The Effect of a Nonlocal Thermoelastic Model on a Thermoelastic Material under Fractional Time Derivatives

Abstract

This article develops a novel nonlocal theory of generalized thermoelastic material based on fractional time derivatives and Eringen’s nonlocal thermoelasticity. An ultra-short pulse laser heats the surface of the medium’s surrounding plane. Using the Laplace transform method, the basic equations and their accompanying boundary conditions were numerically solved. The distribution of thermal stress, temperature and displacement are physical variables for which the eigenvalues approach was employed to generate the analytical solution. Visual representations were used to examine the influence of the nonlocal parameters and fractional time derivative parameters on the wave propagation distributions of the physical fields for materials. The consideration of the nonlocal thermoelasticity theory (nonlocal elasticity and heat conduction) with fractional time derivatives may lead us to conclude that the variations in physical quantities are considerably impacted.

The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory

“…A great deal of research has been carried out on the fractional-order thermoelasticity theory. Hobiny [17] studied the distribution of physical field waves generated by the pulsed laser heating of the surface of an elastic medium and analyzed the effects of non-local parameters and fractional-order derivatives' generation. Abouelregal [18] created a heat transfer model with single-phase hysteresis by introducing fractional calculus into the heat transfer equation, which differs from previous models by including two fractional parameters in the heat equation.…”