Analyzing the Thermoelastic Responses of Biological Tissue Exposed to Thermal Shock Utilizing a Three-Phase Lag Theory

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

3 Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

4 Department of Mathematics, College of Arts and Science in Rijal Alma and the Applied branch, King Khalid University, Abha 61421, Saudi Arabia


This article presents a mathematical analysis of thermoelastic skin tissue using an improved thermal conduction theory known as the refined three-phase-lag (TPL) theory. By accounting for the effects of multiple time derivatives, this advanced model provides a more accurate representation of how skin tissue behaves under different temperature conditions. The thin skin tissue is considered to have mechanically clamped surfaces, which are assumed to be one-dimensional. Furthermore, the skin tissue experiences a thermal shock load on its outer surface while maintaining a constant temperature on its inner surface. The proposed model has led to the derivation of certain generalized thermoelasticity theories in previous studies. The Laplace transform and its associated numerical inversion method are employed to calculate the distributions of temperature, displacement, dilatation, and stress in the system. The obtained outcomes are explicitly depicted to analyze the significant influences on the distributions of the field variables. These findings shed light on the behavior of skin tissue when subjected to a particular temperature distribution at the boundary condition, enhancing our knowledge in this area.


Main Subjects

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Volume 55, Issue 2
April 2024
Pages 144-164
  • Receive Date: 07 October 2023
  • Revise Date: 09 January 2024
  • Accept Date: 07 October 2023