Thermoelastic Field Analysis of Micro-Scale Metallic Structures under Moore–Gibson–Thompson Theory via Differential Transform Method
Author : Dr. Sangita B Pimpare
Abstract :
This paper presents an analytical and computational framework for investigating non-Fourier thermoelastic field responses in micro-scale solid media under the Moore–Gibson–Thompson (MGT) generalized thermoelasticity model. By incorporating a relaxation parameter into the Green–Naghdi Type III heat conduction equation, the MGT framework eliminates the physical paradox of infinite thermal propagation speeds while avoiding standard derivative instabilities. To resolve the resulting coupled third-order partial differential equations, we employ the two-dimensional Differential Transform Method (DTM). Semianalytic expressions for non-dimensional temperature, lateral displacement, and thermal stress components (σxx, σyy, σxy) are explicitly derived. Quantitative evaluations demonstrate the operational behavior of MGT thermoelasticity compared with classical Biot, Lord–Shulman (LS), and Green–Naghdi Type III (GN-III) models.
Keywords :
Thermoelasticity, Moore–Gibson–Thompson (MGT) model, Differential Transform Method (DTM), Non-Fourier heat transfer, Thermal stress analysis.
