Accession Number:

AD0754228

Title:

On an Equation Related to Nonlinear Saturation of Convection Phenomena.

Descriptive Note:

Technical note,

Corporate Author:

MARYLAND UNIV COLLEGE PARK INST FOR FLUID DYNAMICS AND APPLIED MATHEMATICS

Personal Author(s):

• Cap,Ferdinand
• Lashinsky,Herbert

Report Date:

1972-08-01

Pagination or Media Count:

25.0

Abstract:

A number of problems involving convection-like phenomena give rise to an equation of the form y double prime alphay - ay 0 when the problem is treated in the linear approximation. It is proposed that the description of nonlinear saturation of the convection process requires the introduction of a phenomenological cubic term with a positive coefficient to yield an equation of the form y double prime alphay - ay y cubed 0 which provides saturation of the dependent variable when y the square root of ab. The significance of this term in various physical problems is discussed. In the mathematical analysis of the equation the parameter ranges for oscillatory and non-oscillatory solutions are discussed and related to the pertinent physical problems. Author

Descriptors:

• (*CONVECTION(HEAT TRANSFER)
• *NONLINEAR DIFFERENTIAL EQUATIONS)
• FLUID FLOW
• OSCILLATION
• PLASMAS(PHYSICS)
• PARTIAL DIFFERENTIAL EQUATIONS
• NUMERICAL ANALYSIS
• NUMERICAL INTEGRATION

Subject Categories:

• Numerical Mathematics
• Fluid Mechanics
• Thermodynamics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE