2015 1(16)

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Aktershev S.P.1,2, Bartashevich M.V.1,2

1 Institute of Thermophysics SB RAS, Novosibirsk, Russia
2 Novosibirsk State University, Novosibirsk, Russia


Aktershev, S.P. and Bartashevich, M.V., (2015) Heating of the liquid film in the presence of shear stress at the interface, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(16), PP. 33 - 38.


heat transfer; heated liquid film; thermal entrance region; shear stress


Heating the laminar liquid film moving under the action of gravity and gas flow along the wall with the constant temperature is studied analytically and numerically. The effect of the gas flow on the film is accounted through the shear stress and heat transfer coefficient on the liquid surface. The analytical solution, dependent on the self-similar variable is obtained for the thermal initial section, where temperature perturbation has no time to reach the interface. Temperature distribution at the initial section acts as the thermal profile for the subsequent flow region, where heat transfer between liquid and gas takes place and equilibrium temperature distribution in liquid stabilizes. The semi-analytical method based on the Galerkin method is proposed, in this method the temperature field in liquid is presented in the form of a series of basic functions satisfying the boundary conditions on the wall and liquid surface. Comparison of calculations by the Galerkin method with the numerical solution by the finite-difference method shows that the use of 8-10 basic functions is enough for good matching of results. Good coordination takes place for both the case of falling film and cases of the co-current and counter-current gas flows. The proposed approach gives a theoretical estimate of distance, at which the equilibrium temperature distribution is set in liquid, and it can be easily generalized for the arbitrary velocity profile in the film and in the case of the wave flow of a liquid film. The suggested simplified method of calculation due to the efficient computational algorithm allows us to describe in detail the temperature field in the non-isothermal liquid film with the minimal computational costs.


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