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Solution of the heat transfer problem in tissues during hyperthermia by finite difference–decomposition method

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
219
Issue
12
Identifiers
DOI: 10.1016/j.amc.2013.01.020
Keywords
  • Finite Difference Method
  • Adomian Decomposition Method
  • Heat Transfer
  • Nonlinear Partial Differential Equation
  • Hyperthermia
Disciplines
  • Biology
  • Mathematics
  • Medicine
  • Physics

Abstract

Abstract In this article, a mathematical model describing the process of heat transfer in biological tissues with blood perfusion having different values under different temperature range for various coordinate system and different boundary conditions during thermal therapy by electromagnetic radiation is studied. Using the method of finite differences, the boundary value problem governing this process has been converted to an initial value problem of ordinary differential equations, which is solved by the Adomian decomposition method. The effects of blood perfusion rate intended for a different temperature range of temperature at target point during thermal therapy for different boundary conditions are discussed in detail. And we have also checked our results with the result of exact solutions for one case and it shows a good agreement.

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