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.

In this paper, we have considered the Caputo fractional order model for convective fins of rectangular profile with temperature-dependent thermal conductivity. The fractional order energy balance equation is solved by using homotopy perturbation method (HPM). This method is one of the effective tools to solve the fractional order nonlinear diffusion equation with thermosensitive conductivity it requires less computer memory and reduces the computation time. The fin efficiency and the fin effectiveness appeared as a function of thermo-geometric fin parameters. The stresses are solved using stress-displacement relation. The results obtained are illustrated graphically for temperature distribution, efficiency, effectiveness and thermal stresses. The phenomena reveal that the selection of the order of fractional derivative remarkably influences the outcomes. However, careful review of the existing literature reveals that hardly few results of thermal stresses in fins with the energy balance equation of integer order are available. Hence this result may be the novel contribution to the field.