AN INTERVAL FINITE DIFFERENCE METHOD FOR THE BIOHEAT TRANSFER PROBLEM DESCRIBED BY THE PENNES EQUATION WITH UNCERTAIN PARAMETERS
DOI:
https://doi.org/10.7494/mech.2012.31.2.77Keywords:
bioheat transfer modelling, interval finite difference method, Pennes equationAbstract
In this paper the transient bioheat transfer problem given by the one-dimensional Pennes equation with mixed boundary conditions is considered. The model assumes the heat transfer between the skin and its surroundings in the case of a natural and forced convection. For computations the interval finite difference method of Crank- -Nicolson type together with the floating-point interval arithmetic is used. In this way, uncertain geometric and thermophysical parameters can be represented in the form of intervals as well as the resultant temperature distribution over time.
Downloads
References
Jankowska M.A., 2013, The Error Term Approximation in Interval Method of Crank-Nicolson Type, Differential Equations and Dynamical Systems, 21 (1) 185-198.
Jankowska M.A., Marciniak A., An Interval Finite Difference Method for Solving the One-Dimensional Heat Conduction Equation, Lecture Notes in Computer Science (in print).
Jankowska M.A., Sypniewska-Kaminska G., Kaminski H., 2012, Evaluation of the Accuracy of the Solution to the Heat Conduction Problem with the Interval Method of Crank-Nicolson Type, Acta Mechanica et Automatica, 6(1), pp. 36-43.
Jankowska M.A., Sypniewska-Kamińska G., 2013, Interval Finite-Difference Method for Solving the One-Dimensional Heat Conduction Problem with Heat Sources, Lecture Notes in Computer Science, 7782, 473-488.
Kużelewski A., 2008, Opracowanie i implementacja algorytmu modelowania i symulacji nieprecyzyjnie zdefiniowanych zagadnień brzegowych, Ph.D. Thesis, Białystok.
Majchrzak E., Dziatkiewicz G., Paruch M., 2008, Acta of Bioengineering and Biomechanics, 10(2), pp. 29-37.
Majchrzak E., Jasiński M., 2003, Numerical estimation of burn degree of skin tissue using the sensitivity analysis methods, Acta of Bioengineering and Biomechanics, 5(1), pp. 93-108.
Majchrzak E., Mochnacki B., Dziewoński M., Jasiński M., Kałuża G., 2005, Modelowanie numeryczne przepływu biociepła, Nauka, Innowacje, Technika, 2, 9, pp. 30-38.
Marciniak A., 2009, Selected Interval Methods for Solving the Initial Value Problem, Publishing House of Poznan University of Technology, Poznan.
Marciniak A., 2012, An interval version of the Crank-Nicolson method - The first approach, Lecture Notes in Computer Science, 7133, pp. 120-126.
Moore R.E., 1966, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ. Orzechowski Z., Prywer J., Zarzycki R., 2001, Mechanika płynów w inżynierii środowiska, WNT.
Piasecka-Belkhayat A., 2011, Przedziałowa metoda elementów brzegowych w nieprecyzyjnych zadaniach nieustalonej dyfuzji ciepła, Wydawnictwo Politechniki Śląskiej, Gliwice.
Pennes H.H., 1948, Analysis of Tissue and Arterial Blood Temperature in the Resting Human Forearm, Journal of Applied Physiology, 1, pp. 93-122.
Sunaga T., 1958, Theory of interval algebra and its application to numerical analysis, Research Association of Applied Geometry (RAAG), Vol. 2, Misc. II, pp. 547-564.
Szyszka B., 2012, The Central Difference Interval Method for Solving the Wave Equation, Lecture Notes in Computer Science, 7204, pp. 523-532.
Torvi D.A., Dale J.D., 1994, A finite element model of skin subjected to a flash fire, Journal of Biomechanical Engineering, 116, pp. 250-255. Xu F., Seffen K.A., Lu T.J., 2008, Non-Fourier analysis of skin biothermomechanics, International Journal of Heat and Mass Transfer, 51, pp. 2237-2259.
Zieniuk E., 2000, Nowa koncepcja rozwiązywania rozmytych zagadnień brzegowych, Informatyka teoretyczna. Metody analizy informacji niekompletnej i rozproszonej, Politechnika Białostocka, X lat Instytutu Informatyki, Białystok, pp. 182-192.
Downloads
Published
Issue
Section
License
Remember to download, sign, scan and attach the copyright notice
This file should be uploaded as a Supplementary file (Step 4) of the submission procedure.
