On the Problem of Heat Conduction in the Finite Wedge of an Angle, in the Case of Radiation at the Bounding Planes,

This paper deals with the problem of heat conduction in the wedge of an angle bounded by a circular cylinder when the bounding planes radiate into a medium at 0 C while the cylindrical surface is kept at 0 C. No classical solution of this problem exists. The final solution derived here is expressed as an infinite series whose terms do not individually satisfy the differential equation of heat conduction or the prescribed boundary conditions. The method of solution 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-895 217.