Fractional derivative Moore‐Gibson‐Thompson heat equation without singular kernel for a thermoelastic medium with a cylindrical hole and variable properties

Abstract

In this study, a new mathematical model for thermoelasticity with a fractional derivative of the classical Fourier law of thermal conductivity is derived. In the sense of the fractional Caputo-Fabrizio (CF) derivative, the modified heat transfer equation of the proposed model is presented by incorporating the Moore-Gibson-Thompson (MGT) equation. The modified fractional thermal conduction model does not include a single kernel, unlike the Caputo derivative, linking the Green-Naghdi Type III model to the Lord and Shulman model. As an application of this model, the interactions of thermoelastic waves in an infinite orthodontic medium with a cylindrical hole were studied. Also in this investigation, it was taken into account that the thermal conductivity is variable and depends on the change of temperature, in contrast many problems that that often consider this parameter to be constant. Numerical calculations are performed for different values of the fractional order of CF derivatives and the change in thermal conductivity. The numerical results were also presented in tables to compare with the results of previous models to verify the accuracy of the results obtained.

Size‐dependent thermoelastic damping analysis in functionally graded graphene nanoplatelets reinforced composite microplate resonators based on Moore–Gibson–Thompson thermoelasticity

“…Furthermore, the calculated results in the frame of MCST agree well with those obtained from molecular dynamic simulations [43]. So far, extensive investigations were performed to incorporate the MCST in TED analysis [44,45], dynamic thermoelastic response [46,47] and thermoelastic vibration [48,49] of micro/nano-beam.…”

Variable thermal conductivity in context of Green‐Naghdi theory of thermo‐microstretch solids

“…Saeed et al [28] introduced a novel theoretical model including the microstretch properties of elastic semiconductor medium and investigated this model in the context of photo-excitation transport processes through the thermoelasticity theory. Abouelregal [29] derived a new mathematical model for thermoelasticity with a fractional derivative of the classical Fourier law of thermal conductivity. Zhang et al [30] discussed the electro-magneto-hydrodynamic non-Newtonian natural convection through a vertical parallel plate duct containing an isotropic, homogenous non-Darcian porous medium.…”

“…[28] introduced a novel theoretical model including the microstretch properties of elastic semiconductor medium and investigated this model in the context of photo‐excitation transport processes through the thermoelasticity theory. Abouelregal [29] derived a new mathematical model for thermoelasticity with a fractional derivative of the classical Fourier law of thermal conductivity. Zhang et al.…”

Thermal effects of electromagnetic radiation on the skin tissue by considering fourth‐order MGT bioheat model

“…This model integrates a relaxation component into the framework of the Green-Naghdi model of the third kind [42]. Building upon Quintanilla's work, Abouelregal et al [43][44][45] explored various innovative thermoelastic systems and their applications. The revised model has also been utilized to investigate complexities in fluid dynamics and the thermomechanical response to various engineering problems [46][47][48].…”