About One Approach to Calculation of Parameters of Heat Transfer Through Wall in Presence of Condensing Vapor

Abstract

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.