A mixed pseudo-spectral FFT-FE method for asymmetric nonlinear heat transfer of a functionally graded hollow cylinder

Document Type : Article

Authors

1 Faculty of Mechanical Engineering, Malek Ashtar University of Technology, Shahin Shahr, Iran

2 Department of Mechanical Engineering, Yasouj University, P.O. Box 75914-353, Yasouj, Iran

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 FEs 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.

Keywords

Main Subjects

References

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Scientia Iranica
Volume 31, Issue 20
Transactions on Mechanical Engineering (B)
November and December 2024
Pages 1906-1915

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History

  • Receive Date: 08 April 2022
  • Revise Date: 27 February 2023
  • Accept Date: 19 June 2023

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