Heat and Mass Transfer

, Volume 48, Issue 2, pp 301–315 | Cite as

Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape: a new dynamic model

Original

Abstract

Calculation of free convection from bodies of arbitrary shape has been investigated previously. The Body Gravity Function (BGF) which accounts for the geometry of each body shape was considered to be a constant value. In the present study, it is shown that BGF is not a constant value in a wide range of Rayleigh number. Instead, its value changes as Rayleigh number increases. Therefore, by analytical modeling of Dynamic BGF and derivation of a new parameter called Body Fluid Function, a novel method is proposed to calculate laminar free convection heat transfer from isothermal convex bodies of arbitrary shape. Results for 24 different body shapes are compared with the available experimental and numerical data. Excellent agreement shows that the present simple method accurately predicts laminar free convection heat transfer from isothermal convex bodies of arbitrary shape in the whole range of laminar flow and for fluids of any Prandtl number.

List of symbols

A

Total surface area

\( \tilde{A} \)

Fraction of sectional area defined by Eq. 7

BFF

Body fluid function defined by Eq. 18

C

Universal correction factor defined by Eq. 24

\( F(\Pr ) \)

Prandtl number function defined by Eq. 2

G

Body gravity function based on characteristic length \( \sqrt A \)

Gdyn

Dynamic body gravity function

Gr

Grashof number

\( G^{\prime}_{\text{low}} \)

Modified lower bound

h

Convection heat transfer coefficient

hx, hω

Scale factors

k

Thermal conductivity

N

Number of distinct surfaces of a body shape

\( {\text{Nu}}_{\sqrt A } \)

Nusselt number based on characteristic length \( \sqrt A \)

\( {\text{Nu}}_{\sqrt A }^{0} \)

Conduction limit based on characteristic length \( \sqrt A \)

P

Local perimeter of body with respect to gravity vector, m

Pr

Prandtl number

R

Thermal resistance

\( {\text{Ra}}_{\sqrt A } \)

Rayleigh number based on characteristic length \( \sqrt A \)

θ

The angle between normal to the surface and the gravity vector

x, ω

Surface coordinate lines

References

  1. 1.
    Acrivos A (1960) A theoretical analysis of laminar natural convection heat transfer to non-newtonian fluids. AIChE J 6:584–590CrossRefGoogle Scholar
  2. 2.
    Saville DA, Churchill SW (1967) Laminar free convection in boundary layers near horizontal cylinders and vertical axisymmetric bodies. J Fluid Mech 29:391–399MATHCrossRefGoogle Scholar
  3. 3.
    Stewart WE (1971) Asymptotic calculation of free convection in laminar three-dimensional systems. Int J Heat Mass Transf 14:1013–1031MATHCrossRefGoogle Scholar
  4. 4.
    Lienhard JH (1973) On the commonality of equation for natural convection from immersed bodies. Int J Heat Mass Transf 16:2121–2123CrossRefGoogle Scholar
  5. 5.
    Sparrow EM, Ansari MA (1983) A refutation of king’s rule for multi-dimensional external natural convection. Int J Heat Mass Transf 26:1357–1364CrossRefGoogle Scholar
  6. 6.
    Lin FN, Chao BT (1974) Laminar free convection over two-dimensional and axisymmetric bodies of arbitrary contour. ASME J Heat Transf 96:435–442CrossRefGoogle Scholar
  7. 7.
    Raithby GD, Hollands KGT (1975) A general method of obtaining approximate solutions to laminar and turbulent free convection problems. Adv Heat Transf 11:266–315Google Scholar
  8. 8.
    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 187–192Google Scholar
  9. 9.
    Sparrow EM, Stretton AJ (1985) Natural convection from variously oriented cubes and from other bodies of unity aspect ratio. Int J Heat Mass Transf. 28:741–752CrossRefGoogle Scholar
  10. 10.
    Yovanovich MM (1987) New Nusselt and Sherwood numbers for arbitrary isopotential geometries at near zero Peclet and Rayleigh numbers. AIAA 22nd thermophysics conference, Honolulu, HawaiiGoogle Scholar
  11. 11.
    Yovanovich MM (1987) On the effect of shape, aspect ratio and orientation upon natural convection from isothermal bodies of complex shape. ASME HTD 82:121–129Google Scholar
  12. 12.
    Hassani AV, Hollands KGT (1989) On natural convection heat transfer from three-dimensional bodies of arbitrary shape. ASME J Heat Transf 111:363–371CrossRefGoogle Scholar
  13. 13.
    Jafarpur K (1992) Analytical and experimental study of laminar free convective heat transfer from isothermal convex bodies of arbitrary shape. PhD thesis, University of Waterloo, Waterloo, CanadaGoogle Scholar
  14. 14.
    Lee S, Yovanovich MM, Jafarpur K (1991) Effects of geometry and orientation on laminar natural convection from isothermal bodies. J Thermophys Heat Transf 5:208–216CrossRefGoogle Scholar
  15. 15.
    Yovanovich MM, Jafarpur K (1993) Bounds on laminar natural convection from isothermal disks and finite plate of arbitrary shape for all orientations and Prandtl numbers. ASME HTD 264:93–110Google Scholar
  16. 16.
    Yovanovich MM (2000) Natural convection from isothermal convex bodies: simple models for bounds on body gravity function. AIAA 34th thermophysics conference, Denver, COGoogle Scholar
  17. 17.
    Churchill SW, Churchill RV (1975) A comprehensive correlating equation for heat an component transfer by free convection. AICHE J 21:604–606CrossRefGoogle Scholar
  18. 18.
    Hassani AV (1987) An investigation of free convection heat transfer from bodies of arbitrary shape. PhD thesis, University of Waterloo, Waterloo, CanadaGoogle Scholar
  19. 19.
    Eslami M (2008) Dynamic behavior of body gravity function in laminar free convection heat transfer from isothermal convex bodies of arbitrary shape. MSc thesis, Shiraz University, Shiraz, IranGoogle Scholar
  20. 20.
    Bejan A (2004) Convection heat transfer, 3rd edn. Wiley, New YorkGoogle Scholar
  21. 21.
    Bigdely MR (1998) Calculation of conduction limit using panel method. MSc thesis, Shiraz University, Shiraz, IranGoogle Scholar
  22. 22.
    Eslami M, Jafarpur K (2008) Laminar free convection heat transfer from isothermal spheroids: a new dynamic model. In: 16th annual (international) mechanical engineering conference, Kerman, IranGoogle Scholar
  23. 23.
    Eslami M, Jafarpur K (2009) Laminar natural convection heat transfer from isothermal cones with active end. Iran J Sci Tech Trans B Eng 33:217–229MATHGoogle Scholar
  24. 24.
    Eslami M, Jafarpur K (2011) Laminar natural convection heat transfer from isothermal cylinders with active ends. Heat Transf Eng 32:506–513CrossRefGoogle Scholar
  25. 25.
    Chamberlain MJ (1983) Free convection heat transfer from a sphere, cube and vertically aligned bi-sphere. MSc thesis, University of Waterloo, Waterloo, CanadaGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShiraz UniversityShirazIran

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