Skip to main content
SpringerLink
Log in

Effect of different flow regimes on free convection heat transfer from isothermal convex bodies over all range of Rayleigh and Prandtl numbers

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

In the present study, effect of different flow regimes on free convection heat transfer has been examined. In the light of this, a novel analytical method is developed to calculate free convection heat transfer from isothermal convex bodies with arbitrary shape over all range of Rayleigh number in fluids with any Prandtl number. The crux of this method is based on the concept of dynamic behaviors existing in natural convection flow. In the previous models the Body Gravity Function (BGF) and Turbulent Function (TF) have been taken as constant values. In this study, BGF accounts for the effect of body shape and orientation with respect to gravity vector in laminar free convection. Besides, TF accounts for the impact of Prandtl number, body shape and orientation with regard to gravity vector in turbulent free convection. By contrast, it is shown that these two parameters undergo a change through the variation of Rayleigh number and cannot be considered as a constant. These two parameters are modeled based upon the thermal resistance concept. Moreover, two transition criteria happening in free convection heat transfer will be obtained according to this new analytical method (conduction–laminar and laminar–turbulent transitions). Finally, three models (models 1, 2 and 3) are proposed for calculation free convection heat transfer and present results for ten isothermal convex bodies with various aspect ratios (\(0.298 \le \frac{\sqrt A }{P} \le 2.470\)) have been compared with the available experimental and numerical data. Here, the results of model 2 are almost equal to those of model 3. Also, the results of model 1 are more precise than those of model 3 while the parameters computation of model 1 is more intricate in comparison with model 3. On the one hand, the model 1 has an average difference <6 % vis-à-vis numerical data in entire range of Rayleigh number (laminar and turbulent). On the other hand, the average difference of model 1 is not more than 8 % versus experimental data in complete range of Rayleigh number. Outstanding agreement exhibits that the proposed model has a great potential to predict free convection heat transfer from isothermal convex bodies in the whole range of Rayleigh numbers in fluids with any Prandtl number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Abbreviations

A :

Total surface area of the body (m2)

\(\tilde{A}\) :

Segment of body surface area to overall surface area of the body

BFF :

Body Fluid Function defined by Eq. (6)

BGF :

Body Gravity Function

C :

Universal correction factor defined by Eq. (8)

C′:

Constant coefficient correlating \(\bar{C}_{t(low)}\) to \(\bar{C}_{t(up)}\) defined by Eq. (12)

C t :

Local TF

\(\bar{C}_{{t\left( {dyn} \right)}}\) :

DTF characterized by Eqs. (15)–(17)

\(\bar{C}_{{t\left( {low} \right)}}\) :

Lower bound of TF

\(\bar{C}_{{t\left( {up} \right)}}\) :

Upper bound of TF

DBGF :

Dynamic Body Gravity Function

DTF :

Dynamic Turbulent Function

F(Pr):

Laminar Prandtl number function defined by Eq. (2)

\(G_{\sqrt A }\) :

BGF established upon characteristic length \(\sqrt A\)

G L :

BGF established upon characteristic length L

G′ low :

Modified lower bound of BGF described by Eq. (7)

G dyn :

DBGF characterized through Eqs. (5)–(8)

h :

Convection heat transfer coefficient (W/m2 K)

m :

Blending exponent between laminar and turbulent heat transfer described by Eq. (11)

n :

Blending exponent between conduction and convection heat transfer (n = 1)

\(Nu_{\sqrt A }\) :

Nusselt number based on characteristic length \(\sqrt {\text{A}}\)

\(Nu_{\sqrt A }^{0}\) :

Conduction limit according to characteristic length \(\sqrt {\text{A}}\)

Pr :

Prandtl number

P :

Perimeter of projected area onto a horizontal plane (m)

R :

Thermal resistance (K/W)

Ra :

Rayleigh number

TF :

Turbulent Function

References

  1. Churchill SW, Usagi R (1972) A general expression for the correlation of rates of transfer and other phenomena. AIChE J 18:1121–1128. doi:10.1002/aic.690180606

    Article  Google Scholar 

  2. Yovanovich MM (1987) On the effect of shape, aspect ratio and orientation upon natural convection from isothermal bodies of complex shape. ASME HTD 82:121–129

    Google Scholar 

  3. Yovanovich MM (1987) New Nusselt and Sherwood numbers for arbitrary isopotential geometries at near zero Peclet and Rayleigh numbers. AIAA 22nd thermophysics conference, Honolulu, Hawaii

  4. Churchill SW, Churchill RU (1975) A comprehensive correlating equation for heat and component transfer by free convection. AIChE J 21:604–606. doi:10.1002/aic.690210330

    Article  Google Scholar 

  5. Jafarpur K (1992) Analytical and experimental study of laminar free convective heat transfer from isothermal convex bodies of arbitrary shape. Ph.D. thesis, University of Waterloo, Waterloo, Canada

  6. Lee S, Yovanovich MM, Jafarpur K (1991) Effects of geometry and orientation on laminar natural convection from isothermal bodies. J Thermophys Heat Transf 5:208–216. doi:10.2514/3.249

    Article  Google Scholar 

  7. Raithby GD, Hollands KGT (1978) Analysis of heat transfer by natural convection (or Film Condensation) for three dimensional flows. In: Sixth international heat transfer conference, Toronto, Ontario, 7–11 August, pp 187–192

  8. Stewart WE (1971) Asymptotic calculation of free convection in laminar three-dimensional systems. Int J Heat Mass Transf 14:1013–1031. doi:10.1016/0017-9310(71)90200-6

    Article  MATH  Google Scholar 

  9. Eslami M, Jafarpur K (2012) Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape: a new dynamic model. Heat Mass Transf 48:301–315. doi:10.1007/s00231-011-0885-6

    Article  Google Scholar 

  10. Eslami M, Jafarpur K (2011) Laminar natural convection heat transfer from isothermal cylinders with active ends. Heat Transf Eng 32:506–513. doi:10.1080/01457632.2010.506378

    Article  Google Scholar 

  11. Eslami M, Jafarpur K, Yovanovich MM (2009) Laminar natural convection heat transfer from isothermal cones with active end. Iran J Sci Technol Trans B Eng 33:217–229

    MATH  Google Scholar 

  12. Raithby GD, Hollands KGT (1975) A general method of obtaining approximate solutions to laminar and turbulent free convection problems. Adv Heat Transf 11:265–315. doi:10.1016/S0065-2717(08)70076-5

    Article  Google Scholar 

  13. Hassani AV, Hollands KGT (1989) On natural convection heat transfer from three-dimensional bodies of arbitrary shape. ASME J Heat Transf 111:363–371. doi:10.1115/1.3250686

    Article  Google Scholar 

  14. Raithby GD, Hollands KGT (1998) Handbook of heat transfer. In: Rohsenow WM, Hartnett JP, Cho YI (eds) Natural convection, 3rd edn. McGraw-Hill, New York, pp 4.1–4.99

    Google Scholar 

  15. Arabi P (2013) Convection heat transfer from isothermal convex bodies of arbitrary shape for different flow regimes (laminar and turbulent). M.Sc. thesis, Shiraz University, Shiraz, Iran

  16. Arabi P, Jafarpur K (2013) Effect of different flow regimes on natural convection heat transfer from a vertical plate. In: 21st annual (international) mechanical engineering conference, Tehran, Iran

  17. Arabi P, Jafarpur K (2013) Criteria for predicting transitions in free convection heat transfer from isothermal convex bodies in fluids with any Prandtl number: a new analytical model. 15th annual (international) fluid dynamics conference, Bandar Abbas, Iran

  18. Bigdely MR (1998) Calculation of conduction limit using panel method. M.Sc. thesis, Shiraz University, Shiraz, Iran

  19. Warner CY, Arpaci VS (1968) An experimental investigation of turbulent natural convection in air at low pressure along a vertical heated flat plate. Int J Heat Mass Transf 11:397–406. doi:10.1016/0017-9310(68)90084-7

    Article  Google Scholar 

  20. Saunders OA (1936) The effect of pressure upon natural convection in air. Proc R Soc Lond Ser A Math Phys Sci 157:278–291. doi:10.1098/rspa.1936.0194

    Article  Google Scholar 

  21. Yang SM (2001) Improvement of the basic correlating equations and transition criteria of natural convection heat transfer. Heat Transf Asian Res 30:293–300. doi:10.1002/htj.1018

    Article  Google Scholar 

  22. Hassani AV (1987) An investigation of free convection heat transfer from bodies of arbitrary shape. Ph.D. thesis, University of Waterloo, Waterloo, Canada

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Molla-Sadra street, 71348-51154, Shiraz, Iran

    Pouria Arabi & Khosrow Jafarpur

Authors
  1. Pouria Arabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Khosrow Jafarpur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khosrow Jafarpur.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arabi, P., Jafarpur, K. Effect of different flow regimes on free convection heat transfer from isothermal convex bodies over all range of Rayleigh and Prandtl numbers. Heat Mass Transfer 52, 1665–1682 (2016). https://doi.org/10.1007/s00231-015-1683-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-015-1683-3

Keywords

Search

Navigation