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Numerical investigation of thermosolutal natural convection in a rectangular enclosure of an aspect ratio four with heat and solute sources

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Abstract

A numerical study of double-diffusive natural convection in an enclosure with a partial vertical heat and mass sources for an aspect ratio Ar = 4 has been carried out. The influence of various dimensionless parameters (Rayleigh number, buoyancy ratio, source location, Lewis number, and source length) on the flow behavior are investigated. Correlations of average Nusselt and Sherwood numbers are obtained as function of two parameters (Ra, d) and (Le, d), respectively.

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Abbreviations

Ar:

Aspect ratio \(({\text{H}}/{\text{W}})\)

D :

Mass diffusivity (m2/s)

d:

Dimensionless source length, d = (l/W)

c:

Dimensional concentration (kg/m3)

c c :

Concentrations at the right wall (kg/m3)

c h :

Concentrations of heater at the left wall (kg/m3)

C :

Dimensionless concentration, C = (c − c 0/c h  − c c )

f :

Dimensionless frequency

g:

Acceleration of gravity (m/s2)

H :

Height of the enclosure (m)

l :

Dimensional length of the contaminant ant thermal sources (m)

Le :

Lewis number, Le = α/D = Sc/Pr

N :

Buoyancy ratio, \(N = [\beta_{C} (c_{h} - c_{c} )/ \beta_{T} \left( {T_{h} - T_{c} } \right)]\)

\(\overline{Nu}\) :

Average Nusselt number, defined in Eq. (12)

\(\overline{\text{Nuc}}\) :

Correlated average Nusselt number

p :

Pressure (N/m2)

P :

Dimensionless pressure, \(P = pW^{2} / \rho_{0} \alpha^{2}\)

Pr :

Prandtl number, \(\Pr \, = \,( \nu /\alpha )\)

Ra :

Rayleigh number, Ra = gW 3 β T (T h  − T c )/\(\nu \alpha\)

Sc :

Schmidt number, \(Sc = \nu /D\)

\(\overline{\text{Sh}}\) :

Average Sherwood number, defined in Eq. (13)

\(\overline{\text{Shc}}\) :

Correlated average Sherwood number

T c :

Cold wall temperature (K)

T h :

Hot wall temperature (K)

T :

Temperature (K)

t:

Dimensional time (s)

\( {u, v} \) :

Velocity components in x, y directions (m/s)

U, V :

Dimensionless velocity components in X, Y directions

x, y :

Dimensional Cartesian coordinates (m)

X, Y :

Dimensionless Cartesian coordinates

α :

Thermal diffusivity (m2/s)

β T :

Coefficient of thermal expansion (K−1)

β C :

Coefficient of solutal expansion (m3/kg)

Δ:

Difference value

θ :

Dimensionless temperature, θ = (T − T 0)/(T h  − T c )

ν :

Kinematics viscosity (m2/s)

ρ :

Fluid density (kg/m3)

τ :

Dimensionless time, τ = tα/W 2

:

Dimensionless period of time

Φ :

Generic variable (\(U,\,V,\,P,\theta\) or C)

\(\Uppsi\) :

Dimensionless stream function

η:

Dimensionless distance between source centers, η = η1 − η2

η1 :

Dimensionless location of thermal source

η2 :

Dimensionless location of solutal source

max, min:

Maximum, minimum

o:

Reference value or location

C:

Concentration

T:

Temperature

References

  1. Mamou M, Vasseur P, Bilgen E (1996) Analytical and numerical study of double diffusive convection in a vertical enclosure. Heat Mass Transf 32:115–125

    Article  Google Scholar 

  2. Chamkha AJ, Al-Mudhaf A (2008) Double-diffusive natural convection in inclined porous cavities with various aspect ratios and temperature-dependent heat source or sink. Heat Mass Transf 44:679–693

    Article  Google Scholar 

  3. Kamakura K, Ozoe H (1993) Experimental and numerical analyses of double diffusive natural convection heated and cooled from opposing vertical walls with an initial condition of a vertically linear concentration gradient. Int J Heat Mass Transf 36:2125–2134

    Article  Google Scholar 

  4. Gobin D, Bennacer R (1996) Cooperating thermosolutal convection in enclosures—II. Heat transfer and flow structure. Int J Heat Mass Transf 39:2683–2697

    Article  Google Scholar 

  5. Morega A, Nishimura T (1996) Double diffusive convection by Chebyshev collocation method. Technol Rep Univ 5:259–276

    Google Scholar 

  6. Costa VAF (2004) Double-diffusive natural convection in parallelogrammic enclosures. Int J Heat Mass Transf 47:2913–2926

    Article  MATH  Google Scholar 

  7. Makayssi T, Lamsaadi M, Naïmi M, Hasnaoui M, Raji A, Bahlaoui A (2008) Natural double-diffusive convection in a shallow horizontal rectangular cavity uniformly heated and salted from the side and filled with non-Newtonian power-law fluids: the cooperating case. Energy Convers Manag 49:2016–2025

    Article  Google Scholar 

  8. Liang X, Li X, Fu D, Ma Y (2009) Complex transition of double diffusive convection in a rectangular enclosure with height-to-length ratio equal to 4: part I. Commun Comput Phys 6:247–268

    Article  Google Scholar 

  9. Teamah MA, Ahmed FE, Massoud EZ (2012) Numerical simulation of double-diffusive natural convective flow in an inclined rectangular enclosure in the presence of magnetic field and heat source. Int J Thermal Sci 52:161–175

    Article  Google Scholar 

  10. Varol Y, Oztop HF, Koca A, Ozgen F (2009) Natural convection and fluid flow in inclined enclosure with a corner heater. Appl Thermal Eng 29:340–350

    Article  Google Scholar 

  11. Deng QH, Tang GF, Li Y, Ha MY (2002) Interaction between discrete heat sources in horizontal natural convection enclosures. Int J Heat Mass Transf 45:5117–5132

    Article  MATH  Google Scholar 

  12. Ben-Cheikh N, Ben-Beya B, Lili T (2007) Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below. Int Commun Heat Mass Transf 34:369–379

    Article  Google Scholar 

  13. Aminossadati SM, Ghasemi B (2009) Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure. Eur J Mech B Fluids 28:630–640

    Article  MATH  Google Scholar 

  14. Bagchi A, Kulacki FA (2011) Natural convection in fluid–superposed porous layers heated locally from below. Int J Heat Mass Transf 54:3672–3682

    Article  MATH  Google Scholar 

  15. Zhao FY, Liu D, Tang GF (2008) Natural convection in an enclosure with localized heating and salting from below. Int J Heat Mass Transf 51:2889–2904

    Article  MATH  Google Scholar 

  16. Kuznetsov GV, Sheremet MA (2009) Conjugate heat transfer in an enclosure under the condition of internal mass transfer and in the presence of the local heat source. Int J Heat Mass Transf 52:1–8

    Article  MATH  Google Scholar 

  17. Nithyadevi N, Yang RJ (2009) Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects. Int J Heat Fluid Flow 30:902–910

    Article  Google Scholar 

  18. Teamah MA, Dawood MM, El-Maghlany WM (2011) Double diffusive natural convection in a square cavity with segmental heat sources. Eur J Sci Res 54:287–301

    Google Scholar 

  19. Mihaljan JM (1962) A rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid. Astrophys J 136:1126–1133

    Article  MathSciNet  Google Scholar 

  20. Brown DL, Cortez R, Minion ML (2001) Accurate projection methods for the incompressible Navier–Stokes equations. J Comput Phys 168:464–499

    Article  MATH  MathSciNet  Google Scholar 

  21. Hayase T, Humphrey JAC, Greif R (1992) A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures. J Comput Phys 98:108–118

    Article  MATH  Google Scholar 

  22. Ben-Cheikh N, Ben-Beya B, Lili T (2007) Benchmark solution for time-dependent natural convection flows with an accelerated full-multigrid method. Numer Heat Transf B 52:131–151

    Article  Google Scholar 

  23. Barrett R et al. (1994) Templates for the solution of linear systems: building blocks for iterative methods. SIAM Press, Philadelphia

  24. Ben-Beya B, Lili T (2007) Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure. Int J Heat Mass Transf 50:4540–4553

    Article  MATH  Google Scholar 

  25. Oueslati F, Ben-Beya F, Lili T (2011) Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity. C R Mecanique 339:655–665

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mécanique des Fluides, Département de Physique, Faculté des Sciences de Tunis, Université de Tunis El-Manar, El-Manar 2, 2092, Tunis, Tunisia

    Fakher Oueslati, Brahim Ben-Beya & Taieb Lili

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  1. Fakher Oueslati
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  2. Brahim Ben-Beya
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Correspondence to Fakher Oueslati.

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Oueslati, F., Ben-Beya, B. & Lili, T. Numerical investigation of thermosolutal natural convection in a rectangular enclosure of an aspect ratio four with heat and solute sources. Heat Mass Transfer 50, 721–736 (2014). https://doi.org/10.1007/s00231-013-1280-2

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