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The article is dedicated to the study of heat exchangers operation. The main goal of the work was to improve a standard method for calculating a typical heat exchanger based on dependencies approved in engineering practice. The noted technique is presented in educational literature for chemical engineers and it is included in the educational process for the training of engineers. On the basis of practical recommendations stated in literature the working formulas of the process are taken in approximate form. Further, a correction is calculated, which, as calculations show, leads (together with the initial approximation) to an almost exact satisfaction of the initial equations. It is expedient because traditional equations of a heat transfer have not really high precision, which is determined by the processing of numerous experiments. These experiments are rather rough. It is reasonable that the accuracy of the analysis has to be consistent with the model accuracy. This factor justifies the need to simplify the models (use of various recommendations based on the experience of equipment operation, etc.). At the same time, it is desirable to simplify the mathematical model equation so that it is possible to calculate the corrections, i.e. to clarify the solution. We clarify the equation solution meaning more and more exact satisfaction with the initial equation of the mathematical model. In this direction, various variants of perturbation methods can be used. The search for analytical solutions is complicated by the fact that the equations of the mathematical model of energy transfer in a heat exchanger are nonlinear. The three-layer heat transfer problem in a stationary mode is considered.  The first layer is the space of the heat exchanger where a phase transition (first heat transfer agent vapor condensation) occurs. The second layer is the space of the heat exchanger where convective movement of the second heat transfer agent takes place without phase transition. The third layer is a wall separating the heat transfer agent providing some resistance to the heat transfer process. As a result of the simplified model analysis, it became possible to obtain an analytical solution to the problem with such accuracy that the calculated correction turned out to be insignificant i.e. the correction is not appropriate to take into account. The solution found was almost exactly approximated by a simple analytic dependence.

In the present study, the problem of vapor condensation on a flat vertical surface is investigated in the case of an arbitrary dependence of the dynamic viscosity coefficient on temperature according to a fairly general law. At a constant value of this coefficient and other characteristics of a condensing liquid (heat conductivity coefficient, density) this task was considered by Nusselt in a constant gravitational field. The results obtained by Nusselt formed the basis (with certain modifications) for the computational practice of heat exchange equipment of chemical technology in the presence of steam condensation of any heat carrier. Formation of a condensate film occurs due to heat transfer through the liquid film, vapor condensation at the outer edge of the film and the flow of liquid along the surface. The article generalizes the Nusselt theory for the heat transfer coefficient under the indicated conditions, and as a result, convenient calculation formulas for the heat transfer coefficient, which are necessary to describe the operation of heat and mass exchange equipment. Approximate relations are proposed for calculating the dynamic viscosity coefficient, which are useful for calculating film flow on a flat surface. A comparison is made with the previously used ratios in an approximate manner taking into account the dependence of viscosity coefficient on temperature. When in technical applications one wants to determine the average value of two parameters, which are then used to calculate certain characteristics of a process, then, traditionally, the average of these parameters is considered. This article shows that by simplifying the dependence of the effective dynamic viscosity coefficient, more accurate results are obtained by dividing the interval of the width of the current film in the ratio of three to one, where three fourths refer to the wall temperature, and one fourth to the condensation temperature. The analytical dependencies presented in this paper can be used for practical calculations of the heat exchange equipment.