Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

Abstract

this work introduces a mathematical model of thermoelastic skin tissue in the context of the dualphase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.

The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

“…The current results agree with the results of Youssef and Alghamdi 28,37 . Moreover, the current resluts agree with the result in figuer 6 of Kundu and Dewanjee 29 www.nature.com/scientificreports/ Figure 16 show that the current result of the absolute dynamical and conductive temperature are close to the values of the absolute temperature in Kundu and Dewanjee 29 .…”

“…Hence, the initial conditions (19) give the following system of algebraic equations: and For the case of � n > 0 Thus, when t = 0 we have Then, Eqs. (28) and 29introduce the following system and when n = 0 we have Hence, the system in Eqs. (31) and (32) will be reduced to the following system and The equations in (33) and (34) lead to the following two systems of algebraic equations and By solving the above two systems, we get www.nature.com/scientificreports/ Hence, the final solution of the heat conduction temperature increment in this case is: www.nature.com/scientificreports/ By using Eqs.…”

“…Shih et al investigated the coupled effects of the pulsatile blood flow and thermal relaxation time in living tissues during thermal treatments 27 . Youssef and Alghamdi 28 have solved a one-dimensional application of thermoelastic dual-phase-lag skin tissue under specific thermal loading. Kundu and Dewanjee 29 introduced a new method for non-Fourier thermal response in a single layer skin tissue.…”

“…The bioheat transmitting model was developed to measure the time-dependent temperature change as a heat reaction due to the usage of either heat source or thermal heating. The first model of biological tissues was found out by Pennes based on Fourier's law of heat conduction as follows 28 , 36 , 37 : where and are the density, specific heat, and thermal conductivity of the tissue, respectively. , and denote the specific heat of the blood, blood perfusion rate, blood density, and blood temperature, respectively.…”

“…Ventott and Cattaneo modified the classical Fourier thermal drive law by postulating the concept of finite thermal wave propagation speed and taking the following hyperbolic form of the thermal wave 28 , 36 , 37 : where is a material property and is called the relaxation time parameter, and is the thermal diffusivity while is the speed of the thermal wave inside the medium.…”