Analytical solutions of the temperature increment in skin tissues caused by moving heating sources

Aatef D. Hobiny and Ibrahim A. Abbas

Abstract

In this paper, mathematical bioheat transfer model in skin tissues in the bounded domain due to moving heat source are considered. The thermal damage to the tissues is totally evaluated by the denatured protein ranges by the Arrhenius formulation. The temporal complete solutions in Laplace time domain obtained by using the inversion scheme of the Laplace transform, to obtain the general solution (exact solution) for the increment of temperature. The numerical result of temperature and the thermal injurie are graphically demonstrated. In conclusions, parametric analysis are devoted to the identifications of appropriates procedures for choosing serious designs variables to reach the effectives thermal in hyperthermias treatments.

Key Words

bioheat transfer without energy dissipations; laplace transforms; skin tissues; thermal damages

Address

Aatef D. Hobiny: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia Ibrahim A. Abbas: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

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