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Buoyancy effects on heat transfer and liquid solidification-free zone in a convectively-cooled horizontal square channel

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Abstract

The effects of free convection on thermal entrance region problem and liquid solidification-free zone in a convectively-cooled horizontal square channel are studied by numerical method for steady-state fully developed laminar conditions using the large Prandtl number assumption. The Rayleigh number effects on the heat transfer results and the length of liquid solidification-free zone are investigated for Biot number of 2 and 20. It is concluded that the free convection effects should be included in the analysis of ice formation in a convectively-cooled pipe or channel when the Rayleigh number is greater than say 104.

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Abbreviations

A :

cross-sectional area of a channel

Bi :

Biot number,hD e/k

C :

a constant, (D e 2 /μW f)∂P f/∂Z

c p :

specific heat

D e :

hydraulic diameter, 4A/S

Gr :

Grashof number, [(T 0T )D e 3 ]/ν 2

f :

dummy variable

g :

gravitational acceleration

h :

average heat transfer coefficient

h :

heat transfer coefficient between inner wall and ambient defined by −k(∂T/∂N)w=h(T wT )

k :

thermal conductivity

M, N :

number of divisions inX andY directions, respectively, or outward normal at wall forN

Nu :

local Nusselt number,hD e/k

n :

dimensionless outward normal distance to the wall,N/D e, ornth iteration

P f :

pressure for fully developed laminar flow

Pr :

Prandtl number,ν/β

Ra :

Rayleigh number,Pr Gr

Re :

Reynolds number,u f D e/ν

S :

circumference of cross-section

T :

liquid temperature

T 0,T :

uniform entrance temperature and ambient temperature, respectively

T f :

freezing temperature of liquid

U, V :

velocity components of secondary flow inX andY directions, respectively

u, v :

dimensionless quantities foru, v, respectively

W f :

fully developed axial velocity

w f :

dimensionless quantity forW f

X, Y, Z :

rectangular coordinates

x, y, z :

dimensionless quantities forX, Y, Z respectively

z f :

liquid solidification-free length

β :

coefficient of thermal expansion

ε :

superheat ratio, (T 0T f)/(T fT )

θ :

dimensionless temperature difference, (TT )/(T 0T )

κ :

thermal diffusivity,k/ρc p

μ :

viscosity

ν :

kinematic viscosity

ξ :

vorticity function, 2 ψ

ρ :

density

ψ :

dimensionless stream function

b :

bulk average value

w :

value at wall

—:

average value

References

  1. [1]

    Zerkle, R. D. andJ. E. Sunderland, J. Heat Transrer90 (1968) 183.

  2. [2]

    DesRuisseaux, N. andR. D. Zerkle, Canadian J. Chem. Eng.47 (1969) 233.

  3. [3]

    Zerkle, R. D., Proc. 6th Southeastern Seminar on Thermal Sciences (1970) 1.

  4. [4]

    Lock, G. S. H., R. D. J. Freeborn andR. H. Nyren, Proc. 4th Int. Heat Transfer Cont., Versailles (1970) Cu 2.9, Elsevier, Amsterdam.

  5. [5]

    Schneider, P. J., Trans. Am. Soc. Mech. Engrs.79 (1957) 765.

  6. [6]

    Hsu, C. J., Chem. Eng. Sci.23 (1968) 457.

  7. [7]

    Cheng, K. C., S. W. Hong andG. J. Hwang, Int. J. Heat Mass Transfer15 (1972) 1819.

  8. [8]

    Ou, J. W., K. C. Cheng andR. C. Lin, Int. J. Heat Mass Transfer17 (1974) 835.

  9. [9]

    Hwang, G. J. andI. Yih, Int. J. Heat Mass Transfer16 (1973) 681.

  10. [10]

    Ostrach, S., Proc. 3rd Int. Heat Transfer Conf.6 (1966) 31, A.I.Ch.E., New York.

  11. [11]

    Knudsen, J. G. andD. L. Katz, Fluid Dynamics and Heat Transfer, McGraw-Hill, N. Y., 1958, p. 101.

  12. [12]

    Cheng, K. C. andJ. W. Ou, Proc. 5th Int. Heat Transfer Conf.3 (1974) 159.

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Ou, J., Cheng, K.C. Buoyancy effects on heat transfer and liquid solidification-free zone in a convectively-cooled horizontal square channel. Appl. Sci. Res. 30, 355–366 (1975). https://doi.org/10.1007/BF00705610

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Keywords

  • Heat Transfer
  • Biot
  • Prandtl Number
  • Rayleigh Number
  • Free Convection