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Heating of a film flowing over the surface of a rotating heat transfer device

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Abstract

The authors have solved the problem of a liquid flow over the surface of a rotating conic heat-transfer device with thermal boundary conditions of the second kind with account of heat losses to the vapor-gas phase. Relations have been obtained for calculation of the mean mass temperature, the Nusselt number, and other characteristics of the heating process of the film.

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Abbreviations

ν l , ν z :

meridional and normal velocity components, m/sec

ω:

angular velocity, sec−1

μ:

viscosity, Pa·sec

d :

thermal diffusivity, m2/sec

ϱ:

liquid density, m3/sec

g :

gravity acceleration, m2/sec

τ:

shear stress, Pa

q :

heat flux density, W/m2

λ:

thermal conductivity, W/(m·K)

Δ:

thickness of TBL, m

s :

dimensionless thickness of TBL

Q 0 :

liquid flow rate, m3/sec

δ0 :

thickness of the liquid film, m

r :

specific evaporation rate, J/kg

βν:

mass-transfer coefficient, m/sec

α:

heat transfer coefficient, W/(m2·K)

R * :

gas constant, J/(kg·K)

c p :

specific heat, J/(kg·K)

P sat :

saturated vapor pressure, Pa

ν:

kinematic viscosity, m2/sec

D :

diffusion coefficient, m2/sec

F 1 :

projection of the mass force onto the coordinate axisl, −m2/sec

g:

gas medium

s:

surface of the liquid film

0:

initial value of the parameter

References

  1. 1.

    V. M. Olevskii and V. R. Ruchinskii, Rotating Film Heat and Mass Transfer Apparatus [in Russian], Moscow (1977).

  2. 2.

    A. A. Bulatov, F. M. Gimranov, and N. Kh. Zinnatullin, Teor. Osnovy Khim. Tekhnol.24, No. 6, 735–742 (1990).

  3. 3.

    C. Gazley and A. Charwat, in: Heat and Mass Transfer, Minsk (1968), Vol. 10, pp. 401–419.

  4. 4.

    V. V. Dil'man and A. D. Polyanin, Methods of Model Equations and Analogies in Chemical Engineering [in Russian], Moscow (1988).

  5. 5.

    S. S. Kutateladze, Fundamentals of the Heat Transfer Theory [in Russian], Moscow (1979).

  6. 6.

    V. B. Kogan and M. A. Kharisov, Equipment for Vacuum Separation of Mixtures [in Russian], Leningrad (1976).

  7. 7.

    J. Perry, Handbook of a Chemical Engineer [Russian translation], Leningrad (1969), Vol. 1.

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Additional information

Kazan State Technological Institute, Kazan, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 781–788, September–October, 1995.

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Gimranov, F.M., Zinnatullina, G.N., Gavrilov, E.B. et al. Heating of a film flowing over the surface of a rotating heat transfer device. J Eng Phys Thermophys 68, 632–639 (1995). https://doi.org/10.1007/BF00858063

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Keywords

  • Boundary Condition
  • Heat Transfer
  • Statistical Physic
  • Heat Loss
  • Nusselt Number