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Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier's equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors. [ABSTRACT FROM AUTHOR]

This paper introduces size-dependent modeling and investigation of the transverse vibrational behavior of rotating thermoelastic nanobeams by means of nonlocal elasticity theory. In the formulation, a model of thermal conductivity with two-phase delays (DPL) was utilized. By incorporating the interactions between phonons and electrons, this model took into account microstructural influences. Also, we have employed the state-space approach and Laplace transform approach to solve the governing equations, which were developed in the context of the nonlocal Eringen model. The nanobeam material is subjected to a changeable temperature field produced by the graphene tape attached to the nanobeam and connected to an electrical source. In addition, the nanobeam material is fully encompassed by an axially applied magnetic field. It has been revealed how coefficients such as the rotational angular velocity of the nanobeam, nonlocal coefficient, voltage, electrical resistance, and applied magnetic field influence its behavior. [ABSTRACT FROM AUTHOR]