Effective Thermal Conductivity of a Wet Porous Medium—Presence of Hysteresis When Modeling the Spatial Water Distribution for the Pendular Regime

Abstract

This paper deals with the heat transfer between two spherical grains separated by a small gap; dry air is located around the grains and a liquid water meniscus is supposed to be present between them. This problem can be seen as a microscale cell of an assembly of solid grains, for which we are looking for the effective thermal conductivity. For a fixed contact angle and according to the volume of the liquid meniscus, two different shapes are possible for the meniscus, giving a “contacting” state (when the liquid makes a true bridge between the two spheres) and a “noncontacting” one (when the liquid is split in two different drops, separated by a thin air layer); the transition between these two states occurs at different times when increasing or decreasing the liquid volume, thus leading to a hysteresis behavior when computing the thermal flux across the domain.

Ampacity and thermal equivalent modeling of subsea power cables for long distance power transmission and optimization

“…Among those methods, FEM is the most commonly used method [77] [78]. More importantly, numerical methods can provide more accurate results for studies of the physical properties due to their high-efficiency and ability to solve the local problem such as the nonlinear heat transfer boundary value problem [79]. However, the numerical methods including FEM are complicated due to the large number of data processing compared to the analytical method.…”