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Refined Green–Lindsay Model for the Response of Skin Tissue under a Ramp-Type Heating

Author

Listed:
  • Ashraf M. Zenkour

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt)

  • Tareq Saeed

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

  • Khadijah M. Alnefaie

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science and Arts in Almakhwah, Albaha University, Almakhwah 65311, Saudi Arabia)

Abstract

Based on Green–Lindsay generalized thermoelasticity theory, this paper presents a new refined higher-order time-derivative thermoelasticity model. Thinner one-dimensional skin tissue is considered when its inner surface is free of traction and does not show any temperature increase. The skin tissue’s bounding surface has been heated by ramp-type heating. The classical thermoelastic theories are obtained from the present general formula. The governing equations of the present model are obtained. To move the system into a space state, the Laplace transform is used. The inverse of the Laplace transform is also used with Tzuo’s method to solve the problem. As a result, the field quantities are obtained numerically, and the results of the current model are graphically represented with a comparison to two different theories of thermoelasticity. The effects of various parameters on thermomechanical waves through the skin tissue are analyzed. The theory notes a vibrational behavior in heat transfer and a different effect on the parameters discussed in this article.

Suggested Citation

  • Ashraf M. Zenkour & Tareq Saeed & Khadijah M. Alnefaie, 2023. "Refined Green–Lindsay Model for the Response of Skin Tissue under a Ramp-Type Heating," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1437-:d:1098802
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