On Some Two-Dimensional Problems in Heat Conduction for Irregular Domains with Regular or Mixed Boundary Conditions,
NAVAL ORDNANCE LAB WHITE OAK MD
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The report deals with the problem of heat conduction in an infinite cylinder of arbitrary cross section with either regular or mixed boundary conditions. The phrase regular boundary conditions implies that the entire lateral surface is kept at 0 C, is impervious to heat, or radiates into a medium at 0 C while the phrase mixed boundary conditions implies that the given conditions are different over two portions of the boundary. No classical solution of the problems treated here are known. The final solutions are expressed as infinite series whose terms do not individually satisfy either the differential equation of heat conduction or the boundary conditions. The derivation of these infinite series is based on the expansion of the components of arbitrary Hilbert vectors in terms of the components of an infinite sequence of suitably orthornormalized Hilbert vectors. See also AD-895 221.
- Theoretical Mathematics