The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity

This paper presents the singular boundary method for steady-state nonlinear heat conduction problems. In the steady-state nonlinear heat conduction problem, the Kirchhoff transformation is employed to remove the nonlinearity associated with the temperature dependence of the thermal conductivity. Then the transformed Laplace-type equation is investigated by the present singular boundary method with a simple iteration procedure. Finally, the temperature field is derived by the inverse Kirchhoff transformation. The present algorithm is verified on several examples involving various expressions of temperature dependent thermal conductivity and different computational domains. Numerical results show good accuracy and stability of the proposed strategy.