Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

The object of the present paper is to study heat conduction and thermal stresses in a hollow cylinder with nonhomogeneous material properties. The cylinder is subjected to sectional heating at the curved surface. All the material properties except for Poisson’s ratio and density are assumed to be given by a simple power law in the axial direction. A solution of the two-dimensional heat conducti...

We study the heat conduction of two nonlinear lattices joined by a weak harmonic link. When the system reaches a steady state, the heat conduction of the system is decided by the tunneling heat flow through the weak link. We present an analytical analysis by the combination of the self-consistent phonon theory and the heat tunneling transport formalism, and then the tunneling heat flow can be o...