Coupled DQ–FE methods for two dimensional transient heat transfer analysis of functionally graded material

In this paper, a mixed finite element (FE) and differential quadrature (DQ) method as a simple, accurate and computationally efficient numerical tool for two dimensional transient heat transfer analysis of functionally graded materials (FGMs) is developed. The method benefits from the high accuracy, fast convergence behavior and low computational efforts of the DQ in conjunction with the advantages of the FE method in general geometry, loading and systematic boundary treatment. Also, the boundary conditions at the top and bottom surfaces of the domain can be implemented more precisely and in strong form. The temporal derivatives are discretized using an incremental DQ method (IDQM), whose numerical stability is not sensitive to time step size. The effects of non-uniform convective–radiative conditions on the boundaries are investigated. The accuracy of the proposed method is demonstrated by comparing its results with those available in the literature. It is shown that using few grid points, highly accurate results can be obtained.