Transient Radiator Room Heating—Mathematical Model and Solution Algorithm
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-la...
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2018-11-01
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Online Access: | https://www.mdpi.com/2075-5309/8/11/163 |
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doaj-605720eba26b4caa9858cff56c5161392020-11-25T00:24:00ZengMDPI AGBuildings2075-53092018-11-0181116310.3390/buildings8110163buildings8110163Transient Radiator Room Heating—Mathematical Model and Solution AlgorithmArmin Teskeredzic0Rejhana Blazevic1Faculty of Mechanical Engineering, University of Sarajevo, Sarajevo 71000, Bosnia and HerzegovinaFaculty of Mechanical Engineering, University of Sarajevo, Sarajevo 71000, Bosnia and HerzegovinaA 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.https://www.mdpi.com/2075-5309/8/11/163radiator heatingmathematical modelnumerical solution algorithm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Armin Teskeredzic Rejhana Blazevic |
spellingShingle |
Armin Teskeredzic Rejhana Blazevic Transient Radiator Room Heating—Mathematical Model and Solution Algorithm Buildings radiator heating mathematical model numerical solution algorithm |
author_facet |
Armin Teskeredzic Rejhana Blazevic |
author_sort |
Armin Teskeredzic |
title |
Transient Radiator Room Heating—Mathematical Model and Solution Algorithm |
title_short |
Transient Radiator Room Heating—Mathematical Model and Solution Algorithm |
title_full |
Transient Radiator Room Heating—Mathematical Model and Solution Algorithm |
title_fullStr |
Transient Radiator Room Heating—Mathematical Model and Solution Algorithm |
title_full_unstemmed |
Transient Radiator Room Heating—Mathematical Model and Solution Algorithm |
title_sort |
transient radiator room heating—mathematical model and solution algorithm |
publisher |
MDPI AG |
series |
Buildings |
issn |
2075-5309 |
publishDate |
2018-11-01 |
description |
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. |
topic |
radiator heating mathematical model numerical solution algorithm |
url |
https://www.mdpi.com/2075-5309/8/11/163 |
work_keys_str_mv |
AT arminteskeredzic transientradiatorroomheatingmathematicalmodelandsolutionalgorithm AT rejhanablazevic transientradiatorroomheatingmathematicalmodelandsolutionalgorithm |
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1725354500305190912 |