Methodology for modeling multiple no homogeneous thermal zones using lumped parameters technique and graph theory

Abstract

[EN] n residential buildings the asymmetric thermal zones or even not rectangular structures are common. This kind of structure are not easy to model with specialized programs, and difficult to know the heat flows and relationships between different variables. This paper presents a methodology for modeling structures with multiple thermal zones using the graph theory arrangement. The methodology allows the generation of a mathematical model using all walls in each thermal zone. The modeling method uses the lumped parameter technique with two resistances and two capacitors structure for each thermal zone. The internal walls and surfaces in each zone define the thermal resistances, and the elements for the graph arrangement are created by resistances reduction. The structure selected as the study case is similar to a residential apartment, showing the possibility of modeling complex and non-traditional structures. The generated mathematical model accuracy is verified by comparison with experimental data recorded in a scale-reduced model. The reduced model is built using a relationship of 1:10 with an actual apartment. The proposed methodology is used for generating a graph array adjusted to the study case, using the surfaces for building the mathematical model. The experimental data allowed adjusting the simulation results with errors in the range of 1.88% to 6.63% for different thermal zones. This methodology can be used to model different apartments, offices or not asymmetric structures and analyze individual levels in buildings.