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Turbulent natural convection in vertical parallel-plate channels

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Abstract

The problem of buoyancy driven turbulent flow in parallel-plate channels is investigated. The investigation is limited to vertical channels of uniform cross-section with different modes of heating. The details of the flow and thermal fields are obtained from the solution of the conservation equations of mass, momentum, and energy in addition to equations of the low Reynolds number turbulence model. The study covers Rayleigh number ranging from 105 to 107 and focuses on the effect of channel geometry on the characteristic of the flow and thermal fields as well as the local and average Nusselt number variation. A Nusselt number correlation has been developed in terms of a modified Rayleigh number and channel aspect ratio for the cases of symmetrically heated isothermal and isoflux conditions.

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Abbreviations

b :

Half channel width

C P :

Specific heat at constant pressure

C 1ɛ, C 2ɛ, C μ :

Empirical constants in the k − ɛ turbulence model

D :

Extra term in Eq. 6

E :

Roughness parameter

f 1, f 2, f μ :

Wall damping function

g :

Gravitational constant

g i :

Component i of the gravitation vector

G b :

Production of turbulent kinetic energy due to buoyancy

G k :

Production of turbulent kinetic energy due to mean velocity gradient

Gr :

Grashof number = gβb 3(T w − T o)/ν2

h :

Average heat transfer co-efficient

h y :

Local heat transfer coefficient

κ:

Thermal conductivity

k :

Kinetic energy of turbulence

L :

Channel length

Nu y :

Local Nusselt number

\(\overline{{\hbox{Nu}}} \) :

Average Nusselt number

P :

Pressure

Pr:

Prandtl number

Prt :

Turbulent Prandtl number

Ra:

Rayleigh number = (Gr·Pr)

Ram :

Modified Rayleigh number = Ra(b/L)

R y :

Local Reynolds number = k 1/2 y/ν

T :

Temperature

\(\overline{T} \) :

Dimensional temperature

T o :

Ambient temperature

T s :

Channel wall (surface) temperature

u, v :

x- and y-components of velocities, respectively

\(\overline{u}, \;\overline{v} \) :

Time-averaged x and y components of velocities, respectively

u i :

ith component of velocity

x, y :

Cartesian coordinates

α:

Thermal diffusivity

β:

Co-efficient of thermal expansion

ε:

Rate of dissipation of the kinetic energy

μ:

Laminar viscosity

μt :

Turbulent viscosity

ν:

Molecular kinematic viscosity

θ:

dimensionless temperature [=(T − T o)/(T w − T o)]

ρ:

Density

σ k :

Prandtl number for k

σɛ :

Prandtl number for ɛ

avg:

Average

i :

ith component

o:

Ambient

\(\overline{{\;\;\;}}\) :

Time-average value

References

  1. Aung W, Fletcher LS, Sernas V (1972) Developing laminar free convection between vertical parallel plates with asymmetric heating. Int J Heat Mass Transfer 15:2293–2308

    Article  MATH  Google Scholar 

  2. Bessaih R, Kadja M (2000) Turbulent natural convection cooling of electronic components mounted on a vertical channel. Appl Thermal Eng 20(2):141–154

    Article  Google Scholar 

  3. Bessaih R, Kadja M (2000) Numerical study of three-dimensional turbulent natural convection air cooling of heat sources simulating electronic components mounted in a vertical channel. J Enhanced Heat Transfer 7(2):153–166

    Google Scholar 

  4. Bodia JR, Osterle JF (1962) The development of free convection between heated vertical plates. ASME J Heat Transfer 84:40–44

    Google Scholar 

  5. Chang K-P, Hung Y-H (1997) Transient natural convection between vertical finite length heated plates. J Thermophys Heat Transfer 11(2):203–211

    MATH  Google Scholar 

  6. Dalbert AM, Penot F, Peube JL (1981) Convection naturalle laminaire dans un canal vertical chauffe a flux constant. Int J Heat Mass Transfer 24:1463–1473

    Article  MATH  Google Scholar 

  7. Elenbaas W (1942) Heat dissipation of parallel plates by free convection. Physica 9:1–28

    Article  Google Scholar 

  8. Fedorov AG, Viskanta R (1997) Turbulent natural convection heat transfer in an asymmetrically heated, vertical parallel-plate channel. Int J Heat Mass Transfer 40(16):3849–3860

    Article  MATH  Google Scholar 

  9. Habib MA, Said SAM, Ahmed SA, Ouwais I (2001) Turbulent natural convection in vertical short channels. Turbulent Heat Transfer Conference, Alaska, pp 8–12

  10. Habib MA, Said SAM, Ahmed SA, Asghar A (2002) Velocity characteristics of turbulent natural convection in symmetrically and asymmetrically heated vertical channels. Exp Thermal Fluid Sci 26:77–87

    Article  Google Scholar 

  11. Incropera FP, DeWitt DP (1996) Fundamentals of heat and mass transfer, 4th edn. Wiley, New York

    Google Scholar 

  12. Kettleborough CF (1972) Transient laminar free convection between heated vertical plates including entrance effects. Int J Heat Mass Transfer 15:883–896

    Article  MATH  Google Scholar 

  13. Kihm KD, Kim JH, Fletcher LS (1993) Investigation of natural convection heat transfer in converging channel flows using a specklegram technique. ASME J Heat Transfer 115:140–147

    Google Scholar 

  14. Launder BE, Spalding DB (1974) The numerical computation of turbulent flow. Comput Meth Appl Mech Eng 3:269–289

    Article  MATH  Google Scholar 

  15. Lee K-T (1999) Natural convection heat and mass transfer in partially heated vertical parallel plates. Int J Heat Mass Transfer 42(23):4417–4425

    Article  MATH  Google Scholar 

  16. Manca O, Nardini S, Naso V, Ruocco G (1995) Experiments on natural convection and radiation in asymmetrical heated vertical channels with discrete heat source. ASME HTD 317:1309–1319

    Google Scholar 

  17. Miyamoto M, Katoh Y, Kurima J, Sasaki H (1986) Turbulent free convection heat transfer from vertical parallel plates. In: Proceeding of the 8th international heat transfer conference, vol 4, pp 1593–1598

  18. Miyatake O, Fujii T (1972) Free convection heat transfer between vertical plates—one plate isothermally heated and the other thermally insulated [in Japanese]. Kagaku-kogaku 36:405–412

    Google Scholar 

  19. Nakamura H, Yutaka A, Naitou T (1982) Heat transfer by free convection between two parallel flat plates. Numer Heat Transfer 5:95–106

    Google Scholar 

  20. Naylor D, Tarasuk JD (1993a) Natural convective heat transfer in a divided vertical channel. Part I—Numerical study. ASME J Heat Transfer 115:377–387

    Google Scholar 

  21. Naylor D, Tarasuk JD (1993b) Natural convective heat transfer in a divided vertical channel. Part II—Experimental study. ASME J Heat Transfer 115:387–397

    Google Scholar 

  22. Naylor D, Floryan JM, Tarasuk JD (1991) A numerical study of developing free convection between isothermal vertical plates. ASME J Heat Transfer 113:620–626

    Article  Google Scholar 

  23. Nobuhide K, Mitsugu N (1997) Direct numerical simulation of combined forced and natural turbulent convection in a vertical plane channel. Int J Heat Fluid Flow 18:88–99

    Article  Google Scholar 

  24. Oosthuzien PH (1984) A numerical study of laminar free convective flow through a vertical open partially heated plane duct. Fundamentals of natural convection—electronic equipment cooling. ASME HTD 32:41–48

    Google Scholar 

  25. Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing corporation, Washington DC

    MATH  Google Scholar 

  26. Shahin GA, Floryan JM (1999) Heat transfer enhancement generated by the chimney effect in systems of vertical channels. ASME J Heat Transfer 121:230–232

    Google Scholar 

  27. Sparrow EM, Azevedo LF (1985) Vertical-channel natural convection spanning between the fully-developed limit and the single-plate boundary-layer limit. Int J Heat Mass Transfer 28(10):1847–1857

    Article  Google Scholar 

  28. Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics, the finite volume method. Longman Scientific and Technical, New York

    Google Scholar 

  29. Versteegh TA, Nieuwstadt FT (1998) Turbulent budgets of natural convection in an infinite, differentially heated, vertical channel. Int J Heat Fluid Flow 19:135–140

    Article  Google Scholar 

  30. Versteegh TA, Nieuwstadt FT (1999) A direct numerical simulation of natural convection between two infinite vertical differentially heated walls scaling laws and wall functions. Int J Heat Mass Transfer 42:3673–3679

    Article  MATH  Google Scholar 

  31. Yang Z, Shih TH (1993) New time scale based model for near-wall turbulence. Am Inst Aeronaut Astronaut J 31(7):1191–1198

    MATH  Google Scholar 

  32. Zamora B, Hernandez J (1997) Influence of variable property effects on natural convection flows in asymmetrically-heated vertical channels. Int Comm Heat Mass Transfer 24(8):1153–1162

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the support received from King Fahd University of Petroleum and Minerals during the course of this study.

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Authors and Affiliations

  1. Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Box # 322, Dhahran, 31261, Saudi Arabia

    H. M. Badr, M. A. Habib, S. Anwar, R. Ben-Mansour & S. A. M. Said

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  1. H. M. Badr
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  2. M. A. Habib
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  3. S. Anwar
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  4. R. Ben-Mansour
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  5. S. A. M. Said
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Correspondence to H. M. Badr.

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Badr, H.M., Habib, M.A., Anwar, S. et al. Turbulent natural convection in vertical parallel-plate channels. Heat Mass Transfer 43, 73–84 (2006). https://doi.org/10.1007/s00231-006-0084-z

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