2. Materials/methods

The main properties of heat exchangers, such as amount of heat exchange, area of heat exchange, metal capacity and cost of an apparatus depend largely on the size of ribbing, so

One of the authors of this paper, Khrustalev, looked into the criterion to assess the efficiency of heat exchanger design. The paper also suggests theoretical dependencies to calculate technical characteristics of heat exchangers. However, these dependencies do not allow optimization on

A.A. Melekhin in his previous papers studied the multicriterion optimization of the rib in heat

In the given paper the author makes a thermodynamic analysis and optimizes heat exchangers of air-cooling, at the same time these improvements are not based on the complex approach [8].

The occurrence of new methods, namely a complex method, allows combining mathematical modeling with visualization of heat fields, and as a result, obtaining optimal parameters of

The purpose of the given study is improving the efficiency of heat exchangers by optimizing

• we have developed a mathematical model of multicriterion problem to optimize heat

• using the mathematical model we developed, we have determined the mechanism of heat exchanging process and have derived dependencies of temperature distribution on heat

• we have made a comparison of the obtained results with the results based on the

• we have reduced the metal capacity of the heat exchanger by improving its heat engineer-

• we have elaborated a new complex research technique, based on multi-criterion problems

• we have obtained functional dependence of process parameters on heat exchanging sur-

• we have derived semiempirical equations for computing and designing air heating sys-

• we have reduced metal capacity of heat exchangers which are used in air heating systems

exchange surfaces in heating systems of buildings during the heating season;

exchangers based on two criteria; however, other parameters were not considered [7].

the efficiency of the design is determined by the optimal height of the rib [2, 3].

several parameters [4–6].

90 HVAC System

heat exchangers for the given systems.

To achieve this goal we set and solved the following tasks:

exchange on the ribbed heat exchanging surfaces.

established theoretical dependencies;

The novelty of the given paper lies in the following:

The practical value of the paper is in the following:

with generic dependencies, obtained from empirical data.

faces on optimal geometrical parameters of the heat exchanger.

their parameters and design.

ing characteristics.

tems in buildings;

of buildings.

In order to set optimal parameters for the heat exchanger and balance its design with technological elements the author conducted actual studies with the help of the complex method. It comprises optimization of parameters for heat exchanging process based on multicriterion multiparameter mathematical models and experiments with thermal field visualization.

The optimization problems are solved using the method of non-linear optimization in computing complex IOZO NM 3.0b [9].

Besides, the solution of such problems is also possible with the help of non-linear optimization program Generalized Reduced Gradient (GRG2), designed by Leon Lasdon, University of Texas at Austin and Allan Waren, Cleveland State University, and based on the method of conjugate gradients—iterative method for unconstrained optimization in multidimensional space. The main advantage of this software package is that it is able to solve the quadric optimization problem within finite number of moves. So, first the author describes the method of conjugate gradients to optimize the quadric functional, then he derives iterative formulas and estimates convergence rate. Next, the author demonstrates how the method of conjugate gradients is generalized to optimize arbitrary functional, looks at different variations of the method, and assesses convergence. The shortcoming is that controllable and non-controllable parameters and criteria are constrained [10].

It is possible to use as a mathematical model a two-criterion problem of clusterization with fuzzy constraints. The fuzzy constraints can be set by specific preference functions. The solution is made in Boolean variables with the help of stochastic search, improved by heuristics. The algorithm is implemented in the form of a universal software module [11].

Solution of multicriterion multiparameter nonlinear optimization problem of engineering systems in buildings suggested applying software package IOSO NM version 3.0b, where the author entered empirical data from thermal imaging. A special feature of this software is its compatibility with Microsoft Excel and other programs. IOSO package allows setting controllable and noncontrollable parameters, optimal criteria, and constraints for the process. Further, IOSO program establishes optimal process parameters by using the data from Excel.

Preliminary IOSO procedure is forming the initial experiment plan, which can be passive (using the previously obtained information about variable parameters, optimization criteria and constraints), as well as active, when the set is generated in the initial search field in accordance with the preset partition law. Each vector of variable parameters for optimization and constraints implies direct use of mathematical model of the object studied. The number of points in the initial experiment plan depends on the problem dimension and the chosen variant of approximation function.
