Mathematical Modeling of Thermoelastic State of a Functionally Graded Thermally Sensitive Thick Hollow Cylinder with Internal Heat Generation

In this paper, the effect of internal heat generation has been studied in a functionally graded (FG) thick hollow cylinder in context with thermosensitive thermoelastic properties. Initially, the cylinder is kept at reference temperature and the radial boundary surface under consideration dissipates heat by convection according to Newton's law of cooling, heat flux is applied at the lower surface, while the upper surface is insulated. The heat conduction equation due to internal heat generation is solved by integral transform technique and Kirchhoff's variable transformation is used to deal with the nonlinearity of the heat conduction equation. A mathematical model has been constructed for a nonhomogeneous material in which the material properties are assumed to be dependent on both temperature and spatial variable z. A ceramic-metal-based FG material is considered in which alumina is selected as ceramic and nickel as metal. The results obtained are illustrated graphically.