A thermodynamic two-temperature model with distinct fractional derivative operators for an infinite body with a cylindrical cavity and varying properties

Abstract

The current work presents a novel model in the field of thermoelasticity to study an infinitely cylindrical cavity solid medium with variable thermal properties. The governing equations are based on a two-temperature heat conduction model with local and non-local fractional differential operators (Caputo-Fabrizio (CF) and Atangana-Baleanu (AB)). The surface surrounding the cylindrical cavity is due to decreasing heat flow and transport at a constant speed. The effects of different fractional differential operators have been shown and analyzed by making some comparisons and presenting them in tables. The numerical results and figures show the effects of the fractional arrangement parameter and the heat flux velocity significantly on the stress and deformation patterns, but they have little effect on the dynamic temperature and conductivity changes. The thermoelastic model with two temperatures and fractional operators is suitable for describing the phenomenon of heat transfer within elastic and viscous media.