APPROXIMATE SOLUTION OF BOUNDARY LAYER HEAT TRANSFER EIGENVALUE PROBLEMS WITH APPLICATIONS

Abstract

Fox and Libby have developed perturbation solutions to the momentum and energy equations of laminar boundary layer theory. In their investigations, Fox and Libby formulated three eigenvalue problems: (1) For the perturbation of the momentum equation caused by initial values differing from the Blasius profile; (2) for the initial value energy problem with constant wall enthalpy; (3) for the initial value energy problem with zero heat transfer. The purpose of the present paper is three-fold: (1) To extend the approximate eigenvalue results to include the approximate eigenfunctions and norms, and investigate the convergence of some solutions obtained by Fox and Libby, using these eigenvalues and norms. (2) To apply the results of a WKB approximation to obtain another approximate formula for the eigenvalues which is extremely accurate indeed, and should enable numerical calculation of the eigenfunctions and norms with little difficulty in a minimum of computer time. (3) To discuss the insulated wall problem of Fox and Libby further, comparing the eigenfunction series solution with several other approximate solutions, and with a new exact finite difference solution.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1970
Accession Number
AD0700046

Entities

People

  • Nelson H. Kemp

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Boundaries
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Fluid Mechanics
  • Heat Transfer
  • Integrals
  • Laminar Boundary Layer
  • Mechanics
  • Partial Differential Equations
  • Prandtl Number
  • Standards

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  • Mathematics

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  • Calculus or Mathematical Analysis
  • Fluid Mechanics and Fluid Dynamics.

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  • Microelectronics