Stochastic Finite Element Method for Modelling Heat Transfer in the Building Envelope

Technical University of Lodz, Department of Building Physics and Building Materials, Al. Politechniki 6, 90-924 Łódź, Poland

^* Corresponding author: witold.grymin@p.lodz.pl

Abstract

Improving the energy efficiency of the buildings is one of the most effective and fastest ways of reduction of the carbon dioxide emission. However, in the assessment of the energy demand of the buildings, numerous factors are uncertain, i.e. layer thickness, material parameters, climatic conditions, etc. In the present study, mathematical model was developed for analyzing temperature distribution and heat flux in the wall with thermal conductivity of insulation as a random parameter. The results obtained employing a stochastic perturbation technique were compared against the results of the Monte Carlo simulation. Stochastic perturbation technique has been implemented using the tenth order Taylor series expansion. The direct differential method was used to determine the values of Taylor’s coefficient. The obtained results indicate good accordance of the stochastic perturbation technique with the Monte Carlo method. Afterwards, the expected value of the heat flux and its variance were studied for the reference year for a city in the Central Europe. Two cases of the external wall were investigated, in which the thermal insulation was localized either on the internal or the external side of the wall. Performed analyses serve as a good method for assessing the reliability of results obtained using standard, deterministic approach.