove that the new approximate model is valid for a wide range of conditions and can provide quick and reasonably accurate predictions for both the dimensionless molten layer thickness and the melt fraction.