Accession Number:

AD0673128

Title:

VOLUME INTEGRALS OF THE PRODUCTS OF SPHERICAL HARMONICS AND THEIR APPLICATIONS TO VISCOUS DISSIPATION PHENOMENA IN FLUIDS,

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s):

Report Date:

1968-07-01

Pagination or Media Count:

29.0

Abstract:

The equations governing the conversion of kinetic energy into heat in moving viscous media are formulated as volume integrals of products of spherical harmonics. Although the formulation of the fundamental equations is classical, difficulties in the integration of certain products of generalized spherical harmonics over a sphere have permitted heretofore the treatment of only two cases. The closed form evaluation of eight fundamental types of definite integrals of the product of spherical harmonics, some of them new, or at least missing in the literature, makes possible for the first time the evaluation of these volume integrals in closed form for arbitrary order and index. Results are given for motions characterized by spheroidal symmetry and by toroidal symmetry. Author

Subject Categories:

  • Fluid Mechanics
  • Thermodynamics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE