Multi-scale Numerical Modeling of Radial Heat Transfer in Grooved Heat Pipe Evaporators

It is well known that small-scale effects near contact lines have a crucial importance on the radial heat transfer within a grooved heat pipe evaporator. This paper studies this problem using a multi-scale model which is composed of two parts, macroscopic and microscopic. At the macroscopic scale, we solve the heat conduction problem for the solid and the liquid phases, using a finite-element method. In order to avoid the classical singularity problem at the contact line, in addition to taking the solid thermal conductivity into account, we do not impose the saturation temperature but a mixed condition along the interface. The coupling with the microscopic scales is achieved using a correlation for the apparent contact angle, obtained from a lubrication-type theory developed for the contact line region, and taking into account the variation of the saturation temperature with the disjoining pressure and with the meniscus curvature. Our results show a strong influence of this apparent contact angle on the heat transfer within the heat pipe, for two different geometries and as a function of the heat flux.