Thermoelastic response in viscoelastic skin tissue within the context of memory-dependent derivative using modified Green-Lindsay and dual phase lag theory

The viscoelasticity of biological tissue is an inherent property often utilized in cancer detection. Recently, it has been observed that the influence of memory-dependent derivative (MDD) provides a more accurate description of viscoelastic materials, leading to more effective thermal therapeutic techniques. This article aims to implement the viscoelastic property on Pennes’ bio-heat transfer law under the light of the Modified Green-Lindsay (MGL) and dual phase lag (DPL) models based on MDD. A one-dimensional thin skin tissue is considered, with the bounding surface of the skin tissue subjected to three different types of thermal loading. The system of partial differential equations in the space-time domain is transformed to the state-space domain with the help of the Laplace transformation, and its inversion is evaluated numerically. Numerical outcomes and graphical interpretations examine the influence of MDD, various thermal parameters (thermal shock time parameter υ, ramp-type heat parameter t0, and sinusoidal heat parameter ν), time delay parameter ω and the time parameter t on all field quantities (temperature θ, stress σ, and displacement u) for both theories.