Pure mathematics

Heat transfer

Materials science

Thermoelastic damping

Thermal conductivity

Variable (mathematics)

Heat equation

Economics

Thermodynamics

Physics

Kernel (algebra)

Mathematics

Thermal

Mathematical analysis

Financial economics

Time derivative

Heat kernel

Thermal conduction

Fractional calculus

Derivative (finance)

Fourier transform

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

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.

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