A boundary collocation method for anomalous heat conduction analysis in functionally graded materials. (15th April 2021) - Fu, Zhuo-Jia; Yang, Li-Wen; Xi, Qiang; Liu, Chein-Shan
Abstract: This paper applies a semi-analytical boundary collocation method, the singular boundary method (SBM), in conjunction with the dual reciprocity method (DRM) and Laplace transformation technique to solve anomalous heat conduction problems under functionally graded materials (FGMs). In this study, transient heat conduction equation with Caputo time fractional derivative is considered to describe anomalous heat conduction phenomena. In the present numerical implementation, Laplace transformation and numerical inverse Laplace transformation are used to deal with the Caputo time fractional derivative, which avoid the effect of time step on the computational efficiency of the time fractional derivation approximation. The SBM in conjunction with the DRM is employed to obtain the high accurate results in the solution of Laplace-transformed time-independent nonhomogeneous problems. To demonstrate the effectiveness of the proposed method for anomalous heat conduction analysis under functionally graded materials, three numerical examples are considered and the present results are compared with known analytical solutions and COMSOL simulation.