Heat transfer for nonlinear boundary conditions involving radiation for constant and temperature related thermal conductivity material using the MWLS method

Abstract The paper presented the heat transfer analysis for nonlinear boundary conditions involving radiation with constant and temperature related thermal conductivity material. For the constant thermal conductivity, linearizing the fourth power of radiation item, solve the temperature distribution through the global iteration coupled with the meshless weighted least squares (MWLS) method. For the temperature related variable thermal conductivity, the Kirchhoff transformation is usually employed to transform the nonlinear heat transfer problem into the linear Laplace's equation. Through the two-step iteration method, the convection and radiation boundary are converted into Dirichlet and Neumann boundary which is the easy-to-program linear condition after the transformation. In the end, the effectiveness and accuracy of the method were illustrated by some numerical examples .