CONVECTIVE INSTABILITIES IN FULLY DEVELOPED FLOWS

Abstract

This paper considers the possibility of inducing a convective secondary flow in the fully developed channel flow of a quasi-incompressible (Boussinesq) fluid. Instabilities of this type can only occur when the temperature gradient in the direction of the body force exceeds a certain critical value. This temperature gradient is proportional to the Rayleigh number of the fluid. For channels of arbitrary cross section, the critical Rayleigh number is found to be R sub c > or = 1360 (h/d) to the 4th power where h is the arbitrary channel's maximum dimension in the body force direction and d is the diameter of an equal area circular channel. For two special geometries it is possible to improve the above lower bound estimate to the critical Rayleigh number. In a circular channel R sub c > or = 3450 and in a square channel R sub c > or = 2480.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1966
Accession Number
AD0628098

Entities

People

  • Michael B. Sherman

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Bessel Functions
  • Channel Flow
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Flow
  • Heat Capacity
  • Incompressible Flow
  • Pressure Distribution
  • Scientific Research
  • Secondary Flow
  • Steady Flow
  • Temperature Gradients
  • Thermal Conductivity
  • Thermal Diffusivity
  • Variational Principles

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Mechanics and Fluid Dynamics.
  • Plasma Physics / Magnetohydrodynamics