A High Order Control Volume Finite Element Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

This paper describes a new two-dimensional(2-D) control volume finite element method(CV-FEM) for transient heat conduction in multilayer functionally graded materials(FGMs). To deal with the mixed-grid problem, 9-node quadrilateral grids and 6-node triangular grids are used. The unknown temperature and material properties are stored at the node. By using quadratic triangular grids and quadratic quadrilateral grids, the present method offers greater geometric flexibility and the potential for higher accuracy than the linear CV-FEM. The properties of the FGMs are described by exponential, quadratic and trigonometric grading functions. Some numerical tests are studied to demonstrate the performance of the developed method. First, the present CV-FEM with mixed high-order girds provides a higher accuracy than the linear CV-FEM based on the same grid size. Second, the material properties defined location is proved to have a significant effect on the accuracy of the numerical results. Third, the present method provides better numerical solutions than the conventional FEM for the FGMs in conjunction with course high-order grids. Finally, the present method is also capable of analysis of transient heat conduction in multilayer FGM.