# Solution of generalized magnetothermoelastic problem by using finite difference method

## TL;DR

This paper investigates the magnetothermoelastic behavior of a nonhomogeneous, isotropic hollow cylinder under thermal shock using three generalized theories, solved numerically with a finite difference method, and compares the effects of various parameters.

## Contribution

It introduces a numerical approach to solve a complex magnetothermoelastic problem using finite difference method across three generalized theories.

## Key findings

- Displacement, temperature, and stress distributions are computed under different parameters.
- The effects of thermal shock and magnetic field are analyzed.
- Comparative results highlight differences among the three theories.

## Abstract

A magnetothermoelastic problem is considered for a nonhomogeneous, isotropic rotating hollow cylinder in the context of three theories of generalized formulations, the classical dynamical coupled (C-D) 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 subjected to a time dependent exponential thermal shock at its inner boundary. The inner and outer surfaces of the hollow cylinder are assumed to be traction free and the temperature gradient vanishes at its outer surface. The problem is solved numerically using finite difference method by developing Crank-Nicolson implicit scheme. The numerical computations of the displacement component, temperature distribution, radial and hoop stresses have been estimated. A comparison has been made under the effect of different parameters by representing several figures.