Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay

• Published in: Results in physics Vol. 20; p. 103705
• Main Authors: Abouelregal, Ahmed E., Moustapha, Mohamed V., Nofal, Taher A., Rashid, Saima, Ahmad, Hijaz
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2021; Elsevier
• Subjects: Higher-order; Kernel function; Memory-dependent derivative; Thermoelasticity; Time delay; Kernel function; Thermoelasticity; Memory-dependent derivative; Time delay; Higher-order
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2020.103705

•The study higher-order memory-dependent derivative with time delay.•To construct a new model of heat conduction.•To introduce the higher-order Taylor’s series expansion of Fourier’s law involving MDD with a kernel function.•The use of Laplace transform technique for the studied model.•To examine the effects of various choices for kernel function, time delay and the higher order of derivatives. In this investigation, based on the theory of generalized thermoelasticity and memory-dependent derivative (MDD) with time delay, a new model of heat conduction has been constructed. The new model has been incorporated by introducing the higher-order Taylor’s series expansion of Fourier’s law involving MDD with a kernel function. The derived model is an extension and generalization of many models presented in this field which can be obtained as special cases. The thermoelastic vibrations in an infinite medium that is exposed to an instant heat source and a concentrated magnetic field have been discussed based on the formulation model. The solutions and the numerical results of the studied fields are obtained by using the Laplace transform technique. Some comparisons with figures and tables have been presented to examine the effects of various choices for kernel function, time delay and the higher order of derivatives in all fields studied.