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Laminar forced convection heat transfer from isothermal cylinders with active ends and different aspect ratios in axial air flows

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Abstract

In this article a semi-analytical approach is employed to obtain dimensionless heat transfer correlations for forced convection from isothermal circular cylinders with active ends and different aspect ratios \( (l/d \le 8) \) in laminar axial air flows. Then, using the present results and previous works, the modeling is extended to higher aspect ratios \( (l/d \ge 8) \)) as long as the entire flow field remains completely laminar. Validations of the present work are done not only with the available data on drag coefficients but with previous works for long cylinders with inactive ends and long spheroids. Two general correlations are also developed for a rough estimate of forced convection heat transfer from isothermal cylinders with active ends and arbitrary aspect ratios in the range of \( \frac{1}{2} \le \frac{l}{d} \le 8 \) and \( l/d \ge 8 \).

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Abbreviations

A :

Body surface area (m2)

A e :

Surface area of the volume equivalent sphere (m2)

b :

Reynolds’ exponent for best curve fitting (Eqs. 29, 31, 33, 35, 37, 39, 41, 43, 45, 47)

c :

Specific heat (J/kg K)

\( C_{\sqrt A } \) :

Coefficient in Eq. 27 (Eqs. 38–47)

C d :

Coefficient in Eqs. (28–37) (Table 3)

D :

Diameter of tubular domain (m) (Fig. 3)

d :

Diameter (m)

d e :

Diameter of the volume equivalent sphere (m)

h :

Convection heat transfer coefficient (W/m2 K)

k :

Thermal conductivity (W/m K)

L :

Length of tubular domain (Fig. 3)

l :

Cylinder length (m)

Nu :

Nusselt number

\( Nu_{\sqrt A } \) :

Nusselt number based on square root of surface area

\( Nu_{\sqrt A ,\,l.b.l} \) :

Convective Nusselt number obtained for the laminar boundary layer solution

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

Conduction limit based on square root of surface area

\( Nu_{d}^{ \circ } \) :

Conduction limit based on diameter

Nu d :

Nusselt number based on diameter

Pe :

Peclet number

Pr :

Prandtl number

R :

The distance from the axis of symmetry to the surface of the body (m), (Fig. 1)

Fig. 1
figure 1

Coordinates for thin thermal boundary layer approximation

Full size image
Re :

Reynolds number

Re d :

Reynolds numbers based on diameter

\( Re_{\sqrt A } \) :

Reynolds numbers based on square root of surface area

s :

Upstream distance (m) (Fig. 3)

T :

Temperature (K)

T s :

Body surface temperature (K)

T ∞ :

Flow temperature (K)

t :

Time (s)

U :

External flow velocity (m/s)

u x :

Velocity component in the direction of x (m/s)

u y :

Velocity component in the direction of y (m/s)

v :

Axis of abscissa in Fig. 2

Fig. 2
figure 2

Geometric parameters of cylindrical body

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w :

Axis of ordinate in Fig. 2

x :

Coordinate parallel to the surface of the body (Fig. 1)

X :

Dimensionless x, Eq. 10

X M :

Maximum value of X

y :

Coordinate normal to the surface of the body (Fig. 1)

α :

Thermal diffusivity (m2/s)

ɛ :

Average error of curve fitting

ζ s :

Surface vorticity (s−1)

Ξ:

Dimensionless R, Eq. 11

ρ :

Density (kg/m3)

References

  1. Clift R, Grace GR, Weber ME (1978) Bubbles, drops and particles. Academic Press, New York

    Google Scholar 

  2. Polyanin AD, Kutepov AM, Vyazmin AV, Kazenin DA (2002) Hydrodynamics, mass and heat transfer in chemical engineering. Taylor and Francis, London

    Google Scholar 

  3. Kreith F, The CRC (2000) Handbook of thermal engineering. The mechanical engineering handbook series. CRC Press/Springer, New York

    Google Scholar 

  4. Pop I, Kumari M, Nath G (1989) Combined free and forced convection along a rotating vertical cylinder. Int J Eng Sci 27(3):193–202

    Article  Google Scholar 

  5. Richelle E, Tasse R, Riethmuller ML (1995) Momentum and thermal boundary layer along a slender cylinder in axial flow. Int J Heat Fluid Flow 16:99–l05

    Google Scholar 

  6. Agarwala M, Chhabraa RP, Eswaranb V (2002) Laminar momentum and thermal boundary layers of power-law fluids over a slender cylinder. Chem Eng Sci 57:1331–1341

    Article  Google Scholar 

  7. Wiberg R, Lior N (2005) Heat transfer from a cylinder in axial turbulent flows. Int J Heat Mass Transf 48:1505–1517

    Article  Google Scholar 

  8. Sawchuk SP, Zamir M (1992) Boundary layer on a circular cylinder in axial flow. Int J Heat Fluid Flow 13(2):184–188

    Article  Google Scholar 

  9. Bourne DE, Davies DR (1958) Heat transfer through the laminar boundary layer on a circular cylinder in axial incompressible flow. QJMAM 11(1):52–66

    MATH  MathSciNet  Google Scholar 

  10. Seban RA, Bond R (1951) Skin -friction and heat-transfer characteristics of a laminar boundary layer on a cylinder in axial incompressible flow. J Aeronaut Sci 18:671–675

    MATH  Google Scholar 

  11. Nowak W, Stachel AA (2005) Convection heat transfer during an air flow around a cylinder at low Reynolds number regime. J Eng Phys Thermophys 78(6):1214–1221

    Article  Google Scholar 

  12. Hoerner SF (1965) Fluid-dynamic drags (Published by the Author)

  13. Patankar S (1987) Numerical heat transfer and fluid flow. Hemisphere, Washington, DC

    Google Scholar 

  14. Yovanovich MM (1987) Natural convection from isothermal spheroids in the conductive to laminar flow regimes. In: Proceedings of AIAA 22nd Thermophysics Conference, June 8–10, Honolulu, Hawaii

  15. Yovanovich MM (1988) General expression for forced convection heat and mass transfer from isothermal spheroids. In: Proceedings of AIAA 26th Aerospace Science meeting, January 11–14, Reno, Nevada

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

    Article  Google Scholar 

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

  18. Bigdely MR (1998) Conduction limit calculation using panel method. M.S thesis, Shiraz University, Shiraz, Iran

  19. Smythe WR (1956) Charged right circular cylinder. J Appl Phys 27(8):917–920

    Article  MATH  MathSciNet  Google Scholar 

  20. Smythe WR (1962) Charged right circular cylinder. J Appl Phys 33(10):2966–2967

    Article  MATH  Google Scholar 

  21. Yovanovich MM, Culham JR, Lee S (1996) Natural convection from horizontal circular and square toroids and equivalent cylinders. 96–1838 at the 31st AIAA Thermophysics Conference, June 18–20, New Orleans, LA

  22. McAdams (1954) Heat transmission. 3rd edn. McGraw-Hill, New York

  23. White FM (2003) Fluid mechanics. 5th edn. McGraw-Hill Series in Mechanical Engineering

  24. Culham JR, Yovanovich MM, Teertstra P, Wang C-S, Refai-Ahmed G, Min-Tain Ra (2001) Simplified analytical models for forced convection heat transfer from cuboids of arbitrary shape. J Electron Packag 123:182–188

    Article  Google Scholar 

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Authors and Affiliations

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

    Yaser Hadad & Khosrow Jafarpur

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  1. Yaser Hadad
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  2. Khosrow Jafarpur
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Correspondence to Khosrow Jafarpur.

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Hadad, Y., Jafarpur, K. Laminar forced convection heat transfer from isothermal cylinders with active ends and different aspect ratios in axial air flows. Heat Mass Transfer 47, 59–68 (2011). https://doi.org/10.1007/s00231-010-0669-4

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