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Fractional order of refined Lord–Shulman model for a 1D thermoelastic response of skin tissue due to ramp-type heating

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Abstract

This manuscript introduces a novel mathematical formulation employing fractional-order principles to analyze the response of skin tissue exposed to ramp-type heating within the framework of the refined Lord–Shulman generalized thermoelasticity model. The classical, simple Lord–Shulman, and refined Lord–Shulman models are each examined. The governing equations for these three models are derived, and a general solution for the initial and boundary condition problem is obtained using the Laplace transform approach and its inverse. Numerical results are illustrated through figures, providing a comparative analysis across various theories and fractional-order values to elucidate the impact on temperature, displacement, and dilatation distributions. The numerical and graphical exploration of the influence of ramp-type heat on temperature, displacement, and dilatation distributions is conducted, considering different theoretical frameworks. The reduction in the conductivity caused by the fractional parameter and its ensuing effects on temperature, displacement, and stress are determined.

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Authors and Affiliations

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

    A. M. Zenkour & A. A. Al-Raezah

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

    A. M. Zenkour

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

    T. Saeed

  4. Department of Mathematics, Faculty of Science, King Khalid University, 9004, Abha, Saudi Arabia

    A. A. Al-Raezah

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  1. A. M. Zenkour
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Contributions

AMZ, TS and AA contributed to conceptualization; AMZ and AA involved in methodology; TS and AA provided software; AA involved in validation; AMZ, TS and AA involved in formal analysis; AMZ involved in investigation; AA involved in writing—original draft preparation; AMZ, TS and AA involved in writing—review and editing; AA involved in visualization; AMZ involved in supervision; AMZ provided project administration. All authors have read and agreed to the published version of the manuscript.

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Correspondence to A. M. Zenkour.

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Zenkour, A.M., Saeed, T. & Al-Raezah, A.A. Fractional order of refined Lord–Shulman model for a 1D thermoelastic response of skin tissue due to ramp-type heating. Arch Appl Mech 94, 989–1003 (2024). https://doi.org/10.1007/s00419-024-02561-1

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