Influence of Fractional Parameters in a Functionally Graded Elliptical Plate with Thermally Sensitive Material Features

Abstract

In order to examine the relationship between temperature change and thermoelastic deformation in the assumed functionally graded materials (FGMs), the present work involves fractional-order mathematical modeling of a thermoelastic thick elliptical annular plate, where the material properties of the plate are considered thermo-sensitive. To determine the precise thermal response of the problem, the density, heat capacity, and thermal conductivity are also graded axially, in addition to the thermo-sensitivity. The temperature distribution of the plate is assumed to be zero at the start and end of the thickness variation, with convective heat exchange boundary conditions in the spatial direction. Kirchhoff's variable transformation method is used to eliminate temperature-dependent nonlinearity in the heat transfer equations. The Laplace transform for the initial condition and a perturbation solution are obtained through an asymptotic series expansion. The heat transfer problem is ultimately solved using the modified Mathieu transform, the Taylor series technique, and its inversion, yielding the required temperature distribution function in the Laplace domain. Using nickel as the metal and titanium carbide as the ceramic, a model of a ceramic-metal-based FGM is constructed for numerical computations. All results are graphically presented, showing the distributions of temperature, displacement, and stress curves along the spatial variables for two different fractional-order parameters by varying the plate’s thickness. This study enables a deeper understanding of the thermo-mechanical responses of FGMs through its novel application to FGMs with elliptical geometry and its innovative modeling approach incorporating thermally sensitive material properties. It opens the door to optimized designs in thermal industries. The understanding and improvement of thermal behavior in advanced materials have been significantly enhanced by the discovery of the influence of fractional parameters in an FGM elliptical plate.

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Affiliated Institutions

• Zagazig University EG
• Rashtrasant Tukadoji Maharaj Nagpur University IN

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