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Mathematical Problems in Engineering
Volume 2018, Article ID 8781950, 6 pages
Research Article

The Skin Tissue of the Human Head Subjected to Thermal Diffusion

Mathematics Department, College of Science and Arts-Sharoura, Najran University, Najran, Saudi Arabia

Correspondence should be addressed to Eman A. N. Al-Lehaibi; moc.liamg@ibiahellanamerd

Received 26 June 2017; Revised 14 November 2017; Accepted 8 January 2018; Published 31 January 2018

Academic Editor: Elena Benvenuti

Copyright © 2018 Eman A. N. Al-Lehaibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a problem of skin tissue of the human head subjected to thermal diffusion with relaxation time. The bounding surface of the tissue of the human head is subjected to a thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used and the results are obtained numerically using a numerical method for the inversion of the Laplace transform based on Tzou method. The temperature distribution and the concentration distribution are obtained and represented in figures. According to the results, the values of the time and the distance have significant effects on the temperature increment and the concentration. The values of the temperature increment and the concentration increase when the time increases and decrease when the distance increases.