INSTABILITY OF THE RAYLEIGH-BENARD CONVECTION FOR INCLINED LOWER WALL WITH TEMPERATURE VARIATION

Sadoon Ayed, Gradimir Ilić, Predrag Živković, Mića Vukić, Mladen Tomić

DOI Number
10.22190/FUME1602179A
First page
179
Last page
197

Abstract


This paper deals with an analysis of a two-dimensional viscous fluid flow between the two parallel plates inclined with respect to the horizontal plane, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period after which it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, there is a longitudinal sinusoidal temperature variation imposed on the mean temperature. We have investigated the wave number and amplitude influence of this variation on the subcritical stability and the onset of the Rayleigh-Bénard convective cells, by direct numerical simulation of 2D Navier-Stokes and energy equation.

Keywords

DNS, Rayleigh Number, Boussinesq Approximation, Inclined Walls, Non-linear Stability Analysis

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References


Tippelskirch, H., 1956, Über Konvektions-zellen, insbesondere in flüssigemSchwefel, Beitr. Phys. Atmos., 29, pp. 37-54.

Segel, L.A., Stuart, J.T., 1962, On the question of the preferred mode in cellular thermal convection, Journal of Fluid Mechanics, 13(2), pp. 289-306.

Busse, F.H., 1967, The stability of finite amplitude cellular convection and its relation to an extremum principle, Journal of Fluid Mechanics, 30(4), pp. 625-649.

Stengel, K. C., Oliver, D. S. and Booker, J. R., 1982, Onset of convection in a variable-viscosity fluid, Journal of Fluid Mechanics, 120, pp. 411-431.

Busse, F.H., Frick, H., 1985, Square-pattern convection in fluids with strongly temperature-dependent viscosity, Journal of Fluid Mechanics, 150, pp. 451-465.

Subha, S., 2012, Numerical stimulation of Rayleigh Bernard convection in wavy enclosures, International Journal of Instrumentation, Control and Automation (IJICA), 1(3-4), pp. 59-62.

Tracy, N.I., Crunkleton, D.W., 2012, Oscillatory natural convection in trapezoidal enclosures, International Journal of Heat and Mass Transfer, 55, pp 4498–4510.

Yigit, S., Poole, R. J., Chakraborty, N., 2015, Effects of aspect ratio on laminar Rayleigh–Bénard convection of power-law fluids in rectangular enclosures: A numerical investigation, International Journal of Heat and Mass Transfer 91, pp.1292–1307

Park, H.M., 2015, Rayleigh-Bénard convection of nanofluids based on the pseudo-single-phase continuum model, International Journal of Thermal Sciences, 90, pp. 267-278.

Matveev, L.V., 2016, Impurity transport in developed Rayleigh–Bénard convection, International Journal of Heat and Mass Transfer 95 pp. 15–21.

Zimmermann, C., Groll, R., 2015, Computational investigation of thermal boundary layers in a turbulent Rayleigh–Bénard problem, International Journal of Heat and Fluid Flow, 54, pp. 276–291.

Paolucci, S., Chenoweth, D.R., 1987, Departures from the Boussinesq approximation in the laminar Bénard convection, Physics of Fluids, 30(5), pp. 1561-1564.

Fröhlich, J., Laure, P., Peyret, R., 1992, Large departures from Boussinesq approximation in the Rayleigh-Bénard problem, Physics of Fluids A, 4(7), pp. 1355-1372.

Severin, J., Herwig, H., 2001, Onset of convection in the Rayleigh- Bénard flow under non-Boussinesq conditions: an asymptotic approach, Forschung im Ingenieurwesen, 66(4), pp. 185-191.

Ayed, S., Jovanović, M., Tomić, M., Ilić, G., Živković, P., Vukić, M., Dobrnjac, M., 2015, Instability Of Rayleigh-Bénard Convection Affected by Inclined Wall Temperature Variation, Proc. Int. Conf. DEMI, Banjaluka, pp. 397-402.

Sharma, A.K., Velusamy, K., Balaji, C., 2008, Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosure, Heat and mass transfer, 44(10), pp. 1153-1170.

Crunkleton, D.W., Anderson, T.J., 2006, Numerical study of flow and thermal convection, International communications in heat and mass transfer, 33(1), pp. 24-29.

Beya, B.B., Lili, T., 2009, Transient Natural Convection in 3D Tilted Heated from Two Opposite Sites, International communications in heat and mass transfer, 36(6), pp. 604-613.

Kleiser, L., Schumann U., 1980, Treatment of incompressibility and boundary conditions in 3D numerical spectral simulation of plane channel flows, Proc. Third GAMM Conference Numerical Methods in Fluid Dynamics, Vieweg, Braunschweig, pp. 165-173.

Pulicani, J.P., 1988, A spectral multi-domain method for the solution of 1-D Helmholtz and Stokes-type equations, Computers and Fluids, 16(2), pp. 207-215.

Jovanović, M., 2009, Simulation of temporal hydrodynamic instability in plane channel flow, Proc. 2nd Int. Congress of Serbian Soc. of Mechnics - IConSSM, Palić, pp. B09-B23.

Clever, R.M., Busse F.H., 1974, Transition to time dependant convection, Journal of Fluid Mechanics, 65(4), pp. 625-645.

Busse, F.H., Clever R.M. 1979, Instability of convection rolls in a fluid of moderate Prandtl number, Journal of Fluid Mechanics, 91(2), pp. 319-335.




DOI: https://doi.org/10.22190/FUME1602179A

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