Heat transfer in solids with variable thermal properties and orthotropic conductivity

Heat transfer in solids with temperature dependent properties and orthotropic conductivity subjected to either linear or nonlinear boundary conditions has been investigated. In this study, the isoparametric finite element discretization, linearization scheme and the modified Newton-Raphson iteration method are employed. The temperature distribution in a solid is obtained from the minimization of a variational statement that corresponds to the general differential equation of heat conduction. For comparison purposes, finite difference solutions for transient temperature distribution in a rectangular column with variable thermal properties and orthotropic conductivity are also obtained. Both fully implicit and alternating-direction implicit finite difference schemes are utilized. Furthermore, the finite element and finite difference results are compared with that of an exact analytical solution in which case the thermal properties are taken to be constant.