International Journal of Nonlinear Analysis and Applications
Fractional ordered thermoelastic stress analysis of a thin circular plate under axi-symmetric heat supply
Document Type : Research Paper
Authors
1 Department of Engineering Science, Amrutvahini College of Engineering, Sangamner, Maharashtra, 422608, India
2 P. G. Department of Mathematics, N. E. S., Science College, Nanded, Maharashtra, 431605, India
Abstract
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 $T_{0}(r, z)$. 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 $0 < \alpha < 1$, $\alpha = 1$ and $1 < \alpha < 2$ respectively.
Keywords
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Volume 14, Issue 4
April 2023Pages 207-219
- Receive Date: 28 November 2022
- Revise Date: 18 February 2023
- Accept Date: 20 February 2023