Numerical Solution of Temperature-Dependent Thermal Conductivity Problems Using a Meshless Method

In this article, the meshless element-free Galerkin (EFG) method is extended to obtain numerical solution of nonlinear heat conduction problems with temperature-dependent thermal conductivity. The thermal conductivity of the material is assumed to vary linearly with temperature. A quasi-linearization scheme is adopted to avoid the iteration for nonlinear solution, and time integration is performed by the backward difference method. The essential boundary conditions are enforced by Lagrange multiplier technique. Meshless formulations are presented for one- and two-dimensional nonlinear heat conduction problems. MATLAB codes have been developed to obtain the EFG results. The results obtained by the EFG method are compared with those obtained by finite-element and analytical methods.