Fractional Three-Phase-Lag Heat Transfer Model for Analyzing Perfect Conducting Thermelastic Hollow Cylinder

Abstract

This study presents a unified fractional three-phase-lag heat conduction model within the framework of Green–Naghdi thermoelasticity, formulated to describe the coupled magneto-electro-thermoelastic response of a perfectly conducting, infinitely long hollow cylinder subjected to a uniform axial magnetic field. The model introduces fractional-order derivatives to generalize classical and generalized thermoelastic theories (e.g., Biot, Lord–Shulman, GN types I–III) as limiting cases. A single fractional formulation governed by three phase-lag parameters enables a seamless transition across different heat transport behaviors while capturing nonlocal and memory effects. Field equations are derived using Laplace transforms and solved semi-analytically. Numerical inversions provide time-domain distributions of temperature, stress, displacement, and induced electromagnetic fields. Results show that the fractional order significantly influences thermal and mechanical wave propagation, suppressing displacement while amplifying induced magnetic fields. The model offers new insight into the thermal response of materials with memory, and the unified structure supports broader applicability in material characterization and advanced engineering systems.