Tempered fractional thermal conduction model for magnetoelastic solids with spherical holes under time-dependent laser pulse heating

Abstract

This paper presents a modified tempered fractional thermal conductivity model aimed at enhancing the analysis of thermal behavior in magnetic thermoelastic solids, particularly in response to time-dependent laser pulse heating. Current literature lacks comprehensive approaches that effectively account for the complex interactions of thermal, mechanical, and magnetic fields within such materials. This gap is critical, as understanding these interactions is essential for optimizing the performance and reliability of advanced materials in engineering applications. Our study addresses this need by introducing a fractional model that employs modified tempered Caputo fractional derivatives in conjunction with a single-parameter Mittag–Leffler function. This innovative adjustment incorporates a parameter specifically designed to capture memory effects, resulting in a more accurate representation of the intricate thermal dynamics at play. We solved the governing equations directly using the Laplace transform method, providing exact formulas for displacement, temperature, and thermal stresses in copper. The graphical representations included in the study illustrate the material's deformation and the development of thermal stresses under thermal loading conditions. The findings demonstrate that the introduction of the memory effect parameter significantly enhances the thermoelastic model's ability to characterize the behavior of materials and structures subjected to thermal loads, thereby contributing valuable insights to the field of magnetic thermoelasticity.