Abstract
A mathematical model for calculating the thermohydrodynamic situation during film condensation based on the equations of conservation of mass, momentum and energy for the refrigerant in a limited area, the condensate film flowing and the gas phase in a two-dimensional formulation is constructed. The dependence of the viscosity of the working medium on the temperature is taken into account. The boundary conditions of conjugation are specified on the inner wall of the refrigerant flow region, the outer wall through which the condensate film flows, and also at the film-gas interface. The obtained boundary value problem is solved by approximate and numerical methods together with the condition for determining the unknown film thickness, which allows the calculation of all characteristics of the condensation process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. G. Akhmadiev, M. I. Farakhov, and A. A. Akhmitshin, “Mathematical modeling of the film-type condensation process,” Vestnik Tekhnologicheskogo Universiteta, No. 17, 32–35 (2017).
Two-Phase Flow and Heat Transfer, Ed. by D. Butterworth and G. F. Hewitt (Oxford Univ. Press, Oxford, 1977).
A. A. Mikhalevich, Mathematical Modeling of Mass and Heat Transfer during Condensation (Nauka Tekh., Moscow, 1982) [in Russian].
S. S. Kutateladze, Heat Transfer during Condensation and Boiling (Mashgiz, Moscow, 1953) [in Russian].
Handbook on Heat Exchangers, Ed. by B. S. Petukhov and V. K. Shikov (Energoatomizdat, Moscow, 1987) [in Russian].
L. P. Kholpanov and V. Ya. Shkadov, Hydrodynamics and Heat and Mass Transfer with Interface Surface (Nauka, Moscow, 1990) [in Russian].
D. A. Labuntsov, “On the influence of dependence of physical parameters of the condensate on temperature during film condensation of vapor,” Teploenergetika, No. 1, 49–52 (1957).
W. Nusselt, “Surface condensation of water vapours,” Z. Ves. Dt. Ing. 26 (60), 569–575 (1916); Z. Ves. Dt. Ing. 27 (60), 541–546 (1916).
J. A. Al-Jarrah, A. F. Khadrawe, and M. A. AL-Nimr, “Film on condensation on a vertical microchannel,” Int. Commun. Heat Transfer 35, 1172–1176 (2008).
F. Hassaninejadafarahani and S. Ormiston, “Numerical analyses of laminar reflux condensation from gasvapour mixtures in vertical parallel plate channels,” Int. J. Mech. Mechatron. Eng. 9, 794–801 (2015).
S. M. Targ, Fundamental Problems of the Theory of Laminar Flows (Gos. Izd. Tekh. Teor. Liter., Moscow, 1951) [in Russian].
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Akhmadiev, F.G., Farakhov, M.I. & Akhmitshin, A.A. Mathematical Model of Conjugate Heat and Mass Transfer at Film Condensation. Lobachevskii J Math 40, 711–717 (2019). https://doi.org/10.1134/S1995080219060040
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080219060040