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

Frank Florez, Jesús Alejandro Alzate-Grisales, Pedro Fernández de Córdoba and John Alexander Taborda-Giraldo
Additional contact information
Frank Florez: Faculty of Engineering, Universidad Autónoma de Manizales, Manizales 170003, Colombia
Jesús Alejandro Alzate-Grisales: Faculty of Engineering, Universidad Autónoma de Manizales, Manizales 170003, Colombia
Pedro Fernández de Córdoba: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
John Alexander Taborda-Giraldo: Universidad del Magdalena, Santa Marta, Colombia

Energies, 2023, vol. 16, issue 6, 1-20

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; contact matrix; experimental test (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/16/6/2693/pdf (application/pdf)
https://www.mdpi.com/1996-1073/16/6/2693/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:16:y:2023:i:6:p:2693-:d:1096337

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().