Memory‐Dependent Moore–Gibson–Thompson Thermoelasticity for Thermal Damage Prediction in Laser‐Irradiated Hollow Spherical Skin Tissue

Accurate prediction of thermal injury in laser‐irradiated skin requires bioheat models that capture finite‐speed thermal propagation and the history‐dependent behavior of living tissue, features not represented in the classical Pennes equation, which assumes instantaneous heat conduction. Although non‐Fourier and fractional‐order models partially address these limitations, fractional approaches often involve non‐unique operators, ambiguous initial conditions, and considerable computational complexity. This study presents a generalized thermoelastic bioheat framework that incorporates a memory‐dependent derivative (MDD) within the Moore–Gibson–Thompson/Green–Naghdi Type III theory. The novelty lies in embedding a finite‐window MDD, defined through an arbitrary kernel over a controllable delay interval and formulated solely with integer‐order operators, into a relaxation‐based thermoelastic model. This formulation enables simultaneous representation of thermal memory, second‐sound effects, and thermo‐mechanical coupling in a transparent and computationally efficient manner. The model is applied to a thick‐walled spherical segment of perfused skin subjected to a time‐harmonic boundary temperature and a damped oscillatory laser heat source, with blood perfusion and metabolic heat generation explicitly included. The governing equations are non‐dimensionalized, solved analytically in the Laplace domain, and inverted using the Honig–Hirdes Fourier‐series technique. Thermal damage is quantified through the Arrhenius denaturation integral, and a parametric study evaluates the influence of relaxation time, perfusion rate, memory delay, and kernel structure. Results indicate that memory and relaxation mechanisms significantly reduce predicted temperature, displacement, and stress, providing a flexible and physically consistent tool for optimizing laser‐based thermal therapies.