Fractional heat conduction in a thin hollow circular disk and associated thermal deflection

Abstract

The time nonlocal generalization of the classical Fourier law with the “Long-tail” power kernel can be interpreted in terms of fractional calculus and leads to the time fractional heat conduction equation. The solution to the fractional heat conduction equation under a Dirichlet boundary condition with zero temperature and the physical Neumann boundary condition with zero heat flux are obtained by integral transform. Thermal deflection has been investigated in the context of fractional-order heat conduction by quasi-static approach for a thin hollow circular disk. The numerical results for temperature distribution and thermal deflection using thermal moment are computed and represented graphically for copper material.