A Mixed Pseudo-spectral FFT-FE Method for Asymmetric Nonlinear Heat Transfer of a Functionally Graded Hollow Cylinder

Abstract

In this article, a novel spectral method based on the integral transform and finite element (FE) method is introduced for nonlinear thermal analysis of a hollow cylinder under asymmetric boundary excitations. The material properties are temperature-dependent and vary in terms of spatial coordinates. This dependency makes the problem to be nonlinear. The intended nonlinear heat conduction equation is discretized using finite elements in the radial direction. Fast Fourier transform (FFT) technique with the uniform distribution of the harmonics in the circumferential direction, is used to discretize the periodic domain and boundary conditions. The use of the FFT algorithm is accompanied by a significant save in computational times and efforts. In such problems, the Pseudo-spectral technique, as an evolved model of the spectral method, is utilized whenever the material properties vary in terms of the periodic variables or there exists a nonlinear term. The convolution sum technique is appropriately used to transform the nonlinear terms in the Fourier space. Thermal boundary conditions at the inner surface of the cylinder are considered in asymmetrical form. In compliance with the other analytical and numerical solutions, the present mixed-method benefits from the fast rate of convergence and high accuracy.