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 : AUG 1972

Pagination or Media Count : 25

Abstract : A number of problems involving convection-like phenomena give rise to an equation of the form y double prime + (alpha)y' - 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 + (alpha)y' - ay + (y cubed) = 0 which provides saturation of the dependent variable when y = the square root of (a/b). 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