Thermoviscoelastic response of skin tissue via fractional Pennes bioheat and fractional viscoelasticity

Abstract

In this paper, the thermoviscoelastic response of skin tissue, as a typical class of viscoelastic biological tissue, subject to thermal shock is studied based on the fractional Kelvin-Voigt model and fractional Pennes bioheat conduction. A time-fractional biothermoviscoelastic governing equation is derived and initial-boundary value conditions are given for monolayer skin tissue of finite thickness. The temperature change and thermal stress of viscoelastic skin tissue are obtained by the Laplace transform and its inversion using matlab software. The influences of viscosity coefficient, relaxation times, fractional-order viscosity/heat parameter, and blood perfusion rate of skin tissue on the temperature distribution and the elastic displacement are analyzed. The numerical results show that fractional-order viscosity does not affect temperature, whereas fractional-order heat flow does. Moreover, fractional-order heat flow affects the sensitivity of blood perfusion rate to the thermodynamic response.