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On the modeling of aiding mixed convection in vertical channels

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Abstract

This paper aims at showing that to prescribe a flow rate at the inlet section of a vertical channel with heated walls leads to surprising and counterintuitive physical solutions, especially when the problem is modeled as elliptical. Such an approach can give rise to the onset of recirculation cells in the entry region while the heat transfer is slightly increased under the influence of the buoyancy force. We suggest an alternative model based on more realistic boundary conditions based on a prescribed total pressure at the inlet and a fixed pressure at the outlet sections. In this case, the pressure and buoyancy forces act effectively in the same direction and, the concept of buoyancy aiding convection makes sense. The numerical results emphasize the large differences between solutions based on prescribed inlet velocity and those obtained with the present pressure-based boundary conditions.

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Abbreviations

a :

Thermal diffusivity (m2 s−1)

A :

Aspect ratio, A = H/D

c p :

Specific heat (J K−1 kg−1)

c x , c z :

Stretching parameters, Eq. 13

D :

Plate spacing (m)

D h :

Hydraulic diameter, D h  = 2D (m)

g :

Gravitational acceleration (m s−2)

Gr H :

Grashof number based on H, Gr H  = gβ 0ΔTH 3/ν 20

h :

Heat transfer coefficient (W m−2 K−1)

H :

Channel height (m)

k :

Thermal conductivity (W m−1 K−1)

L :

Channel length in the spanwise direction (m)

\( \dot{m} \) :

Mass flow rate (kg s−1)

n x , n z :

Numbers of grid points in x- and z-directions

p :

Pressure (Pa)

p s :

Pressure at the outlet section (Pa)

Pr :

Prandtl number, Pr = ν0/a 0

Q :

Heat flux (W)

Q en :

Enthalpy heat flux (W)

Q 2w :

Convective heat flux along the two channel walls (W)

Re :

Reynolds number based on D h , Re = w 0 D h /ν0

Ri :

Richardson number, Ri = Gr/Re 2

S c :

Area of the channel cross section, S c  = DL (m2)

t :

Time (s)

T :

Temperature (K)

u, w :

Velocity components (m s−1)

x, z :

Coordinates (m)

β :

Coefficient of thermal expansion, β = 1/T 0 (K−1)

ΔT :

Temperature difference, ΔT = (T h  − T 0) (K)

μ :

Dynamic viscosity (Pa s)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

θ :

Dimensionless temperature ratio, θ = (T − T 0)/ΔT

τ :

Dimensionless time

a, b :

Analytical solutions

h :

Hot wall

H :

Quantity based on channel height

nc :

Natural convection

0:

Inlet section

−:

Averaged quantity

*:

Dimensionless quantity

References

  1. Ingham DB, Keen DJ, Heggs PJ, Morton BR (1990) Recirculating pipe flows. J Fluid Mech 213:443–464

    Article  Google Scholar 

  2. Ait Hammou Z, Benhamou B, Galanis N, Orfi J (2004) Laminar mixed convection of humid air in a vertical channel with evaporation or condensation. Int J Therm Sci 43:531–539

    Article  Google Scholar 

  3. Desrayaud G, Lauriat G (2009) Flow reversal of laminar mixed convection in the entry region of symmetrically heated, vertical plate channels. Int J Therm Sci 48:2036–2045

    Article  Google Scholar 

  4. Laaroussi N, Lauriat G, Desrayaud G (2009) Effects of variable density for film evaporation on laminar mixed convection in a vertical channel. Int J Heat Mass Transf 52:151–164

    Article  MATH  Google Scholar 

  5. Aung W, Worku G (1986) Theory of fully developed, combined convection including flow reversal. ASME J Heat Transf 108:485–488

    Article  Google Scholar 

  6. Aung W, Worku G (1986) Developing flow and flow reversal in a vertical channel with asymmetric wall temperatures. ASME J Heat Transf 108:289–304

    Google Scholar 

  7. Gau C, Yih K, Aung W (1992) Measurements of heat transfer and flow structure in heated vertical channels with buoyancy assisted and opposed flows. AIAA J Thermophys Heat Transf 6:707–712

    Article  Google Scholar 

  8. Gau C, Yih K, Aung W (1992) Reversed flow structure and heat transfer measurements for buoyancy-assisted convection in a heated vertical duct. ASME J Heat Transf 114:928–935

    Article  Google Scholar 

  9. Cheng CH, Huang S, Aung W (1997) Enhancement of flare method for predicting buoyancy-induced flow reversal in vertical ducts via parabolic model. Numer Heat Transf Part B 31:327–345

    Article  Google Scholar 

  10. Yang CS, Jeng DZ, Yih KA, Gau C, Aung W (2009) Numerical and analytical study of reversed flow and heat transfer in a heated vertical duct. J Heat Transf 131:072501

    Article  Google Scholar 

  11. Aung W (1987) Mixed convection in internal flow. In: Kakaç S, Shah RK, Aung W (eds) Handbook of single-phase convective heat transfer. Wiley, New York

    Google Scholar 

  12. Gebhart B, Jaluria Y, Mahajan RL, Sammakia B (1988) Buoyancy induced flows and transport. Springer, New York

    MATH  Google Scholar 

  13. Bejan A (2004) Convection heat transfer, 3rd edn. Wiley, Hoboken

    Google Scholar 

  14. Chen TS, Armaly BF, Aung W (1985) Mixed convection in laminar boundary layer flow. In: Kakaç S, Aung W, Viskanta R (eds) Natural convection: fundamentals and applications. Hemisphere Pub. Corp., Washington, pp 699–725

  15. Barletta A, Zanchini E (1999) On the choice of the reference temperature for fully-developed mixed convection in a vertical channel. Int J Heat Mass Transf 42:3169–3181

    Article  MATH  Google Scholar 

  16. Chen YC, Chung JN (1996) The linear stability of mixed convection in a vertical channel flow. J Fluid Mech 325:29–51

    Article  MATH  Google Scholar 

  17. Bar-Cohen A, Rohsenow WM (1984) Thermally optimum spacing of vertical, natural convection cooled, parallel plates. ASME J Heat Transf 106:116–123

    Article  Google Scholar 

  18. Bejan A, Sciubba E (1992) The optimal spacing of parallel plates cooled by forced convection. Int J Heat Mass Transf 35:3259–3264

    Article  Google Scholar 

  19. Chénier E, Eymard R, Touazi O (2006) Numerical results using a colocated finite volume scheme on unstructured grids for incompressible fluid flows. Numer Heat Transf Part B 49:259–276

    Article  Google Scholar 

  20. Touazi O, Chénier E, Eymard R (2008) Simulation of natural convection with the collocated clustered finite volume scheme. Comput Fluids 37:1138–1147

    Article  MATH  Google Scholar 

  21. Goda K (1979) A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. J Comput Phys 30:76–95

    Article  MATH  Google Scholar 

  22. Sun H, Li R, Chénier E, Lauriat G, Padet J (2012) Optimal plate spacing for mixed convection from an array of vertical isothermal plates. Int J Therm Sci. doi:10.1016/j.ijthermalsci.2011.12.013

  23. Padet C, Mladin EM, Padet J, Dobrovicescu A (2009) Minimization of entropy production in fully developed mixed thermal convection. In: International symposium on convective heat and mass transfer in sustainable energy, 28 April–1 May 2009, Tunisia, CD-ROM paper 69

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Authors and Affiliations

  1. Laboratoire de Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 5 bd Descartes, 77454, Marne-la-Vallée, France

    Hua Sun, Ru Li, Eric Chénier & Guy Lauriat

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  1. Hua Sun
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  2. Ru Li
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  3. Eric Chénier
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  4. Guy Lauriat
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Correspondence to Guy Lauriat.

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Sun, H., Li, R., Chénier, E. et al. On the modeling of aiding mixed convection in vertical channels. Heat Mass Transfer 48, 1125–1134 (2012). https://doi.org/10.1007/s00231-011-0964-8

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