Fractional order heat conduction and thermoelastic response of a thermally sensitive rectangular parallelopiped

Abstract

In the present paper, the problem of finite dimensional rectangular parallelepiped in isotropic thermoelastic medium with convective type heating is considered. The heat conduction equation (HCE) of the region is described by time HC of fractional order with Caputo derivative form. The non-linear form of heat conduction equation is converted to linear form with Kirchhoff’s transformation. Integral transform technique is used to deal with the spatial variables and Laplace transform technique is used to deal with Caputo type time fractional derivative. Inverse Laplace transform and inverse finite Fourier transform are employed to expose the solution in the transformed domain. Numerical results are obtained for temperature distribution, deflection, stress resultants and thermal stress distribution for different values of time fractional order parameter. These results are presented graphically and discussed for various values of time fractional parameters. The obtained results show significant influence of the time fractional order derivative on the temperature as well as stress distribution. Thermosensitivity plays a vital role in the analysis of any real thermoelastic problems and one should consider their effect while dealing with materials in high temperature environment.

Keywords

• Fractional order
• Heat conduction
• Deflection
• Stress resultants
• Thermal stresses

References

1. The Authors are presently working in the field of Engineering Mechanics and studying different problems on heat conduction and their thermal behaviour.