Computational model on magnetothermoelastic analysis of a rotating cylinder using finite difference method

Abstract

We consider a magnetothermoelastic problem for a non-homogeneous, isotropic rotating hollow cylinder in the context of three theories of generalized formulations, the classical dynamical coupled (CD) theory, the Lord and Shulman's (L-S) theory with one relaxation time parameter as well as the Green and Lindsay's (G-L) theory with two relaxation time parameters. The inner surface of the cylinder is assumed to be traction free and subjected to a time-dependent exponential order thermal shock, whereas the temperature gradient and radial stress component are taken to be zero at the outer surface. The problem is solved numerically using the finite difference method by developing a Crank-Nicolson implicit scheme. The effect of the Maxwell stress component and rotation are illustrated graphically in the theory of magnetothermoelasticity. The computations of the displacement component, temperature distribution, radial and hoop stresses have been estimated. Furthermore, we have validated our numerical results with the results of the existing literature. The study shows that the rotational parameter with larger values has significant effects on the displacement, temperature distribution, and stress components. Thus the study predicts that the material has to be strong at the surface of the inner cylinder when it is in a rotating system.