Thermal characteristics of a multilayered annular disk with thermosensitive features using a fractional-order heat conduction model

Abstract

The fractional theory addresses microscopic physical processes and predicts delayed responses to stimuli observed in nature. This study establishes a mathematical model that incorporates the non-local Caputo-type temporal fractional-order derivative in the heat conduction equation to analyze the thermal behavior of a thermosensitive multilayered annular disk. The disk’s inner and outer layers are subjected to convective heat exchange constraints to emphasize the significance of the fractional framework. Using Kirchhoff’s variable transformation and considering the material’s inherent thermal nonlinearity, the equations are linearized. The resulting linear equations are solved using the integral transformation method to derive mathematical expressions for deflection, resultant forces, shear forces, resultant moments, and thermal stresses. Finally, a three-layered disk composed of copper, zinc, and aluminum is constructed for numerical calculations using a fractional-ordered thermosensitive structure, enabling graphical representation of how various fractional parameters influence temperature and thermal fluctuations.