THE MATHEMATICAL MODEL OF BIOLOGICAL TISSUE HEATING UNDER LASER RADIATION
DOI:
https://doi.org/10.15587/1729-4061.2012.4558Keywords:
temperature distribution, laser radiation, semitransparent environment.Abstract
There is great number of mathematical models of thermal action of laser radiation on a biological tissue. However, the semitransparent borders in the connections between various layers of biological tissue were given little attention. This article represents for the first time the calculation of the temperature distribution to the biological tissue with semitransparent borders. In addition, this model takes into consideration multiple scattering and absorption of laser radiation by biological tissues. The article represents the model that imitates the thermal action of laser radiation on biological tissues. One should pay attention that the model takes into consideration blood perfusion that is considered as a source of heat transfer. The model appropriateness, where the results of the numerical and analytical work are compared, is submitted for the discussion.References
- Зигель Р. Теплообмен излучением / Р. Зигель, Дж. Хауэлл ; пер. с англ. ; под ред. Б. А. Хрусталева. — М. : Мир, 1975. — 934 с.
- Оцисик М. Н. Сложный теплообмен / М. Н. Оцисик ; пер. с англ. ; под ред. Н. А. Анфимова. — М. : Мир, 1976. — 616 с.
- Cергеев О. А. Теплофизические свойства полупрозрачных материалов / О. А. Cергеев, А. А. Мень. — М. : Стандартов, 1977. — 288 с.
- Chai J. C. Finite volume radiative heat transfer procedure for irregular geometries / J. C. Chai, H. S. Lee, S. V. Patankar // AIAA J. Themophys. Heat Transfer. — 1995. — Vol. 9, No 3. — P. 410—415.
- Murthy J. Y. Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes / J. Y. Murthy, S. R. Mathur // J. Thermophys. Heat Transfer. — 1998. — Vol. 12. — P. 313—321.
- Murthy J. Y. A finite-volume scheme for radiative heat transfer in semitransparent media / J. Y. Murthy, S. R. Mathur // Numerical Heat Transfer. — 2000. — Part B, 37. — P. 25—43.
- Патанкар С. Численные методы решения задач теплообмена и динамики жидкости / Патанкар С. ; пер. с англ. В. Д. Виленского. — М. : Энергоатомиздат, 1984. — 153 с.
- ANSYS, Inc. ANSYS FLUENT User’s Guide Documetation.
- Калиткин Н. Н. Численные методы : учеб. пособие / Н. Н. Калиткин ; под ред. А. А. Самарского. — М. : Наука, 1978. — 512 с.
- Справочник по математике для научных работников и инженеров / Г. Корн, Т. Корн. — М. : Наука, 1984. — 831 с.
- Holmes D. G. Solution of the 2D navier-stokes equations on unstructured adaptive grids / D. G. Holmes, S. D. Connell // AIAA 9th Computational Fluid Dynamics Conference, 1989. : AIAA Paper. — P. 83—169.
- Rauch R.D. Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computations / R. D. Rauch, J. T. Batira, N. T. Yang // Technical Report AIAA-91-1106, 1991.— 172 р.
- Siegel R. Effect of refractive index and diffuse or specular boundaries on a radiating isothermal layer / R. Siegel, C. M. Spuckler // Journal of Heat Transfer. — 1994. — Vol. 116. — P. 787—790.
- Лыков А.В. Теория теплопроводности // Издательство: Высшая школа. г. 1967. с.600.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Олександр Дмитрович Мамута, Марина Сергіївна Рибалко, Леонід Федорович Головко
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.