Predicting Thermomechanical Responses and Informing Control in Two‐Dimensional Skin Tissue During Ramp‐Type Heating Using a Fractional‐Order Dual‐Phase‐Lag Bioheat Model

ABSTRACT

Thermal therapies, such as hyperthermia, require accurate prediction of temperature and stress distributions in skin tissue to ensure effective treatment while minimizing collateral damage. However, classical bioheat models based on Fourier's law fail to account for memory effects and finite heat propagation speeds inherent in biological tissues. To address this gap, this study presents a fractional‐order dual‐phase‐lag (DPL) bioheat model for predicting the thermomechanical response of two‐dimensional (2D) skin tissue subjected to ramp‐type heating. The governing equations couple non‐Fourier heat transfer with linear thermoelasticity and are solved analytically using Laplace and Fourier transforms combined with displacement potential functions. Numerical inversion is performed using the Stehfest algorithm and Gaussian quadrature. The results demonstrate that fractional order parameters significantly influence temperature decay, stress magnitudes, and displacement patterns. The Atangana–Baleanu Caputo derivative (ABC) produces smoother thermal responses compared to the Caputo (C) derivative, particularly for long‐term processes. The model provides practical guidelines for optimizing hyperthermia protocols, planning cryosurgery, laser therapy, and assessing burn injuries by enabling more realistic predictions of thermal damage and stress‐induced tissue injury. These predictive insights inform clinical control decisions by defining safe and effective operating windows, such as appropriate ramp rates to balance therapeutic temperature delivery with mechanical safety thresholds.