Modeling the conduction of heat in living tissue requires the consideration of sudden spatial discontinuities in property values as well as the presence of the body's circulatory system. This paper presents a description of the separation of variables method that results in a remarkably simple solution of transient heat conduction in a perfuse composite slab for which at least one of the layers experiences a zero perfusion rate. The method uses the natural analytic approach and formats the description so that the constants of integration of each composite layer are expressed in terms of those of the previous layer's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. The method is presented in the context of the Pennes bioheat equation for which the solution is developed for a system composed of any number of N layers with arbitrary initial conditions.
One-Dimensional Transient Heat Conduction in Composite Living Perfuse Tissue
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 1, 2011; final manuscript received October 27, 2012; published online June 21, 2013. Assoc. Editor: Franz-Josef Kahlen.
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Becker, S. M. (June 21, 2013). "One-Dimensional Transient Heat Conduction in Composite Living Perfuse Tissue." ASME. J. Heat Transfer. July 2013; 135(7): 071002. https://doi.org/10.1115/1.4024063
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