Accession Number : AD0262453

Title :   COMMENTS ON E. PALM'S PAPER - ON THE TENDENCY TOWARDS HEXAGONAL CELLS IN STEADY CONVECTION

Corporate Author : RENSSELAER POLYTECHNIC INST TROY N Y

Personal Author(s) : SEGEL,L.A. ; STUART,J.T.

Report Date : 18 AUG 1961

Pagination or Media Count : 1

Abstract : This analysis refines the earlier work of Palm (J. Fluid Mech. 8:183-92, 1960) concerning the finite amplitude steady state of cellular convective motion attained when a horizontal layer of fluid becomes unstable as a result of being heated from below. The pair of nonlinear ordinary differential equations to which the problem was reduced by Palm (under certain conditions) are given in a corrected form, andARE THEN ANALYZED IN SOME DETAIL. Results are that, for the model considered, hexagonal convection cells may be the equilibrium state only if the variation of viscosity with temperature is sufficiently great. Under the same circumstances a two dimensional roll cell is also possible, the initial conditions det rmining which state actually occurs. The analysis enables conclusions to be drawn concerning the flow direction at the cell centre, and also shows that a disturbance of sufficient magnitude may grow even though the situation is a stable one by linearized theory. Comparison with experiment is discussed. (Author)

Descriptors :   *CONVECTION, *PERTURBATION THEORY, MATHEMATICAL ANALYSIS, NONLINEAR DIFFERENTIAL EQUATIONS, PERIODIC VARIATIONS, STABILITY, TEMPERATURE, THEORY, THERMAL CONDUCTIVITY, VISCOSITY

Distribution Statement : APPROVED FOR PUBLIC RELEASE