Analytical study of two-dimensional thermo-mechanical responses of viscoelastic skin tissue with temperature-dependent thermal conductivity and rheological properties

Abstract

The generalized thermo-viscoelastic theory without energy dissipation is used in this work to investigate the transfer of bioheat and the mechanical heat-induced response in a human skin plane tissue with variable thermal and rheological properties. Integral transformations are used for Laplace and Fourier. In the scheme of two-dimensional equations, the exponential matrix procedure, which forms the basis of the state-space approach of modern control theory, is applied. The resulting formulation is applied to a thermal shock half-space problem. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions. Comparisons between computational measurements and Penne’s experimental verification indicate that the Green–Naghdi (II) bioheat mathematical model is an effective method for estimating the transition of bioheat to viscoelastic skin tissue. The influences of variable thermal conductivity and volume materials properties on all fields are examined.