Refined Lord-Shulman Theory for 1D Response of Skin Tissue under Ramp-Type Heat

Abstract

In this article, we present a mathematical model of thermoelastic skin tissue based on a refined Lord-Shulman heat conduction theory. A small thickness of skin tissue is considered to be one-dimensional with mechanical clamped surfaces. In addition, the skin tissue's outer surface is subjected to ramp-type heating while its inner surface is adiabatic. A simple Lord-Shulman theory, as well as the classical coupled thermoelasticity, are also applied in this article. Laplace transform techniques and their inversions are calculated to return to the time domain. Numerical outcomes are represented graphically to discuss the significant impacts on the temperature, dilatation, displacement, and stress distributions. Such results provide a more comprehensive and better insight for understanding the behavior of skin tissue during the temperature distribution of a specific boundary condition.

Keywords: bio-thermoelasticity; ramp-type heating; refined L–S model; skin tissue.

Figure 1

The model of skin tissue with boundary conditions.

Figure 2

Distributions of temperature ($\theta$) through the skin tissue using various theories.

Figure 3

Distributions of displacement ($u$) through the skin tissue using various theories.

Figure 4

Distributions of dilatation ($e$) through the skin tissue using various theories.

Figure 5

Distributions of stress ($\sigma$) through the skin tissue using various theories.

Figure 6

Distributions of temperature ($\theta$) through the skin tissue according to various values of the ramp-type heating parameter.

Figure 7

Distributions of displacement ($u$) through the skin tissue according to various values of the ramp-type heating parameter.

Figure 8

Distributions of dilatation ($e$) through the skin tissue according to various values of the ramp-type heating parameter.

Figure 9

Distributions of temperature ($\theta$) through the skin tissue according to various values of the relaxation time: (a) L–S (simple) and (b) L–S (refined).

Figure 10

Distributions of displacement ($u$) through the skin tissue according to various values of the relaxation time: (a) L–S (simple) and (b) L–S (refined).

Figure 11

Distributions of dilatation ($e$) through the skin tissue according to various values of the relaxation time: (a) L–S (simple) and (b) L–S (refined).

Figure 12

3D distributions of temperature ($\theta$) versus time and across the skin tissue according to various theories.