We consider the problem of finding a geometrical form of a body in a thermal radiation field, for which the thermal balance between the body and the surrounding air is minimal. The case of a point source of heat is investigated. To consider an analogous problem for buildings, one must know the value of incoming thermal energy to a unit square in relation to its orientation. We develop an application package in MATLAB that represents this relation in table form and takes into consideration the direct, diffuse, ground-reflected solar radiation and the thermal radiation of atmosphere.

No abstract

To calculate the optimal parameters of outbuildings, a mathematical model and method for optimizing the shape and resistance of heat transfer for opaque and transparent structures with a certain constant number of faces, building volume and amount of insulation to minimize the thermal balance of enclosing structures with the environment during the heating period In the course of calculations the geometrical parameters of translucent, opaque structures in the heat-insulating shell of buildings are determined taking into account heat losses, heat influx from solar radiation by the criterion of ensuring minimum heat losses through enclosing structures, rational parameters (buildings) The given technique and mathematical models should be used in the future in the design of energy efficient buildings in the reconstruction and thermal modernization of buildings. This will increase their energy efficiency and, accordingly, the energy efficiency class of buildings. For the research faceted attached building in the form of a triangular pyramid, the reduction in heat loss was 14.82 percent only due to the optimization of the shape and redistribution of the insulation. Similar results were obtained for other initial forms. For the first time, a computerized method was proposed, an algorithm and application package Optimparam for multiparameter shape optimization and insulation of translucent and opaque structures for outbuildings with a given number of arbitrarily arranged faces were developed.