Abstract
In this paper we have analytically characterizes the temperature distribution in a living tissue for more effective thermal treatment of tumor cells based on the modified Pennes bioheat transfer equation subjected to constant, oscillatory, cosine heat flux as well as sinusoidally heating criteria. A thorough parametric study has been made and determined optimal values of the parameters that lead to reach the temperature above therapeutic value \(43^\circ \mathrm{C}\). We assumed that heat mainly propagates in the direction perpendicular to the skin surface. The analytical solutions of the thermal wave model of one-dimensional bioheat transfer equation with different heating conditions are obtained by using Laplace transform technique. The effects of thermal relaxation time and heat flux on the skin-surface, the blood perfusion rate, thermal conductivity and frequency of heating on temperature distribution are analyzed qualitatively as well as quantitatively. The study shows that the temperature distribution has an enhancing effect on the thermal relaxation time and heat flux at the skin-surface. Further, the blood perfusion rate has reducing effect on the temperature of the living tissues.
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The authors wish to convey their sincere thanks to all the esteemed reviewers for their comments and suggestions based upon which the present version of the manuscript has been revised. One of the authors (G. C. Shit) is thankful to the Institute of Mathematical Sciences, Chennai for providing sufficient research facility to carry out this investigation during his stay at IMSc., Chennai as Visiting Associate.
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Shit, G.C., Bera, A. Temperature Response in a Living Tissue with Different Heating Source at the Skin Surface Under Relaxation Time. Int. J. Appl. Comput. Math 3, 381–394 (2017). https://doi.org/10.1007/s40819-015-0120-0
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DOI: https://doi.org/10.1007/s40819-015-0120-0