# Application of Mathematical Models in Analysis of Heat Losses in the Buildings

## DOI:

https://doi.org/10.17770/etr2003vol1.1987## Keywords:

mathematical modelling, heat losses of building, heat balance of building, conductive, convective and radiation heat losses, LBN 002-01, apportionment of heat losses and sources in building, HeatMod## Abstract

*Physical model of heat balance for separate living room is discussed, which allows to analyse the distributions of the flow of air and temperature depending on the physical conditions and geometry. The model enables to choose the optimal surface area of building elements and their properties in order to decrease the heat losses and improve the conditions of thermal comfort. Room with bounding constructions and real dimensions is modelled that helps to understand the peculiarities of heat transfer process in the room as well as distribution of various characteristic quantities and their dependence on the different conditions. Multiple parameters are varied in 2D calculations and their influence on the distributions of temperature and velocity fields is analysed, which characterises the conditions of the thermal comfort. On the basis of considered model, the quantity of heat has been estimated that inflows or outflows through the bounding constructions. The power of convector is estimated, too, at a given temperature of the surface of convector. It is possible to estimate the heat transfer coefficients of the surfaces of bounding constructions with various properties, what requires considerable effort in real conditions of exploitation. One of the conditions of comfort is the temperature difference between frontal walls of the room – it should be less than some degrees. Essential role is played also by the intensity of air flow mostly because it increases heat transfer. Hence, flows between the room and outside environment are created with significant heat losses (so called convective heat losses). The influence of various geometric parameters on the character of the flow of air is analysed. The software ANSYS/FLOTRAN 5.5, where the turbulence is described by k- ? model, has been used for the elaboration of the heat balance model of the room.*

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## References

ANSYS 5.5. Theory Reference. http://www1.ansys.com/customer/conten/documentation/60/ Hlp_C_CH1.html

Самойлович, Г. С. Гидгогазодинамика. Москва, 1990.

Под редакцией Фроста, У., Моулдена, Т. Турбулентность. Принципы и применения. Москва, 1980.

Ландау, Л. Д., Лифшиц, Е. М.. Теоретическая физика – VI. Гидродинамика. Москва, 1986.

Jakovičs, A., Gendels, S., Trümmann, H. Modelling of Air Fluxes and Temperature Distribution in Heated Rooms. International Scientific Colloquium “Modelling of Saving Resources”, Rīga, Latvija, 17.-18. maijs, 2001.

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## Published

2006-06-26

## Issue

## Section

IT and Mathematical Methods in Environmental Sciences

## How to Cite

[1]

S. Gendels, “Application of Mathematical Models in Analysis of Heat Losses in the Buildings”,

*ETR*, vol. 1, pp. 341–346, Jun. 2006, doi: 10.17770/etr2003vol1.1987.