Modeling Coupled Heat and Mass Transfer upon Film Condensation
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ling Coupled Heat and Mass Transfer upon Film Condensation F. G. Akhmadieva, *, M. I. Farakhovb, and A. A. Akhmitshinb aKazan b
State University of Architecture and Engineering, Kazan, 420043 Republic of Tatarstan, Russia OOO Engineering-Promotional Center Inzhekhim, Kazan, 420049 Republic of Tatarstan, Russia *e-mail: [email protected] Received January 31, 2020; revised February 7, 2020; accepted February 14, 2020
Abstract—A mathematical model of film condensation is constructed which is obtained based on the equations for the conservation of mass, momentum, and energy for a heat-transfer fluid in the limited region of the condensate film and gas phase flowing down the surface of the wall of a heat exchanger in a two-dimensional setting. Equations for conserving the momentum of this model take into account the change in the physical properties of the heat-transfer fluid and condensate film depending on temperature. The boundary conditions of coupling are written for the regions on the inner wall of the flow range of the heat-transfer fluid and outer wall along which the condensate film flows, as well as at the film–gas interface. The boundary problem is solved by approximate and numerical methods, together with the condition for determining the unknown thickness of the film for different settings of the thermodynamic problem. Computational and physical experiments are conducted to study the main parameters and regularities of the process. Keywords: mathematical model, coupled heat and mass transfer, film condensation, computational experiment DOI: 10.1134/S0040579520040132
INTRODUCTION The heat- and mass-transfer processes upon condensation and vaporization (boiling) are widely used in various fields of engineering and technology when cooling various working surfaces in technological processes, in the energy sector, etc. Condensation is one of the most common technology processes. Processes with condensation have a high ratio in chemical technology and related industrial sectors. Multiple works, including reviews [1–6], are devoted to studying various aspects of the processes of condensation. Depending on the possible mechanisms of formation of a condensate, the following condensation modes are distinguished [1]: film, homogeneous, and drop condensations; condensations upon a direct contact; and the condensation of vapors of immiscible liquids. Film condensation is the most common type of mode in the industrial apparatuses. Success in the development and industrial implementation of principally new process schemes of condensation and highly effective apparatuses, as well as intensification of the operation of the existing ones, are only possible in the case of the existence of modern, accurate, and reliable methods for calculating them constructed based on mathematical models of the corresponding processes. The mathematical modeling of the processes of heat and mass transfer upon condensation is a complex problem. In real condens-
ers, there is a combination of various hydrodynamic flow regimes of the gas and c
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