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A slab is heated on both faces with known fluxes which are partly dissipated by conduction into the slab, partly lost to the exterior media, and partly stored in a boundary layer with only heat capacity. This description of each boundary condition is known as a Type 5 condition and in the current literature is labeled X55. The initial temperature of the slab is zero (T0).
The motivation for considering the X55T0 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 Slab X55 with Type 5 Boundary Conditions, http://nanohub.org/resources