A novel localized collocation solver based on a radial Trefftz basis for thermal conduction analysis in FGMs with exponential variations

Xu, Wenzhi; Fu, Zhuojia; Xi, Qiang

doi:10.1016/j.camwa.2022.04.007

Cited by 14 publications

(1 citation statement)

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“…Similar to other numerical methods for solving 2D cylinder problems, a finite difference method was utilized to analyze temperature and stress distributions in the FGM‐made hollow cylinder in steady and transient modes by Awaji and Sivakumar [25]. Xu et al [26] developed a new method for analyzing heat transfer in 2D FGM with exponentially varying properties.…”

Section: Introductionmentioning

confidence: 99%

A general unsteady Fourier solution for orthotropic heat transfer in 2D functionally graded cylinders

Delouei,

Emamian,

Ghorbani

et al. 2023

Math Methods in App Sciences

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In the present research, an analytical solution is presented for unsteady heat transfer in a two‐dimensional finite cylinder made of functionally graded Materials (FGM). The governing equation, as an unsteady partial differential equation (PDE), is solved with general boundary conditions (BCs). The thermal conductivity coefficients are considered as a power function of the radius, both in the longitudinal and radial directions of the FGM cylinder. The presence of non‐constant coefficients and general BCs will confront us with the challenge of solving an unsteady problem with high complexity. A combination of Laplace transform, Fourier transform, and meromorphic functions are utilized to deal with this complex PDE. The Laplace transform was applied to transform to the frequency domain, the Sturm–Liouville equation was used to extract the orthogonal basis Fourier series, and the meromorphic function was deployed to transform back from the frequency domain to the time domain. Results were well verified against previous research works. Results showed that the proposed analytical solution could well predict the temperature distribution. The current analytical solution is useful to better understand unsteady heat transfer in FGMs.

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Section: Introductionmentioning

confidence: 99%