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

Witold Grymin,Marcin Koniorczyk,J Kurnitski,T Kalamees

doi:10.1051/e3sconf/202017208007

Witold Grymin, Marcin Koniorczyk + Show 2 more

Open Access

https://doi.org/10.1051/e3sconf/202017208007

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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.

Highlights

In the calculations of the heat transfer in the building envelope, assumption of the strictly determined material parameters is usually made
Thermal conductivity of expanded polystyrene (EPS) was assumed as normally distributed with the parameters N(0.037, 0.0056)
The external temperature has been determined according to the climatic reference year for Poland [13] – see Fig. 1

Summary

Introduction

In the calculations of the heat transfer in the building envelope, assumption of the strictly determined material parameters is usually made. One of the properties which may differ from the values assumed in the mathematical models is the material thermal conductivity. In majority of the works concerning propagation of the uncertainty in the calculations of the energy demand, Monte Carlo method is usually applied. In this method, one has to determine the probability distribution of the uncertain parameters, perform sampling procedure and execute multiple runs of the mathematical models in order to determine distribution of the results. Probabilistic moments of the random field b(x), expected value and variance, may be defined as:

Mathematical model

Results

Conclusions