Theoretical analysis of close-contact melting on superhydrophobic surfaces

Abstract

The present study deals with close-contact melting of a vertical cylinder on a horizontal isothermal superhydrophobic surface with an array of circular posts. A new numerical model for this phenomenon is formulated under several simplifying assumptions. For the limiting case of perfect slip and thermal contact, based on the model assumptions, it is demonstrated that superhydrophobic surfaces can enhance the melting time by no more than 30 %. Numerical solution of the new model reveals that the effect of superhydrophobic hydrodynamic slip can decrease the molten layer thickness. However, due to the dominant effect of thermal slip, the heat transfer rate can be decreased significantly, and the melting time can be roughly doubled. An approximate analytical model is developed for understanding the problem dynamics better. The analytical model predictions are compared extensively against the numerical model results. For sufficiently low surface volume fractions, the analytical model provides excellent estimations of the numerical model predictions. Dimensional analysis reveals that according to the analytical model, the ratio between the melting times for superhydrophobic and regular surfaces is governed by a single dimensionless group. Moreover, according to the analytical model, the melting time on a superhydrophobic surface is always longer than on a regular surface, which agrees qualitatively with the numerical model results. Based on this analysis, a dimensionless condition for the analytical model range of validity is formulated. Finally, a conservative criterion for the liquid–gas interface stability under a close-contact melting process is established.

Close-contact melting of shear-thinning fluids

“…The dimensionless form of (2.42) is where is the solid–liquid density ratio and the Stefan number is defined as Substitution of (2.41) into (2.43) yields the comprehensive expression for the transient velocity relationship with and Considering the scaling of , leads to Then, with the scaling of , (2.45) and (2.46) can be simplified respectively as and Note that (2.47) can be written in the following Taylor expansion form: This implies that (2.47) can be approximated to which is the pure conductive form consistent with previous studies (Kozak et al. 2019; Kozak 2022).…”