This paper describes a multi-scale model for evaluating the radial heat transfer within a grooved heat pipe evaporator. The model is composed of two parts, macroscopic and microscopic, which cannot be decoupled from each other. In the macroscopic part, we solve the heat conduction problem in the solid and in the liquid phases, thanks to a finite-element method allowing high flexibility in the definition of the groove geometry. In order to avoid the classical singularity problem at the contact line (where the liquid-vapor interface meets the groove wall), in addition to taking the solid thermal conductivity into account, we do not impose the saturation temperature but a mixed condition along the interface. We show in particular that the interface temperature equals the saturation temperature (at given vapor pressure), except in the microscopic region where it increases and reaches the solid temperature. In this microscopic zone, a classical lubrication-type theory allows to determine the apparent contact angle, taking into account the influence of small-scale effects, such as the variation of the saturation temperature with the disjoining pressure and with the meniscus curvature. In particular, analytical relationships and correlations are presented for the apparent contact angle, which allow an efficient coupling between macroscopic and microscopic scales. In this paper, attention is devoted to the numerical treatment of both regions, their coupling, and the influence of the macroscopic heat flux and local small-scale effects on the distribution of temperature in the groove.

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