
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 convectionlike 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 nonoscillatory 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