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A hollow cylinder is heated on both surfaces with known fluxes which are partly dissipated by conduction into the cylinder, partly lost to the exterior media, and partly stored in boundary layers with only heat capacity. This description of each boundary condition is known as a Type 5 condition and in the current literature is labeled R55. The initial temperature of the cylinder is zero (T0).
The motivation for considering the R55T0 case is to solve several interesting sub-cases in one formula. By specializing parameters, we can write the solutions for 15 additional sub-cases by removing the heat loss terms and the heat capacity terms from each boundary one at a time. This is accomplished by setting coefficient parameters to zero. The numbering system is shorthand for lengthy prose when talking about a variety of boundary conditions and geometries and is valuable in enumerating the sub-cases. This numbering system can be found in http://Exact.unl.edu .
This work was supported by
NSF Award 1250625, Exact Analytical Conduction Toolbox,
administered by the University of Nebraska,
Kevin Cole, Director
- Cole, KD, Beck, JV, et. al. (2010), Heat Conduction Using Green's Functions, 2nd Ed., CRC Press Boca Raton, 643pp
- Amos, DE, (2014) Green's Function for Heat Conduction in a Hollow Cylinder R55 with Type 5 Boundary Conditions, http://nanohub.org/resources
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