A modified mathematical model for thermo-viscous thermal conduction incorporating memory-based derivatives and the Moore–Gibson–Thomson equation

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2024-03-02 DOI:10.1007/s00161-024-01284-6

Ahmed E. Abouelregal, Marin Marin, Sameh S. Askar, Abdelaziz Foul

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Abstract

Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier’s equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors.

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包含基于记忆的导数和摩尔-吉布森-汤姆森方程的热粘性热传导修正数学模型

分析材料（尤其是聚合物）的粘弹性特征对于了解其机械性能及其在不同条件下的工作能力至关重要。本文介绍了一种新型粘弹性传热模型，该模型将基于记忆的导数与摩尔-吉布森-汤姆森（MGT）方程整合在一起。其目的是研究材料的粘弹性特征，评估材料在一定时间内对外部应力和变形的响应。除了结合格林和纳格迪提供的第三类热弹性模型外，该热粘弹性模型的推导还包括将热流及其时间导数纳入傅里叶方程。为了验证和理解所提出的模型，将其应用于考虑浸没在均匀磁场中的无界粘弹性半空间，并将非高斯激光辐射作为热源。对计算结果进行了分析，以评估所考虑的场变量的行为如何受到粘弹性系数和基于记忆的导出因子的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.