Thermal behavior of a finite hollow cylinder in context of fractional thermoelasticity with convection boundary conditions

Abstract

This paper presents an axisymmetric problem of two-dimensional finite hollow cylinder with the fractional order derivative of order $0<\alpha \le 2$ occupying the space $D=\{(x,y,z)\in R^3:a\le r\le b,-h\le z\le h\}.$ Convection boundary conditions are applied on the curved surface of cylinder and heat sources are generated as a linear function of temperature. The analytical solution for temperature, displacement, and thermal stresses are obtained applying finite Marchi-Zgrablich, finite Marchi-Fasulo, and Laplace transform technique. Some numerical results of temperature change and stress distribution are illustrated graphically and are shown in figures with the help of Mathematica software.

Keywords:

• Caputo fractional derivative
• finite hollow cylinder
• Marchi-Fasulo and Laplace transform
• Marchi-Zgrablich
• Mittag-Leffler function
• temperature distribution
• thermal stresses

Acknowledgment

The authors sincerely thank the referees and Professor Martin Ostoja-Starzewski, Editor in Chief, for their constructive comments which have improved the manuscript greatly.