A polygonal element differential method for solving two-dimensional transient nonlinear heat conduction problems

Zhou, Ling; Lv, Jun; Cui, Miao; Peng, Hao; Gao, Xiao‐Wei

doi:10.1016/j.enganabound.2022.10.015

Cited by 7 publications

(6 citation statements)

References 16 publications

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“…Mutually, boundary conditions are considered to be as Eq. (3)(4)(5)(6)(7). Considering a Sobolev space () HQ  ( 0   ) with the corresponding norm of () n HQ    and desired infinity domain…”

Section: Assuming the Temperature Filed ( )mentioning

confidence: 99%

“…Substituting the above approximations into Eq. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) in the Fourier space, we have…”

Section: Assuming the Temperature Filed ( )mentioning

confidence: 99%

“…So, heat conduction analyses of these materials are extremely concerned by many scholars. Up to now, a set of advanced numerical solutions based on the finite element method is investigated for heat conduction problems [2][3][4]. Annasabi and Erchiqui [2] solved the nonlinear heat equation in terms of the Kirchhoff transformation,   T  .…”

Section: Introductionmentioning

confidence: 99%

“…In a challenging problem, an enriched finite element method, where the basis functions are augmented with a summation of exponential functions, has been executed for nonlinear transient heat transfer in functionally graded materials [3]. In a similar work, a novel polynomial element differential method (PEDM) was presented by Ling Zhou et al [4] for solving two-dimensional nonlinear transient heat conduction problems. New shape functions with respect to isoparametric coordinates were derived to conduct the polynomial elements with an internal node.…”

Section: Introductionmentioning

confidence: 99%

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

2023

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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.

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Section: Assuming the Temperature Filed ( )mentioning

confidence: 99%

“…Substituting the above approximations into Eq. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) in the Fourier space, we have…”

Section: Assuming the Temperature Filed ( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2023

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“…Unlike the above numerical methods, the element differential method (EDM) [18] is a strong-form technique to solve ordinary or partial differential equations. The most important feature of the EDM is that the derived spatial derivatives can be directly substituted into the governing equation and boundary conditions to form the final system of algebraic equations [19].…”

Section: Introductionmentioning

confidence: 99%

Element Differential Method for Non-Fourier Heat Conduction in the Convective-Radiative Fin with Mixed Boundary Conditions

Sun

2022

Coatings

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Fin is an efficient and straightforward way to enhance heat transfer rate. When the heat source varies dramatically in a very short time, non-Fourier heat conduction should be considered. In the paper, taking advantage of numerical stability and no integral and easy-to-implement features of an element differential method, a numerical model is developed to evaluate the fin efficiency of the convective-radiative fin within non-Fourier heat conduction. In this fin, heat is generated by an internal heat source and dissipated by convection and radiation. Both periodic and adiabatic boundary conditions are considered. The accuracy and efficiency of the element differential method is validated by several numerical examples with analytical solutions. The results indicate that the element differential method has high precision and flexibility to solve non-Fourier heat conduction in convective-radiative fin. Besides, the effects of Vernotte number, dimensionless periodicity, thermal conductivity coefficient, and emissivity coefficient on dimensionless fin tip temperature, instantaneous fin efficiency, and average fin efficiency are comprehensively analyzed.

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A machine learning approach for identifying vertical temperature gradient in steel-concrete composite beam under solar radiation

Chu,

Zhang,

et al. 2024

Advances in Engineering Software

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A polygonal element differential method for solving two-dimensional transient nonlinear heat conduction problems

Cited by 7 publications

References 16 publications

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

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

Element Differential Method for Non-Fourier Heat Conduction in the Convective-Radiative Fin with Mixed Boundary Conditions

A machine learning approach for identifying vertical temperature gradient in steel-concrete composite beam under solar radiation

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