A study of the 3-phase lag model to a two-dimensional isotropic micro-polar thermoelastic medium with memory-dependent properties

• Published in: Journal of thermal stresses Vol. 47; no. 3; pp. 363 - 382
• Main Authors: Jojare, Kirti K., Gaikwad, Kishor R.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.03.2024; Taylor & Francis Ltd
• Subjects: Conduction heating; Conductive heat transfer; Differential equations; Eigenvalues; Exact solutions; Fourier series; Impact analysis; Kernel functions; Laplace transforms; Material properties; Memory-dependent-derivative; micro-polar; Phase lag; Response time; Rotating machinery; Series expansion; Structural analysis; thermoelasticity; three-phase-lag model; two-dimensional
• ISSN: 0149-5739; 1521-074X
• DOI: 10.1080/01495739.2023.2285798

This article enlightens the two-dimensional (2D) isotropic micro-polar thermoelastic problem of the three-phase-lag (3PHL) model and heat conduction equation is formulated in the context of memory-dependent derivative (MDD). The equations are converted into the domain of the Laplace transform vector matrix differential equation form and solved by using the eigenvalue technique. To obtain an analytical solution of displacement, temperature, and stress components Silicon material properties are used. Inversion of the Laplace transform with Fourier series expansion technique is used to obtain the numerical solution. For obtaining graphical results Mathematica software is used. For the purpose of exhibiting the beauty of MDD in the present model comparisons are made between the time delay parameters and kernel functions (constant, linear, and non-linear kernels), respectively, over the micro-polar panel. The results obtained have a valuable impact on structural analysis, especially in the design of rotating machinery structures using accurate material properties.