Temperature profiles and thermal stresses due to heat conduction under fading memory effect

Abstract

Examining the thermal stresses in thermally loaded materials used in the construction of technological devices is a fundamental problem to determine how functionally durable they are. Therefore, it is noteworthy to analyze heat conduction models under prescribed initial and/or boundary temperatures from different perspectives. From this necessity, present work aims to achieve the temperatures and thermal stresses resulting from a fractional heat conduction model based on the Cattaneo's constitutive law equipped with a time-dependent exponential kernel. For a limiting cylindrical material, the effect of the surface temperature on the heating process is tried to be revealed. It is considered that heat conduction occurs axially symmetrically under two different boundary conditions. The Laplace and Hankel integral transform techniques are utilized to obtain analytical solutions to temperature distributions. Using the temperature functions and applying the constitutive relations of uncoupled thermoelasticity theory give the thermal stress components. The dependency of the temperatures and stresses on the fractional parameter, namely on the fading memory effect, is interpreted from the graphics obtained with MATLAB software. Simulation results show that the change in temperature and the change in associated thermal stresses for the heat conduction with fading memory are significantly dependent on the boundary temperatures. Therefore, the surface temperature of a material whose heat transfer is described with the model discussed here is quite decisive for its use in technological devices. This is the first study to examine the thermoelastic properties of the heat conduction model with regular fading memory in a bounded curvilinear region.