\Transient Heat Diffusion Problems with Variable Thermal Properties Solved by Generalized Integral Transform Technique

Abstract

In this work, studies of two-dimensional transient heat diffusion problems in domains of rectangular and elliptical geometries, submitted to boundary conditions of first kind, were carried out. For the problem formulation, diffusive means with variable thermophysical properties were considered. The differential equation that governs the energy conservation is non-linear. In this context, the diffusion equation was linearized by the Kirchhoff Transformation. Transformations of the coordinate systems were performed in order to facilitate the boundary conditions application. The resulting differential equation after these transformations does not allow the application of the variable separation techniques. Thus, the Generalized Integral Transform Technique (GITT) was used to solve the energy equation. As result of this transformation a coupled ordinary differential equation system that can be solved through classic numerical methods was obtained. Therefore, for the determination of the temperature field evolution, the inversion formulas of all the performed transformations were used. Physical parameters of interest were, then, calculated and compared for several cylindrical cross section geometries.