Magneto-Thermoelasticity in Solids: Mathematical Theory, Wave Propagation, and Boundary Value Problems

Authors: Prasad S. Patil, C.M. Jadhav

DOI: https://doi.org/10.37082/IJIRMPS.v13.i2.233194

Short DOI: https://doi.org/

Country: India

Full-text Research PDF File:   View   |   Download

Abstract: This paper develops and solves an extended half-space thermal-shock boundary value problem in magneto-thermoelastic solids, incorporating three physical effects relevant to real structural and geophysical media beyond the idealized stationary, unstressed, ideally conducting continuum: steady rotation, initial mechanical stress, and Hall current. Building on the Lord–Shulman generalized theory and the perfectly conducting magneto-thermoelastic coupling, each of the three extensions is shown to enter the governing half-space problem through exactly one analytically separable term of a single extended characteristic equation: the Hall parameter reduces the effective magnetic pressure number, the initial stress modifies the leading elastic coefficient directly, and rotation enters solely through a substitution in the transformed inertial term.
The resulting Laplace-domain solution is inverted numerically (Stehfest's algorithm) to obtain the transient temperature and stress response at a fixed interior point, for each effect in isolation and in combination. The computations show that all three effects shift the transient stress peak later in time and increase its magnitude relative to the un-extended half-space problem, with initial stress producing the largest individual departure among the three at the parameter values considered; combining all three departs from the sum of their individual contributions by a modest but non-negligible margin, indicating the three effects are close to, but not exactly, additive. The Hall parameter is further shown to weaken the magnetic stiffening of the dilatational wave monotonically, reducing the effective magnetic pressure number toward zero as the Hall parameter grows.
These results are situated against the literature on rotating, initially stressed, and Hall-current-bearing magneto-thermoelastic media, and the paper closes by identifying the natural further extensions of the present formulation within the broader landscape of multiphysics coupling in solids — two-temperature theory, porous and micropolar media, fractional-order heat conduction, and semiconductor photothermal coupling.

Keywords: magneto-thermoelasticity; rotation; initial stress; Hall current; Lord–Shulman theory; boundary value problems; Laplace transform

Paper Id: 233194

Published On: 2025-04-05

Published In: Volume 13, Issue 2, March-April 2025

Share this