Fractional ordered thermoelastic stress analysis of a thin circular plate under axi-symmetric heat supply

The main objective of the current study is to investigate the fractional ordered thermoelastic stress analysis of a thin circular plate under axi-symmetric heat supply. Initially, the plate is characterized by the initial temperature T_{۰}(r, z). The boundary value problem is formulated with a circular plate model where the perimetric edge is clamped and convection, and the upper and lower surfaces are subjected to heat convection with convection coefficient h_{c} and fluid temperature T_{\infty}. The variable separable technique and Green's function approach scheme have been employed to solve the heat conduction equation. The impacts of the fractional ordered derivative of some other parameters on temperature, deflection, and stress profiles will be analyzed in detail. For instance, the results indicate that the temperature and thermal deflection are directly proportional to the fractional order parameter \alpha. Also, the parameter \alpha represents the weak, normal, and strong conductivity, within the range of ۰ < \alpha < ۱, \alpha = ۱  and ۱ < \alpha < ۲ respectively.

کلیدواژه ها:

Caputo fractional derivative ، Green’s Function ، Axi-symmetric heat source ، Thin circular plate ، Mittag-Leffler functions