FEATURES OF OPTIMIZATION PROBLEM FOR SELECTING MATERIALS TO MINIMIZE HEAT LOSS THROUGH THE WALL

Abstract

The relevance. Heat storage and its effective use is associated with the selection of materials for thermal insulation of the walls. Such materials are represented by a wide range of thermophysical properties and cost in the market. Then the optimization problem arises, its solution should provide the smallest heat loss through the wall with a limited choice of materials with the given thermal conductivity coefficients. However, when solving the optimization problem, difficulties may arise in assessing the correctness of the results obtained. Therefore, this issue needs a detailed discussion. The main aim of the research is mathematical modeling of stationary modes of heat transfer, formulation of the minimax problem of heat loss through the wall, construction of the solution area of the minimax problem, the analysis of the results and conclusions. Object: wall, heat-insulating materials, heat fluxes, minimalist conditions, optimal solutions. Methods: solving a minimax problem using analytical methods. Results. The authors have stated the simple minimax problem: a two-layer flat wall is given with arbitrary heat conductivity coefficients and fixed thicknesses. On the right and left borders of the wall, a constant and different temperature is set. The maximum heat flux through the wall and the range of possible values of the thermal conductivity coefficients (i. e., possible materials) for each wall layer are also specified. It is required to find such heat conductivity coefficients from this region that ensure the heat flux below a given maximum value. This example shows that the solution of the minimax problem posed can lead to an incorrect result: either the whole range of feasible solutions can be obtained, or the problem may not have a solution. This means the need for a strict attitude to the formulation and method of solving optimization problems for heat transfer.