3D hybrid finite element enthalpy for anisotropic thermal conduction analysis

Abstract

The anisotropic problem of thermal conduction in a solid is generally treated in a reference coordinate system, which adequately describes its thermal conductivity tensor (Cartesian, cylindrical or spherical). For this problem, numerical treatment is difficult, especially if the thermophysical properties are non-linear or if the anisotropic medium undergoes a phase change. In this paper, we propose an approach using a Cartesian reference system to treat the anisotropic thermal conduction of problems for which the solid medium is characterized by a set of tensors of thermal conductivity of different natures (Cartesian and/or cylindrical and/or spherical), with or without phase change. For this purpose, we the anisotropic thermal conductivity tensor, with respect to a cylindrical or spherical coordinate system, is transformed by an equivalent tensor into global Cartesian coordinates. The nonlinear heat conduction problem involving phase changes, such as wood freezing, is solved using hybrid three-dimensional volumetric specific enthalpy based on finite-element analysis. The proposed approach is validated with analytical testing for two anisotropic media and with two experimental tests related to the heating of frozen woods. As an application, we have numerically quantified, on the one hand, the minimum time required for the thaw and, on the other hand, the freezing of a log of wood, such as white pine, according to the length of its radius (7.5, 10, 15, 20 and 25 cm). The thermophysical properties are a function of temperature, moisture content and structural orientation.