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Journal of engineering physics

, Volume 39, Issue 4, pp 1043–1046 | Cite as

Heat exchange in a draining liquid film in the initial thermal part

  • V. M. Sobin
Article

Abstract

An approximate solution of the heat-transfer problem in a draining liquid film with a parabolic velocity profile and boundary conditions of the second kind is given.

Keywords

Boundary Condition Statistical Physic Approximate Solution Velocity Profile Heat Exchange 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

Θ=(t−to)/(Hδ/λ)

dimensionless temperature

to

temperature of the liquid at the entrance

Θ1, Θ2

dimensionless temperature of the wall and free surface

Θav

dimensionless average temperature of the liquid over the transverse cross section of the film

H

density of the heat flow on the wall

ξ=(x/δ)Pe, η=y/δ

dimensionless coordinates

δ

thickness of the film

Pe=uoδ/a

Peclet criterion

uo

velocity on the free surface

λ,a

thermal conductivity and thermal diffusivity of the liquid

q(ξ)

thickness of the thermal boundary layer

n1, n2

parameters of the temperature profile in the first and second stages of the process

Nu=aδ/λ, <Nu>=<a>δ/λ

local and average Nusselt numbers

α, <a>

local and average heat-transfer coefficients

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Literature cited

  1. 1.
    E. G. Vorontsov and Yu. M. Tananaiko, Heat Exchange in Liquid Films [in Russian], Tekhnika, Kiev (1972).Google Scholar
  2. 2.
    V. Besckov, C. Boyadjiev, and G. Peev, “On the mass transfer into a falling laminar film with dissolution,” Chem. Eng. Sci.,33, No. 1, 65–69 (1978).Google Scholar
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    R. A. Seban and A. Faghri, “Wave effects on the transport to falling laminar liquid films,” Trans. ASME J. Heat Transfer,100, No. 1, 143–147 (1978).Google Scholar
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    A. I. Veinik, Approximate Calculation of Thermal Conduction Processes [in Russian], Gosénergoizdat, Moscow-Leningrad (1959).Google Scholar
  5. 5.
    M. A. Biot, Variational Principles in Heat Transfer, Oxford Univ. Press (1970).Google Scholar
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    B. Vujanovic and Dj. Djukic, “On the variational principle of Hamilton's type for nonlinear heat transfer problem,” Int. J. Heat Mass Transfer,15, No. 5, 1111–1123 (1972).Google Scholar
  7. 7.
    N. N. Koval'nogov, “Effect of certain factors on the heat transfer of laminar liquid films,” Izv. Vyssh. Uchebn. Zaved., Aviatsion. Tekh., No. 1, 53–58 (1978).Google Scholar
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    P. L. Kapitsa, “Wavy flow of thin layers of a viscous liquid,” Zh. Eksp. Teor. Fiz.,18, No. 1, 3–28 (1948).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • V. M. Sobin
    • 1
  1. 1.S. M. Kirov Belorussian Technological InstituteMinsk

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