Nonlinear transient heat transfer analysis using two integration methods with different distribution of integration points in the domain in a meshless formulation

In this article, the transient heat transfer problem with both convection and radiation boundary conditions is studied. The meshless Radial Point Interpolation Method (RPIM) is implemented in this numerical study. Also, two integration methods, the Cartesian Transformation Method (CTM) and the Gaussian Quadratuer (GQ) method which uses background cells, are employed for domain integral calculations. First the problem of transient heat transfer in a homogenouse domain with both convection and radiation boundary conditions is considered. The temperature distribution results of the meshless domain using the proposed method, are compared with the analytical temperature results in this problem and excellent agreement is obtained. Then, to verify the better accuracy of results obtained from CTM, compared to those obtained from conventional background cell method, a number of example problems in a layered composite and a Functionally Graded (FG) sample with both convection and radiation boundary conditions are solved and the temperature results are compared with those of ABAQUS software. Consequently, using CTM in compare with using background cell method in convection boundary conditions reduce error to half and in radiation boundary conditions reduce error to one quarter. This numerical method is a meshless method which doesn’t need any background mesh. Moreover, the amount of error using the background cell method in problems with radiation boundary conditions is more than thoes with convection boundary conditions. This shows the advantage of using CTM in problems with radiation boundary conditions which have a higher degree of nonlinearity, due to the temperature dependent boundary conditions.