Influence of moving heat sources on thermoviscoelastic behavior of rotating nanorods: a nonlocal Klein–Gordon perspective with fractional heat conduction

Abstract

This study investigated magneto-thermoelastic interactions in rotating viscoelastic nanorods under moving heat sources, advancing the modeling of nanoscale systems. A key innovation was the adoption of Klein–Gordon-type nonlocal elasticity theory, which incorporated internal length and time scales to capture small-scale interactions effectively. Additionally, a fractional heat conduction model using two-parameter tempered-Caputo derivatives introduced memory effects and nonlocality, ensuring finite thermal wave speeds and overcoming the limitations of the classical Fourier model. The inclusion of the Kelvin–Voigt viscoelastic framework accounted for energy dissipation, enhancing the model’s accuracy. By integrating rotation, viscoelasticity, magnetic forces, and fractional heat conduction, the study developed a comprehensive nonlinear model of nanorod behavior. Numerical simulations demonstrated that fractional-order heat conduction and nonlocal elasticity significantly influenced the thermal and mechanical responses, reducing discrepancies in heat propagation predictions. These findings showed that the fractional and tempering parameters controlled thermal dissipation rates and thermal wave propagation velocity, ensuring physically realistic thermal responses. The incorporation of nonlocal length scale and time scale parameters enabled accurate representation of size-dependent behaviors, including stiffness reduction and stress redistribution in nanorods. These parameters also influenced memory effects affecting wave propagation and relaxation in viscoelastic materials.