Meshless analysis of unsteady-state heat transfer in semi-infinite solid with temperature-dependent thermal conductivity

In this paper, meshless element-free Galerkin (EFG) method has been extended to obtain the numerical solution of linear and non-linear heat transfer in semi-infinite solids. A model problem has been solved using constant and temperature-dependent thermal conductivities of the material. For the linearization of nonlinear equations, quasilinearization scheme is adopted to avoid iterations and for time integration, backward difference method has been used. The meshless formulation has been presented for a non-linear heat transfer in semi-infinite solids. The EFG results have been obtained for a model problem using cubic spline weight function. The results obtained by the EFG method are compared with those obtained by finite element and analytical methods.