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A numerical and experimental study of natural convective heat transfer from two-sided circular and square horizontal plates having a finite thickness

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Abstract

Several numerical and experimental studies of natural convective heat transfer from two-sided heated horizontal plates are available. In the numerical studies it has usually been assumed that the plate is thin, effectively having no thickness, whereas plates of finite thickness have been used in the experimental studies. The main aim of the present study is to determine whether the plate thickness has a significant influence on the heat transfer rates from the plate surfaces. The effect of the vertical side surface thermal boundary condition and the effect of the plate shape on the heat transfer rates have been also studied. Heat transfer results have, therefore, been numerically obtained for circular and square plates having various thicknesses. The upper and lower plate surfaces have been assumed to be isothermal and at the same temperature. Both the cases where the vertical side surface of the plate is isothermal and at the same temperature as the upper and lower plate surfaces and the case where this vertical side surface is adiabatic have been considered. The solution has been obtained using ANSYS FLUENT©. Variations of the mean Nusselt number with Rayleigh number for various dimensionless plate thicknesses for the two vertical side surface conditions have been obtained for both plates. To validate the numerical results, a limited range of experiments has been undertaken for both shapes. Mean heat transfer rates have been obtained using the lumped capacity method. Results have only been obtained for the case where the plates are exposed to air.

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Abbreviations

A plate :

area of the top surface of plate and of bottom surface of plate (m2)

A side :

area of the vertical side surface of plate (m2)

A total :

sum of the areas of the heated surfaces of plate (m2)

c :

specific heat of material from which plate is made (J/kg K)

d :

diameter of circular plate (m)

g :

gravitational acceleration (m/s2)

h :

thickness of plate (m)

h t :

total heat transfer coefficient (W/m2 K)

h r :

radiant heat transfer coefficient (W/m2 K)

h c :

convective heat transfer coefficient (W/m2 K)

H :

dimensionless thickness of plate, h/l (−)

k :

thermal conductivity (W/m K)

l :

length scale of plate, i.e., d or w (m)

m :

mass of plate (kg)

Nu :

mean Nusselt number (−)

Nu total :

mean Nusselt number based on the mean heat transfer rate per unit area over heated surfaces of plate (−)

Nu top :

mean Nusselt number based on the mean heat transfer rate per unit area over upper surface of plate (−)

Nu bot :

mean Nusselt number based on the mean heat transfer rate per unit area over lower surface of plate (−)

Nu side :

mean Nusselt number based on the mean heat transfer rate per unit area over vertical side surface of plate (−)

P :

perimeter of surface (m)

Pr :

Prandtl number (−)

\( \overline{Q\hbox{'}} \) :

total heat transfer rate from the heated surfaces of plate (W)

\( {\overline{Q\hbox{'}}}_{top} \) :

total heat transfer rate from the upper surface of plate (W)

\( {\overline{Q\hbox{'}}}_{bot} \) :

total heat transfer rate from the lower surface of plate (W)

\( {\overline{Q\hbox{'}}}_{side} \) :

total heat transfer rate from the vertical side surface of plate (W)

r :

radius of circular plate (m)

Ra :

Rayleigh number (−)

t :

time (s)

T w :

temperature of heated surfaces of plate (K)

T f :

temperature of fluid far from plate (K)

T i :

initial temperature of plate (K)

T e :

final temperature of plate (K)

T m :

mean temperature of plate (K)

T s :

temperature of the surroundings to which plate is radiating (K)

w :

side length of square plate (m)

α :

thermal diffusivity (m2/s)

β :

bulk coefficient of expansion (1/K)

v :

kinematic viscosity (m2/s)

σ :

Stefan-Boltzmann constant (W/m2 K4)

ε :

emissivity of plate (−)

References

  1. Chambers B, Lee TYT (1997) A numerical study of local and average natural convection Nusselt numbers for simultaneous convection above and below a uniformly heated horizontal thin plate. J Heat Transf 119(1):102–108

    Article  Google Scholar 

  2. Sparrow EM, Carlson CK (1986) Local and average natural convection Nusselt numbers for a uniformly heated, shrouded or unshrouded horizontal plate. Int J Heat Mass Transf 29(3):369–379

    Article  Google Scholar 

  3. Wei JJ, Yu B, Wang HS, Tao WQ (2002) Numerical study of simultaneous natural convection heat transfer from both surfaces of a uniformly heated thin plate with arbitrary inclination. J Heat and Mass Transfer 38(4–5):309–317

    Article  Google Scholar 

  4. Wei JJ, Yu B, Kawaguchi Y (2003) Simultaneous natural-convection heat transfer above and below an isothermal horizontal thin plate. Numer Heat Transfer Part A 44(1):39–58

    Article  Google Scholar 

  5. Pera L, Gebhart B (1973) Natural convection boundary layer flow over horizontal and slightly inclined surfaces. Int J Heat Mass Transf 16(6):1131–1146

    Article  Google Scholar 

  6. Friedrich MK, Angirasa D (2001) The interaction between stable thermal stratification and convection under a heated horizontal surface facing downward. Int J Non-Linear Mechanics 36(5):719–729

    Article  Google Scholar 

  7. Aihara T, Yamada Y, Endo S (1972) Free convection along the downward-facing surface of a heated horizontal plate. Int J Heat Mass Transf 15(12):2535–2549

    Article  Google Scholar 

  8. Corcione M, Habib E, Campo A (2011) Natural convection from inclined plates to gases and liquids when both sides are uniformly heated at the same temperature. Int J Thermal Sci 50(8):1405–1416

    Article  Google Scholar 

  9. Churchill SW, Chu HH (1975) Correlating equations for laminar and turbulent free convection from a vertical plate. Int J Heat Mass Transf 18(11):1323–1329

    Article  Google Scholar 

  10. Hassan KE, Mohamed SA (1970) Natural convection from isothermal flat surfaces. Int J Heat Mass Transf 13(12):1873–1886

    Article  Google Scholar 

  11. Fontana L (2014) Free convection heat transfer from an isothermal horizontal thin strip: the influence of the Prandtl number. J Thermal Science 23(6):586–592

    Article  Google Scholar 

  12. Oosthuizen PH, Kalendar AY (2016) A numerical study of the simultaneous natural convective heat transfer from the upper and lower surfaces of a thin isothermal horizontal circular plate. Proceedings of the 2016 ASME international mechanical engineering congress and exposition (IMECE2016), Phoenix, Arizona, USA, 8 pages

  13. Hassani AV, Hollands KGT (1989) On natural convection heat transfer from three-dimensional bodies of arbitrary shape. J Heat Transf 111(2):363–371

    Article  Google Scholar 

  14. Kobus CJ, Wedekind GL (2001) An experimental investigation into natural convection heat transfer from horizontal isothermal circular disks. Int J Heat Mass Transf 44(17):3381–3384

    Article  Google Scholar 

  15. Manna R, Oosthuizen PH (2018) A numerical study of natural convective heat transfer from two-sided circular and square heated horizontal isothermal plates having a finite thickness. Proceedings of the 3rd Thermal & Fluids Engineering Conferrence (TFEC2018), paper TFEC-21540, Fort Lauderdale, Florrida, USA

  16. Savill AM (1993) Evaluating turbulence model predictions of transition. ERCOFTAC Special Interest Group Project, Appl Sci Res 51(1–2):555–562

    Google Scholar 

  17. Schmidt RC, Patankar SV (1991) Simulating boundary layer transition with low-Reynolds-number k-ε turbulence models: part 1-an evaluation of prediction characteristics. J Turbomach 113(1):10–17

    Article  Google Scholar 

  18. Plumb OA, Kennedy LA (1977) Application of a k-e turbulence model to natural convection from a vertical isothermal surface. J Heat Transf 99(1):79–85

    Article  Google Scholar 

  19. Zheng X, Liu C, Liu F, Yang CI (1998) Turbulent transition simulation using the k-ω model. Int J Num Meth Eng 42(5):907–926

    Article  Google Scholar 

  20. Albets-Chico X, Oliva A, Perez-Segarra CD (2008) Numerical experiments in turbulent natural convection using two-equation eddy-viscosity models, J. Heat Transfer. 130(7):072501-1–072501-11

  21. Xamán J, Álvarez G, Lira L, Estrada C (2005) Numerical study of heat transfer by laminar and turbulent natural convection in tall cavities of Façade elements. Energy Buildings 37(7):787–794

    Article  Google Scholar 

  22. Kalendar A, Kalendar AY, Alhendal Y (2016) Evaluation of turbulence models for natural and forced convection from flat plates. Computational Thermal Sci: Int J 8(6):567–582

    Article  Google Scholar 

  23. Kline SJ, McClintock FA (1953) Describing uncertainties in single-sample experiments. Mech Eng 75(1):3–8

    Google Scholar 

  24. Oosthuizen PH (2015) A numerical study of natural convective heat transfer from horizontal isothermal heated elements of complex shape. Proceedings of the 1st Thermal & Fluid Engineering Summer Conference (TFESC), New York City, USA, 843-854

  25. Oosthuizen PH, Kalendar AY (2016) Numerical study of natural convective heat transfer from horizontal heated elements of relatively complex shape having a uniform surface heat flux. 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2016), Costa del Sol, Spain, 1129-1134

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Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through its Discovery Grant Program (Grant RGPIN-2015-06444).

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  1. Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Rafiq Manna & Patrick H. Oosthuizen

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  1. Rafiq Manna
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Correspondence to Rafiq Manna.

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Manna, R., Oosthuizen, P.H. A numerical and experimental study of natural convective heat transfer from two-sided circular and square horizontal plates having a finite thickness. Heat Mass Transfer 56, 2225–2238 (2020). https://doi.org/10.1007/s00231-020-02851-8

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