Evaluation of building heating loads with dimensional analysis: Application of the Buckingham π theorem

Dimensional analysis is a means of simplifying a physical problem by appealing to dimensional homogeneity to reduce the number of relevant variables. In this work, the authors investigated an alternative approach to assess the thermal energy demand of a high-performance-non-residential building. It was possible to define some dimensionless numbers that synthetically describe the links between the main characteristic parameters of the thermal balance by applying the Buckingham π theorem. After a detailed description of the Buckingham π theorem and of its application concerning the evaluation of the building energy balance, the authors identified nine “ad hoc” dimensionless numbers. The proposed methodology has been validated by the comparison of the heating energy demand calculated by detailed dynamic simulations carried out in TRNSYS according to the standards and laws of building energy requirements in seven different European countries. Applying a set of criteria, it was possible to employ a dimensionless number to determine, immediately and without any calculation or use of steady/dynamic software, the heating energy demand with an reliability >90%.