2026/08/01 by Mofareh Alhazmi
Engineering · Mathematics · #Bioheat transfer #Displacement (psychology) #Fractional Differential Equations Solutions #Gaussian #Heat equation #Heat transfer #Laplace transform #Numerical methods in engineering #Temperature control #Thermal #Thermoelastic and Magnetoelastic Phenomena
paper · doi:10.1002/zamm.70547
crossref issued 2026/08/01 · crossref published 2026/08/01 · crossref published-print 2026/08/01 · openalex publication_date 2026/08/01 · crossref published-online 2026/08/03 · crossref created 2026/08/03 · crossref deposited 2026/08/03 · crossref indexed 2026/08/03 · openalex created_date 2026/08/04 · openalex updated_date 2026/08/05
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.