Non-parallel plane Rayleigh Benard convection in cylindrical geometry

A. Golbabai

ArticleOriginal scientific text

Title

Non-parallel plane Rayleigh Benard convection in cylindrical geometry

Authors ¹

Affiliations

Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

Abstract

This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form

z = ε^{2} g (s)

, s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near the center.

Keywords

ENG

inner solution, perturbed wall

S. N. Brown and K. Stewartson, On finite amplitude Benard convection in a cylindrical container, Proc. Roy. Soc. London Ser. A 360 (1978), 455-469.
S. Chandrasekhar, Hydrodynamics and Hydromagnetic Stability Theory, Oxford University Press, London, 1961.
P. G. Daniels, Finite amplitude two-dimensional convection in a finite rotating system, Proc. Roy. Soc. London Ser. A 363 (1978), 195-215.
P. G. Daniels, The effect of centrifugal acceleration on axisymmetric convection in a shallow rotating cylinder or annulus, J. Fluid Mech. 99 (1980), 65-84.
P. M. Eagles, A Benard convection problem with a perturbed lower wall, Proc. Roy. Soc. London Ser. A 371 (1980), 359-379.
A. Golbabai, Finite amplitude axisymmetric convection between rigid rotating planes, J. Comput. Appl. Math. 16 (1986), 355-369.
Lord Rayleigh, On convection currents in a horizontal layer of fluid when the higher temperature is on the under side, Phil. Mag. 32 (1916), 529-546.

Title

Non-parallel plane Rayleigh Benard convection in cylindrical geometry

Affiliations

Abstract

Keywords

Bibliography