Abstract
Steady, laminar, double diffusion natural convection flow in a square enclosure with partially active vertical wall is considered. The enclosure is filled with a binary fluid and subjected to horizontal temperature and concentration gradients. The flow is driven by cooperating thermal and solutal buoyancies. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on five parameters: thermal Rayleigh number (Rat = 103–106), Prandtl number (Pr = 7), Schmidt number (Sc = 240), buoyancy forces ratio (N = 1) and the aspect ratio of the enclosure (A = 1). The active location takes three positions in the left wall: top (T), middle (M) and bottom (B). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat and mass transfer rates. The results including the streamlines, isotherm and iso-concentration patterns, flow velocity and the average Nusselt and Sherwood numbers for different values of Rat. The obtained results show that the increase of Rat leads to enhance heat and mass transfer rates. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also by moving the active location from the top to the bottom on the left vertical wall, convection and heat and mass transfer rates are more important in case (B). Furthermore for high Rayleigh number (Rat = 106), Convection mechanism in (T) case is principally in the top of the enclosure, whereas in the remaining cases it covers the entire enclosure.
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Abbreviations
- A:
-
Aspect ratio H/L
- C:
-
Dimensionless concentration (C* − Cmin)/∆C*
- Le:
-
Lewis number, Le = α/D
- \( \overline{Nu} \) :
- N:
-
Buoyancy ratio number (βs∆C*)/(βt ∆T)
- P:
-
Dimensionless pressure p/(α/H)2
- Pr:
-
Prandtl number of the fluid υ/α
- Rat :
-
Thermal Rayleigh number gβt H3∆T/υα
- Sc:
-
Schmidt number υ/D
- \( \overline{Sh} \) :
- t:
-
Dimensionless time t*/(H2/α)
- U, V:
-
Dimensionless velocity components u/(α/H), v/(α/H)
- X, Y:
-
Non-dimensional cartesian coordinates x/H, y/H
- θ:
-
Non-dimensional temperature, (T − Tmin)/∆T
- ψ:
-
Non-dimensional stream function, \( {\text{U}} = \partial \psi /\partial {\text{Y}} \)
- ∆T:
-
Temperature difference (Tmax − Tmin)
- ∆C* :
-
Concentration difference, (Cmax − Cmin)
References
Kamotani, Y., Wang, J.S., Ostrah, S., Jiang, H.D.: Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradient. Int. J. Heat Mass Transf. 28(1), 165–173 (1985)
Ouriemi, M., Vasseur, P., Bahloul, A., Robillard, L.: Natural convection in a horizontal layer of a binary mixture. Int. J. Thermal Sci. 45, 752–759 (2006)
Borjini, M.N., Aissia, H.B., Halouani, K., Zeghmati, B.: Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid. Int. J. Heat Mass Transf. 49, 3984–3996 (2006)
Yahiaoui, M.A., Bahloul, A., Vasseur, P., Robillar, L.: Natural convection of a binary mixture in a vertical closed annulus. Chem. Eng. Commun. 194, 924–937 (2007)
Ostrach, S.: Natural convection with combined driving forces. Physico-chem Hydrodyn. 1, 233–247 (1980)
Lee, J., Hyun, M.T., Kim, K.W.: Natural convection in confined fluids with combined horizontal temperature and concentration gradients. Int. J. Heat Mass Transf. 31, 1969–1977 (1988)
Bennacer, R., Gobin, D.: Cooperating thermosolutal convection in enclosures-I. Scale analysis and mass transfer. Int. J. Heat Mass Transf. 39(13), 2671–2681 (1996)
Gobin, D., Bennacer, R.: Cooperating thermosolutal convection in enclosures-II. Heat transfer and flow structure. Int. J. Heat Mass Transf. 39(13), 2683–2697 (1996)
Sezai, I., Mohamed, A.A.: Double diffusion convection in a cubic enclosure with opposing temperature and concentration gradients. Phys. Fluids 12, 2210–2223 (2000)
Nithyadevi, N., Yang, R.J.: Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects. Int. J. Heat Fluid Flow. 30, 902–910 (2009)
Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere, McGraw-Hill, Washington, DC (1980)
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Belazizia, A., Benissaad, S., Abboudi, S. (2017). Cooperating Double Diffusion Natural Convection in a Square Enclosure with Partially Active Vertical Wall. In: Boukharouba, T., Pluvinage, G., Azouaoui, K. (eds) Applied Mechanics, Behavior of Materials, and Engineering Systems. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-41468-3_45
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DOI: https://doi.org/10.1007/978-3-319-41468-3_45
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