On Some Two-Dimensional Problems in Heat Conduction for Irregular Domains with Regular or Mixed Boundary Conditions,

Abstract

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).

Document Details

Document Type
Technical Report
Publication Date
Sep 19, 1951
Accession Number
AD0895217

Entities

People

  • Arnold N. Lowan

Organizations

  • Naval Ordnance Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Equations
  • Infinite Series
  • Mathematical Analysis
  • Mathematics
  • Sequences
  • Sequences (Mathematics)
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Combustion and Flow Dynamics.
  • Operations Research
  • Plasma Physics / Magnetohydrodynamics