Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape: a new dynamic model Original First Online: 20 August 2011 Received: 03 November 2010 Accepted: 04 August 2011 DOI :
10.1007/s00231-011-0885-6

Cite this article as: Eslami, M. & Jafarpur, K. Heat Mass Transfer (2012) 48: 301. doi:10.1007/s00231-011-0885-6
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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 \( \sqrt A \)

G _{dyn} Dynamic body gravity function

Gr Grashof number

\( G^{\prime}_{\text{low}} \) Modified lower bound

h Convection heat transfer coefficient

h _{x} , h _{ω} 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.

Acrivos A (1960) A theoretical analysis of laminar natural convection heat transfer to non-newtonian fluids. AIChE J 6:584–590

CrossRef Google Scholar 2.

Saville DA, Churchill SW (1967) Laminar free convection in boundary layers near horizontal cylinders and vertical axisymmetric bodies. J Fluid Mech 29:391–399

MATH CrossRef Google Scholar 3.

Stewart WE (1971) Asymptotic calculation of free convection in laminar three-dimensional systems. Int J Heat Mass Transf 14:1013–1031

MATH CrossRef Google Scholar 4.

Lienhard JH (1973) On the commonality of equation for natural convection from immersed bodies. Int J Heat Mass Transf 16:2121–2123

CrossRef Google Scholar 5.

Sparrow EM, Ansari MA (1983) A refutation of king’s rule for multi-dimensional external natural convection. Int J Heat Mass Transf 26:1357–1364

CrossRef Google Scholar 6.

Lin FN, Chao BT (1974) Laminar free convection over two-dimensional and axisymmetric bodies of arbitrary contour. ASME J Heat Transf 96:435–442

CrossRef Google Scholar 7.

Raithby GD, Hollands KGT (1975) A general method of obtaining approximate solutions to laminar and turbulent free convection problems. Adv Heat Transf 11:266–315

Google Scholar 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 187–192

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. 28:741–752

CrossRef Google Scholar 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, Hawaii

11.

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

Google Scholar 12.

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

CrossRef Google Scholar 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, Canada

14.

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

CrossRef Google Scholar 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 264:93–110

Google Scholar 16.

Yovanovich MM (2000) Natural convection from isothermal convex bodies: simple models for bounds on body gravity function. AIAA 34th thermophysics conference, Denver, CO

17.

Churchill SW, Churchill RV (1975) A comprehensive correlating equation for heat an component transfer by free convection. AICHE J 21:604–606

CrossRef Google Scholar 18.

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

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, Iran

20.

Bejan A (2004) Convection heat transfer, 3rd edn. Wiley, New York

Google Scholar 21.

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

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, Iran

23.

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

MATH Google Scholar 24.

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

CrossRef Google Scholar 25.

Chamberlain MJ (1983) Free convection heat transfer from a sphere, cube and vertically aligned bi-sphere. MSc thesis, University of Waterloo, Waterloo, Canada

Authors and Affiliations 1. School of Mechanical Engineering Shiraz University Shiraz Iran