Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties

Abstract

In this study, the fractional model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue. The model is applied to a problem of cancerous layer with arbitrary thickness and its outer surface traction free. The bounding plane of the cancerous tissue is subjected to two different types of thermal loading; a non-Gaussian laser beam and harmonic heating. The problem is solved analytically by Kirchhoff and Laplace transformation. The exact solution in Laplace’s transform domain is obtained. Numerical results for the temperature, displacement, and stress distributions are given and illustrated graphically. The effects of time-fractional parameter and materials properties on the behavior of various fields are examined.

Keywords:

• Fractional calculus
• Laplace transforms
• Pennes’ bioheat transfer
• thermo-viscoelastic theory
• variable thermal conductivity
• volume relaxation effects