Spatio‑temporal nonlocal magneto‑thermoelastic framework via memory‑dependent Gurtin–Pipkin–Moore–Gibson–Thompson heat conduction
Nitin Chandel, Vinod Varghese, Nilesh Deotale, Madhuri Kotewar
Abstract
In this work, a unified nonlocal magneto‑thermoelastic framework is developed for a semi‑infinite half‑space subjected to simultaneous thermal memory and electromagnetic field effects. Heat conduction is modeled through a generalized Gurtin–Pipkin (GP)–Moore–Gibson–Thompson formulation incorporating memory‑dependent derivatives, thereby ensuring finite thermal wave speed and capturing hereditary influence. Spatial nonlocality is introduced via an Eringen‑type constitutive relation, enabling the representation of long‑range interactions at micro‑ and nanoscales. The medium is excited by an instantaneous boundary heat source under a uniform transverse magnetic field, and the governing coupled equations for temperature, displacement, and stress are established in a one‑dimensional setting. These equations are transformed into the Laplace domain and solved exactly using a state‑space eigenvalue approach, followed by numerical inversion techniques. Parametric studies highlight the roles of nonlocal length scales, memory kernels, magnetic field intensity, and relaxation times in shaping the thermoelastic response. This study aims to develop a unified magneto-thermoelastic model by combining GP memory with Eringen’s nonlocal elasticity, and to analyze wave propagation under electromagnetic coupling using Laplace-domain solutions, providing a bridge between classical and modern theories of heat conduction and elasticity.