Nonlinear heat conduction in materials with temperature-dependent thermal conductivity using hybrid finite element model

The boundary-type hybrid finite element formulation is established to solve nonlinear heat conduction in solids with temperature-dependent material definition. The Kirchhoff transformation is first used to convert the nonlinear heat transfer system into a linear system, which is then solved by the presented hybrid finite element model, in which the fundamental solutions are used to approximate the element interior fields and conventional shape functions are used for the element boundary fields. The weak integral functional is developed to link these two fields and establish the stiffness equation. The accuracy and stability of the algorithm are tested on two examples involving various thermal conductivities to verify the present formulation.