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 under constant heat flux on the wall, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(16), PP. 14 - 19.


heat transfer; heated liquid film; thermal entrance region


The classical problem of heating the laminar liquid film flowing down an inclined surface with a given heat flux on the wall is solved by analytical and numerical methods. The coefficient of heat transfer between liquid and gas is set on the film surface. For the thermal initial region, where liquid heating occurs in a thin near-wall layer and temperature disturbance does not have time to reach the interface, the analytical solution dependent on the self-similar variable is obtained. Temperature distribution at the end of the thermal initial region acts as the thermal profile for the subsequent flow region, where heat transfer between liquid and gas takes place and equilibrium temperature distribution is settled in liquid. The semi-analytical approach to description of heat transfer in the film based on the Galerkin method is proposed, in this approach, the deviation of liquid temperature from the equilibrium distribution is presented in the form of a series of basic functions satisfying the boundary conditions on the wall and interface. According to comparison of results obtained by the proposed method with the numerical solution by the finite-difference method, the results agree satisfactorily, when 8-10 basic functions are used. Calculation results obtained by the suggested semi-analytical method agree with experimental data at different heat fluxes and Reynolds numbers. The advantage of semi-analytical approach to the description of heat transfer in the liquid film lies in the effectiveness of the computational algorithm, which allows us to describe in detail the temperature field in the non-isothermal film with minimal computational costs. The suggested approach estimates theoretically the 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, in particular, for the case of a turbulent film.


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