Design of an Algorithm for Modeling Multiple Thermal Zones Using a Lumped-Parameter Model

Pedro Fernández de Córdoba, Frank Florez Montes (), Miguel E. Iglesias Martínez, Jose Guerra Carmenate, Romeo Selvas and John Taborda
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Pedro Fernández de Córdoba: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Frank Florez Montes: Faculty of Engineering, Universidad Autónoma de Manizales, Manizales 170003, Colombia
Miguel E. Iglesias Martínez: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Jose Guerra Carmenate: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Romeo Selvas: Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, FCFM Av. Universidad S/N, Cd. Universitaria, San Nicolas de los Garza 66455, Nuevo León, Mexico
John Taborda: Faculty of Engineering, Universidad del Magdalena, Santa Marta 470003, Colombia

Energies, 2023, vol. 16, issue 5, 1-22

Abstract: The generation of mathematical models for the analysis of buildings with multiple thermal zones is a large and complex task. Furthermore, the order and complexity of the dynamical model are increased by the number of included thermal zones. To overcome this problem, this paper presents an algorithm to define the mathematical model automatically, using the geometric and physics parameters as inputs. Additionally, the spatial position of each thermal zone must be recorded in an arrangement called a contact matrix. The algorithm for modeling systems with multiple thermal zones is the main contribution of this work. This algorithm is presented in pseudocode format and as an annex, an implementation in MATLAB software. One of the advantages of this methodology is that it allows us to work with parallelepipeds and not necessarily cubic thermal zones. The algorithm allows us to generate mathematical models with symbolic variables, starting from the knowledge of how many thermal zones compose the system and its geometric organization. This information must be organized in a matrix arrangement called a contact matrix. Different arrays of thermal zones were constructed with wooden boxes to verify the functionality of the models generated with the algorithm. Each case provided information that allowed us to adjust the mathematical models and their simulations, obtaining a range of errors between experimental and simulated temperatures from 2.08 to 5.6 , depending on the number of thermal zones studied.

Keywords: buildings; lumped parameters; algorithm; mathematical model; experimental tests; reduced-scale models (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
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