# Non-parallel plane Rayleigh Benard convection in cylindrical geometry

Applicationes Mathematicae (1995)

- Volume: 23, Issue: 1, page 25-36
- ISSN: 1233-7234

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topGolbabai, A.. "Non-parallel plane Rayleigh Benard convection in cylindrical geometry." Applicationes Mathematicae 23.1 (1995): 25-36. <http://eudml.org/doc/219114>.

@article{Golbabai1995,

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.},

author = {Golbabai, A.},

journal = {Applicationes Mathematicae},

keywords = {inner solution; perturbed wall; boundary conditions; linear amplitude equation},

language = {eng},

number = {1},

pages = {25-36},

title = {Non-parallel plane Rayleigh Benard convection in cylindrical geometry},

url = {http://eudml.org/doc/219114},

volume = {23},

year = {1995},

}

TY - JOUR

AU - Golbabai, A.

TI - Non-parallel plane Rayleigh Benard convection in cylindrical geometry

JO - Applicationes Mathematicae

PY - 1995

VL - 23

IS - 1

SP - 25

EP - 36

AB - 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.

LA - eng

KW - inner solution; perturbed wall; boundary conditions; linear amplitude equation

UR - http://eudml.org/doc/219114

ER -

## References

top- [1] 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. Zbl0395.76066
- [2] S. Chandrasekhar, Hydrodynamics and Hydromagnetic Stability Theory, Oxford University Press, London, 1961. Zbl0142.44103
- [3] P. G. Daniels, Finite amplitude two-dimensional convection in a finite rotating system, Proc. Roy. Soc. London Ser. A 363 (1978), 195-215. Zbl0393.76061
- [4] 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. Zbl0464.76097
- [5] P. M. Eagles, A Benard convection problem with a perturbed lower wall, Proc. Roy. Soc. London Ser. A 371 (1980), 359-379. Zbl0466.76078
- [6] A. Golbabai, Finite amplitude axisymmetric convection between rigid rotating planes, J. Comput. Appl. Math. 16 (1986), 355-369. Zbl0609.76038
- [7] 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. Zbl46.1249.04

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