Estimation of Thermoelastic State of a Thermally Sensitive Functionally Graded Thick Hollow Cylinder: A Mathematical Model

Document Type : Research Paper


1 Department of Mathematics, Priyadarshini J.L. College of Engineering, Nagpur , India

2 Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India

3 Department of Mathematics, RTM Nagpur University, Nagpur, India


The object of the present paper is to study temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature. The nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity is reduced to linear form by applying Kirchhoff’s variable transformation. Solution for the two dimensional heat conduction equation with internal heat source is obtained in the transient state. The influence of thermo-sensitivity on the thermal and mechanical behavior is examined. For theoretical treatment all physical and mechanical quantities are taken as dimensional, whereas for numerical computations we have considered non-dimensional parameters. A mathematical model is constructed for both homogeneous and nonhomogeneous case. Numerical computations are carried out for ceramic-metal-based functionally graded material (FGM), in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.


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