RAYLEIGH-BÉNARD CONVECTION INSTABILITY IN THE PRESENCE OF TEMPERATURE VARIATION AT THE LOWER WALL
Abstract
This paper analyzes the two-dimensional viscous fluid flow between two parallel
lates, where the lower plate is heated and the upper one is cooled. The
emperature difference between the plates is gradually increased during a certain
ime period, and afterwards it is temporarily constant. The temperature
istribution on the lower plate is not constant in x-direction, and there is
ongitudinal sinusoidal temperature variation imposed on the mean temperature.
e investigate the wave number and amplitude influence of this variation on the
tability of Rayleigh-Benard convective cells, by direct numerical simulation of 2-
Navier-Stokes and energy equation.
Dates
- Submission Date2012-05-05
- Revision Date2012-09-20
- Acceptance Date2012-09-25
References
- Tippelskirch, H., Über Konvektions-zellen, insbesondere in flüssigem Schwefel, Beitr. Phys. Atmos., 29 (1956), pp. 37-54.
- Paolucci, S., Chenoweth, D.R., Departures from the Boussinesq approximation in the laminar Bénard convection, Physics of Fluids, 30 (1987), 5, pp. 1561-1564.
- Somerscales, E.F.C, Dougherty, T.S., Observed flow patterns at the initiation of convection in a horizontal liquid layer heated from below, Journal of Fluid Mechanics, 42 (1970), pp.755-768.
- Richter, F.M., Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature, Journal of Fluid Mechanics, 89 (1978), pp. 553-560.
- Stengel, K.C., Oliver, D.S., Booker, J.R. Onset of convection in a variable-viscosity fluid, Journal of Fluid Mechanics, 120, (1982), pp. 411-431.
- Busse, F.H., Frick, H. Square-pattern convection in fluids with strongly temperature-dependent viscosity, Journal of Fluid Mechanics, 150 (1985), pp. 451-465.
- Severin, J., Herwig, H., Onset of convection in Rayleigh-Bénard flow with temperature-dependent viscosity: an asymptotic approach, ZAMP, 50 (1999), pp. 375-386.
- Fröhlich, J., Laure, P., Peyret, R., Large departures from Boussinesq approximation in the Rayleigh- Bénard problem, Physics of Fluids A, 4(7), (1992) ,pp. 1355-1372.
- Severin, J., Herwig, H., Onset of convection in the Rayleigh- Bénard flow under non-Boussinesq conditions: an asymptotic approach, Forschung im Ingenieurwesen, 66 (2001), pp.185-191.
- Nourollahi M., Farhadi M., Kurosh S., Numerical study of mixed convection and entropy generation in the Poiseuille-Bénard channel in different angles. Thermal Science, 14 (2010), 2, pp.329-340.
- Gupta U.,Argawall U.,Thermal instability of compressible Walters' (B-Model) fluid in the presence of Hall currents and suspended particles. Thermal Science, 15 (2011), 2,pp.487-500.
- Kleiser L., Schumann U.,:Treatment of incompressibility and boundary conditions in 3D numerical spectral simulation of plane channel flows. Hirschel E.H.(ed.): Third GAMM Conference Numerical Methods in Fluid Dynamics, 1980, Vieweg, Braunschweig, pp. 165-173.
- Pulicani, J.P. A spectral multi-domain method for the solution of 1-D Helmholtz and Stokes-type equations. Computers and Fluids, 1988 ,16, pp. 207-215.
- Jovanovic M., Simulation of temporal hydrodynamic instability in plane channel flow, 2nd international congress of Serbian society of mechanics (IConSSM), Paliæ, Subotica, Serbia, 1-5th June 2009, Proceedings B09-B23.
- Canuto C., et al., Spectral methods. Fundamentals in single domain, Springer Verlag, 2007.
- Clever R.M. and Busse F.H.,.Transition to time dependant convection. Journal of Fluid Mechanics, (1974), 65, pp. 625-645.
- Busse F.H., Clever R.M. Instability of convection rolls in a fluid of moderate Prandtl number. Journal of Fluid Mechanics, (1979), 91, pp. 319-335.
Volume
16,
Issue
12,
Pages281 -294