Transient Radiator Room Heating—Mathematical Model and Solution Algorithm

• Published in: Buildings (Basel) Vol. 8; no. 11; p. 163
• Main Authors: Teskeredzic, Armin, Blazevic, Rejhana
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 18.11.2018
• Subjects: Air temperature; Algorithms; Conduction heating; Conductive heat transfer; Conductivity; Energy consumption; Energy efficiency; Energy equation; Exact solutions; Finite volume method; Green buildings; Heat; Heat exchange; Heat flux; Heat transfer; Heating; Mathematical analysis; mathematical model; Mathematical models; Multilayers; numerical solution algorithm; radiator heating; Radiators; Robustness (mathematics); Temperature gradients; Thermal energy; Transient heat conduction; Transport equations; Ventilation; Walls
• ISSN: 2075-5309; 2075-5309
• DOI: 10.3390/buildings8110163

A mathematical model and robust numerical solution algorithm for radiator heating of an arbitrary room is presented in this paper. Three separate and coupled transient thermal energy equations are solved. A modified transient heat conduction equation is used for solving the heat transfer at multi-layer outer walls and room assembly. Heat exchange between the inner walls and the observed room are represented with their own transport equation and the transient thermal energy equation is solved for radiators as well. Explicit coupling of equations and linearization of source terms result in a simple, accurate, and stabile solution algorithm. Verification of the developed methodology is demonstrated on three carefully selected test cases for which an analytical solution can be found. The obtained results show that even for the small temperature differences between inner walls and room air, the corresponding heat flux can be larger than the transmission heat flux through outer walls or windows. The benefits of the current approach are stressed, while the plans for the further development and application of the methodology are highlighted at the end.