A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

size-dependent thermo-viscoelastic coupling, generalized thermoelasticity with LS and without energy dissipation (GN-II), polymer micro-rod, fractional calculus

Received: August 1, 2024; Revised: September 25, 2024; Accepted: October 14, 2024; Published: October 25, 2024

How to cite this article: Mohamed H. Hendy, Magdy A. Ezzat, Esraa M. Al-lobani and Ahmed S. Hassan, A problem in fractional order thermo-viscoelasticity theory for a polymer micro-rod with and without energy dissipation, Advances in Differential Equations and Control Processes 31(4) (2024), 583-607. https://doi.org/10.17654/0974324324030

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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