Methodology for Modeling Multiple Non-Homogeneous Thermal Zones Using Lumped Parameters Technique and Graph Theory

Abstract

Asymmetric thermal zones or even non-rectangular structures are common in residential buildings. These types of structures are not easy to model with specialized programs, and it is difficult to know the heat flows and the relationships between the different variables. This paper presents a methodology for modeling structures with multiple thermal zones using the graph theory arrangement. The methodology allows for generating a mathematical model using all the walls of each thermal zone. The modeling method uses the lumped parameter technique with a structure of two resistors and two capacitors for each thermal zone. The walls and internal surfaces of each zone define the thermal resistances, and the elements for the network structure are created by reducing resistances. The structure selected as a case study is similar to a residential apartment, which demonstrates the possibility of modeling complex and non-traditional structures. The accuracy of the generated mathematical model is verified by comparison with experimental data recorded in a scaled-down model. The reduced model is constructed using a 1:10 ratio with a real apartment. The proposed methodology is used to generate a graph arrangement adjusted to the case study, using the surfaces to build the mathematical model. The experimental data allowed to adjust 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 non-asymmetric structures and to analyze individual levels in buildings.

Keywords

• mathematical model
• graph theory
• buildings
• lumped parameters
• thermal zones
• scale-reduced model