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Mathematical modeling of first to third degree burn injury by sinusoidal heating source

Rai K. N., Srivastava V.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 2

489-500

The object of this study is to provide a generalized mathematical model of burn injury due to a sinusoidal heat source at the skin surface. An application of double Fourier cosine transform is applied to convert this problem into a boundary value problem of ordinary differential equations. The solution thus obtained is transferred into a standard form with the help of the inverse discrete Fourier cosine transform. Finally, the numerical results obtained for the distribution of temperature in different layers of the skin during burn injury are discussed and displayed graphically.

Numerical solution of bioheat transfer equation by means of the dual reciprocity BEM

Drozdek J., Majchrzak E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

47-56

Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. It results from the presence of internal heat sources in the biological tissue (metabolic and perfusion sources). In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As example, the problem of temperature field computations in heating biological tissue domain is solved.

Application of the multiple reciprocity BEM for numerical solution of bioheat transfer equation

Majchrzak E., Drozdek J., Kałuża G.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2002

Vol. 1, nr 1

113--124

Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As the example, the problem of the pair of vessels (artery and vein) surrounded by the tissue is analyzed, and the temperature field in the tissue sub-domain is found.