Fractional two-temperature thermoelastic analysis of electromagnetic heating in skin tissue for thermal damage assessment and safety evaluation

A fractional two-temperature dual-phase-lag (TTDPL) bioheat model is developed to investigate thermoelastic heat transfer in human skin tissue subjected to electromagnetic radiation. The proposed formulation incorporates Caputo fractional derivatives, two-temperature theory, blood perfusion, temperature-dependent metabolic heat generation, and electromagnetic heating within the modified Pennes bioheat framework. To describe the coupled interactions among thermal, mechanical, and electromagnetic fields, the heat transfer equation is integrated with Maxwell’s equations and the thermoelastic equation of motion. The governing equations are transformed into a dimensionless form and solved analytically using the Laplace transform technique, while the corresponding physical-domain solutions are obtained through numerical inversion based on the Fourier series expansion method. The effects of the fractional-order parameter, phase-lag times, electromagnetic intensity, and metabolic heat source on the thermal response and tissue behavior are examined in detail. The results reveal a distinct difference between conductive and thermodynamic temperatures, highlighting the importance of the two-temperature concept in characterizing non-equilibrium heat transfer. Furthermore, the fractional-order parameter significantly influences memory-dependent heat conduction, whereas phase-lag parameters and electromagnetic loading strongly affect temperature evolution. Thermal damage analysis is also performed to identify safe and critical exposure conditions. The developed model provides a useful framework for evaluating thermal responses during electromagnetic and thermal therapeutic applications.