Document Type : Research Paper
Authors
^{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, Faculty of Science, King Khalid University, Abha 9004, Saudi Arabia.
Abstract
This paper presents a new mathematical perfect of fractional order to deal with the response of skin tissue subjected to ramp-type heating based on the refined Lord–Shulman generalized thermoelasticity model. Three different models; the classical, the simple Lord–Shulman as well as the refined Lord–Shulman will be discussed. The governing equivalences of the present three models are attained. The general solution for the initial and boundary condition problem is found by employing the Laplace transform approach and its inverse. Numerical results are represented in figures with a comparison to the different theories with different values of fractional order to discuss the impact of the fractional order on temperature, displacement, and dilatation distributions. The effect of ramp-type heat is studied numerically and graphically on distributions of temperature, displacement, and dilatation according to different theories.
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