Comparative Analysis of Generalized Thermoelasticity Models for Heat Conduction in a Circular Micro-Plate Using Kirchhoff–Love Plate Theory
Year: 2026
Type: preprint
Abstract: This research introduces a comprehensive mathematical model for examining heat conduction and thermomechanical properties in an isotropic, homogeneous, thermoelastic circular microplate, grounded on the Kirchhoff–Love plate theory. The formulation integrates many generalized thermoelasticity models, such as Green–Lindsay, Biot, Lord–Shulman, Green–Naghdi Type-I, Green–Naghdi Type-III, and Moore–Gibson–Thompson theories, into a coherent framework of governing differential equations. The examination employs scaled thermoelasticity for a circular micro-plate that is supported at its periphery and exposed to ramp-type thermal loading. The Laplace transform method is used to provide analytical solutions for the governing equations, while Tzou’s iterative approach is employed for the numerical inversion of the Laplace transform to assess the transient thermoelastic response. A comprehensive parametric analysis examines the influence of ramp-time heating, plate thickness, and material characteristics on thermomechanical wave transmission in a silicon microplate. We provide visual comparisons of several thermoelastic models to emphasize their dynamic properties and commonalities in mechanical behavior. The findings reveal that the Green–Naghdi Type-III and Moore–Gibson–Thompson models have the most similar mechanical behavior, followed by the Biot and Lord–Shulman models. Moreover, the research indicates that ramp-time heating and geometric factors may proficiently modulate thermomechanical wave transmission in micro-scale architectures.
Source: Research Square
Author: Hamdy Youssef
Institution: Umm al-Qura University
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225300050