Boundary dependent sensitivity of thermo viscoelastic Rayleigh waves in skin tissue using a fractional nonlocal TPL framework

• First global sensitivity analysis of Rayleigh waves in skin tissue under contrasting thermal boundaries. • Thermal boundaries dramatically shift parameter dominance: thermal non–locality controls attenuation under cooling, while phase lags dominate under insulation. • Fractional–order viscoelasticity strongly modulates wave penetration depth and heat loss, especially in insulated therapeutic scenarios. • Practical factor–fixing guidelines reduce model complexity by up to 89% without sacrificing predictive accuracy. This work conducts a global sensitivity analysis of Rayleigh wave propagation in viscoelastic skin with a three-phase-lag bioheat model, extended with non-local elasticity and fractional viscoelasticity to account for memory and finite speed of heat, for two boundary value problems: isothermal (cooling skin) and thermally insulated (dressed wounds). Six parameters are investigated using Sobol variance-based sensitivity analysis: elastic non-locality ( ∊ 1 ) , thermal non-locality ( ∊ 2 ) , fractional order ( α ) , and phase-lag times τ q , τ v , τ T , for phase velocity, attenuation, penetration depth, and heat loss. The results reveal sensitivity to boundary conditions: for isothermal, ∊ 2 is dominant ( ≈ 61 % attenuation, ≈ 99 % heat loss), while for insulated, phase-lag times are dominant, with τ v controlling > 70 % of penetration depth variability. The fractional order α is important for both penetration depth and heat loss in both boundary conditions. These results provide useful guidelines for model reduction with acceptable loss of accuracy and have immediate applications in Rayleigh wave elastography and thermal therapies (laser surgery and cryotherapy).