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

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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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ν l , ν z :

meridional and normal velocity components, m/sec


angular velocity, sec−1


viscosity, Pa·sec

d :

thermal diffusivity, m2/sec


liquid density, m3/sec

g :

gravity acceleration, m2/sec


shear stress, Pa

q :

heat flux density, W/m2


thermal conductivity, W/(m·K)


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


mass-transfer coefficient, m/sec


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


kinematic viscosity, m2/sec

D :

diffusion coefficient, m2/sec

F 1 :

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


gas medium


surface of the liquid film


initial value of the parameter


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