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Analysis of laminar film boiling in boundary layer flows with appreciable radiation

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Summary

This paper presents the theoretical study of the heat transfer and friction characteristics in the natural convection film boiling on an inclined surface and a sphere, the forced convection film boiling over a horizontal plate, and the stagnation flow film boiling when radiation is appreciable. The boiling liquid is either at the saturation temperature or subcooled. The two phase flow and heat transfer problems have been formulated exactly within the framework of boundary layer theory with the consideration of the shear stress and vapor velocity at the liquid-vapor interface. Through the use of the similarity transformation expressions are obtained to determine the vapor film thickness, skin friction, and heat transfer rate. It is disclosed that the presence of surface radiation results in an increase in the heat transfer rate and a decrease in the skin friction.

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Abbreviations

a :

constant defined with U ∞=ax for stagnation flow

A :

physical parameter, (15f)

B :

physical parameter, (7g)

B 1 :

physical parameter, (15f)

C p :

specific heat

D :

physical parameter, (13c)

E :

physical parameter, defined as h fg Pr C −1p (T w−T s)−1

F :

temperature variable, (9c) and (18d) for natural convection film boiling and (25c) and (28b) for forced convection film boiling

f :

velocity variable, (9b) and (18c) for natural convection film boiling and (25b) for the forced convection film boiling

g :

gravitational acceleration

h :

local heat transfer coefficient, q/(T w−T s)

h fg :

latent heat of evaporation

k :

thermal conductivity

Nu :

Nusselt number

Pr :

Prandtl number

Re :

Reynolds number

p :

pressure

q :

local heat flux from wall to vapor

R :

radius of sphere

T :

temperature: T w = wall temperature; T s = saturated temperature; T ∞ = free stream temperature

U ∞ :

free stream velocity

u :

velocity component of vapor in x direction

v :

velocity component of vapor in y direction

x :

coordinate measuring distance along the plate from leading edge

y :

coordinate normal to plate

α :

thermal diffusivity

α r :

absorption coefficient of vapor

β :

coefficient of thermal expansion

δ :

thickness of vapor film, (8) and (18a) for natural convection film boiling and (24) for forced convection film boiling

ε :

emissivity

η :

similarity variable, (9a) and (18b) for natural convection film boiling and (25a) and (28a) for forced convection film boiling

ησ:

dimensionless vapor film thickness

θ :

dimensionless temperature defined as (T−T s)/(T w−T s) for vapor film and (T L−T ∞)/(T s−T ∞) for liquid layer.

ν :

kinematic viscosity

ρ :

density

ρ r :

refractivity

σ :

Stefan-Boltzmann constant

φ :

angle of inclination or x/R

ψ :

stream function, (9b) and (18c) for natural convection film boiling and (25b) and (28b) for forced convection film boiling

L:

liquid phase

r:

radiation

s:

at saturated state

w:

wall surface

∞:

free stream

‴, ″, ′:

differentiation with respect to η

References

  1. Yeh Hsu-Chieh and Wen-Jei Yang, Radiation Effects on Film Boiling in Natural- and Forced-Convection Boundary-Layer Flows, report No. 66-WA/HT-6, ASME Winter Meeting, New York 1966.

  2. Bromley, L. A., Chem. Eng. Progress 46 (1950) 221.

    Google Scholar 

  3. Ellion, M. E., A Study of the Mechanism of Boiling Heat Transfer, Memo No. 20-88, JPL, Cal. Inst. of Techn., Pasadena (Cal.) 1954.

    Google Scholar 

  4. Hsu, Y. Y. and J. W. Westwater, Chem. Eng. Progress Symp. Ser. (Heat Transfer-Storrs) 56 (No. 30, 1960) 15.

  5. McFadden, P. W. and R. J. Grosh, Intern. J. Heat Mass Transf. 1 (1961) 325.

    Google Scholar 

  6. Cess, R. D., Trans. ASME Ser. C 81 (1959) 1.

    Google Scholar 

  7. Koh, S. C. Y., ASME J. Heat Transf. Ser. C 84 (1962) 52.

    Google Scholar 

  8. Sparrow, E. M. and R. D. Cess, ASME J. Heat Transf. Ser. C 84 (1962) 149.

    Google Scholar 

  9. Koh, J. C. Y. and T. W. Nilson, Simultaneous Convection and Radiation in Laminar Film Boiling on Vertical Surfaces, report No. 63-HT-2, ASME, New York 1963.

    Google Scholar 

  10. Cess, R. D. and E. M. Sparrow, ASME J. Heat Transf. Ser. C 84 (1962) 370.

    Google Scholar 

  11. Cess, R. D. and E. M. Sparrow, ASME J. Heat Transf. Ser. C 84 (1962) 377.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mech. Eng., The University of Michigan, Ann Arbor, Mich., USA

    Hsu-Chieh Yeh & Wen-Jei Yang

Authors
  1. Hsu-Chieh Yeh
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  2. Wen-Jei Yang
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Yeh, HC., Yang, WJ. Analysis of laminar film boiling in boundary layer flows with appreciable radiation. Appl. Sci. Res. 20, 178–204 (1969). https://doi.org/10.1007/BF00382392

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  • DOI: https://doi.org/10.1007/BF00382392

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