Thermal plane waves in unbounded non-local medium exposed to a moving heat source with a non-singular kernel and higher order time derivatives

Abstract

In this paper, the thermoelastic characteristics of a nonlocal unbounded viscoelastic medium due to an instantaneous heat source is investigated by considering a modified dual-phase-lag model with higher-order time derivatives. The fractional derivative and Eringen's non-local theory are also applied in the considered model. To extend the application of the classical Kelvin-Voigt model, a fractional derivative operator with non-single kernels based on the Atangana and Baleanu's concept is proposed. After applying the Laplace transform method, the governing systems of equations are expressed as vector-matrix differential form and solved by constructing an eigenvalue problem. Some comparative results are presented to analyze the effects of heat source velocity, nonlocal parameter, structural viscoelastic coefficients, phase lags, fractional and higher-order parameters on the behavior of physical fields.