1. Introduction

The conduct of practical studies to optimize basic parameters in engineering systems of buildings is urged by power-saving requirements.

The given practical problem of improving engineering systems is to optimize the design of the heat exchanger in air heating systems of buildings.

Air heating systems of buildings are resource-consuming systems, for this reason, improving their resource efficiency appears to be of great significance.

Heating of air is provided by heat exchangers, which have been studied quite thoroughly. The studies involved different authors to deal with particular aspects of improving heat exchange elements [1].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

2. Materials/methods

puting complex IOZO NM 3.0b [9].

criteria are constrained [10].

mation function.

3. Results and discussion

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 Solution of Private Problems of Optimization for Engineering Systems

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The optimization problems are solved using the method of non-linear optimization in com-

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

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.

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,

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 approxi-

To find the minimum mass of the ribs of the heat-exchange apparatus with the maximum of its heat productivity developed mathematical model of multi-criteria optimization problem

The algorithm is implemented in the form of a universal software module [11].

IOSO program establishes optimal process parameters by using the data from Excel.

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 several parameters [4–6].

A.A. Melekhin in his previous papers studied the multicriterion optimization of the rib in heat exchangers based on two criteria; however, other parameters were not considered [7].

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 heat exchangers for the given systems.

The purpose of the given study is improving the efficiency of heat exchangers by optimizing their parameters and design.

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


The novelty of the given paper lies in the following:


The practical value of the paper is in the following:

