Hierarchical MMGTn framework for generalized thermoelastic heat conduction with a fractional perspective

Classical Fourier heat conduction predicts infinite thermal wave speed and fails to capture memory effects observed in ultrafast and microscale thermal processes. To address these challenges, this study develops a unified hierarchical thermoelastic framework based on the Modified Moore–Gibson–Thompson (MMGTn) model. The formulation systematically extends MMGT1 to arbitrary order n, enabling multi-stage damping and enhanced control over thermal wave propagation and memory depth. Structural analogies with electrical and mechanical systems are employed to provide physical insight and parameter interpretation. Furthermore, fractional time derivatives are incorporated to capture anomalous heat conduction effects. The coupled thermoelastic response of a semi-infinite strip under thermal shock is analyzed using Laplace transform techniques and numerical inversion. Comparisons with CV, GN, and fractional models show that MMGTn achieves better control of thermal wave speed, stress concentration, and memory effects. This unified framework offers a robust and interpretable tool for multiscale thermal analysis, with applications ranging from bio-thermoelastic modeling to laser treatment, RF ablation, and advanced material design.