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A theoretical study of free convection in turbulent film boiling on a horizontal elliptical tube

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Abstract

The present theoretical study investigates turbulent film boiling on an isothermal elliptical tube under quiescent liquid. The effect of radiation is included in the present analysis. The results of the boiling heat transfer under the turbulent vapor show both the temperature and velocity present the non-linear distribution. Besides, under the free convection turbulent film boiling with higher Rayleigh values, the elliptical tube can get a better heat transfer efficiency than a circular tube. However, when Rayleigh values are low, the eccentricity of an elliptical tube seldom influences the heat transfer. Finally, a comparison between the results of the present study and those reported in a previous theoretical and experimental data is provided.

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Abbreviations

a, b :

semimajor, semiminior axis of ellipse

C p :

specific heat capacity (J/kg K)

D e :

equivalent circular diameter of elliptical tube (Eq. 8)

D + e :

shear parameter, D e u */νs

e :

eccentricity of ellipse, \({\sqrt {1 - (b/a)^{2}}}\)

\(Gr_{D_{e}}\) :

modified Grashof number, \(\frac{{g{\left({D_{\rm e}/2} \right)}^{3}}}{{\nu^{2}_{\rm s}}}\frac{{\rho_{\rm l} - \rho_{\rm s}}}{{\rho _{\rm s}}}\)

g :

acceleration due to gravity (m/s2)

h :

heat transfer coefficient [W/(m2 K)]

h fg :

latent heat (J/kg)

k :

thermal conductivity (W/m K)

k + :

k(T)/k(T s), Eq. (19)

D + e :

dimensionless shear parameter, D e u */νs

\((Nu_{D_{\rm e}})\) :

Local Nusselt number, h(D e/2)/k s

Nu m :

mean Nusselt number for whole tube surface

NR :

radiation parameter, ɛσT 3 s (D e/2)/k s

Pr :

Prandtl number, C p μ/k

Ra :

modified Rayleigh number, \(Gr_{D_{\rm e} Pr [0.5 + 1/S(T_{\rm r}-1)]}\)

S :

heat capacity parameter, C p T s/h fg

T :

temperature (K)

T r :

temperature ratio, T w/T s

T + :

dimensionless temperature, (T − T s)/(T w−T s)

u :

vapor velocity in x-direction (m/s)

u * :

shear velocity, \({\sqrt {\tau_{\rm w}/\rho}}\)

u + :

dimensionless velocity, u/u *

\({\mathop V\limits^{ \bullet}}\) :

local acceleration (m/s2)

v :

velocity normal to the direction of flow (m/s)

x :

peripheral coordinate (m)

y :

coordinate measured distance normal to elliptical surface (m)

y + :

dimensionless distance, yu */νs

δ:

vapor film thickness (m)

δ+ :

dimensionless film thickness (δu */νs)

μ:

absolute viscosity (kg/ms)

μ+ :

Eq. (17) (μ/μ s )

ν:

kinematic viscosity (m2/s)

ρ:

density (kg/m3)

τ:

shear stress (N/m2)

θ:

angle measured from bottom of tube

ϕ:

angle between the tangent to tube surface and the normal to direction of gravity

ɛm :

eddy diffusivity for momentum

ɛh :

eddy diffusivity for energy

ɛ:

emissivity

σ:

Stefan–boltzmann constant, W/m2 K4

l :

liquid

s :

vapor at saturation temperature

v :

vapor

w :

tube wall

x :

x-direction

δ:

vapor–liquid interface

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Acknowledgments

The current authors gratefully acknowledge the support provided to this project by the National Science Council of the Republic of China under Contract Number NSC-95-2221-E-165-001.

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Authors and Affiliations

  1. Department of Marine Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan, ROC

    Hai-Ping Hu

  2. Department of Mechanical Engineering, National Cheng Kung University, Tainan, 70101, Taiwan, ROC

    Cha’o-Kuang Chen

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  1. Hai-Ping Hu
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Correspondence to Cha’o-Kuang Chen.

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Hu, HP., Chen, CK. A theoretical study of free convection in turbulent film boiling on a horizontal elliptical tube. Heat Mass Transfer 44, 1171–1178 (2008). https://doi.org/10.1007/s00231-007-0354-4

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