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Heat conduction in two and three dimensions : computer modelling of building physics applications

Blomberg, Thomas LU (1996) In Report TVBH 1008.
Abstract
The first aim of this doctoral work has been to develop a new generation of computer programs for transient and steady-state heat conduction in two and three dimensions.



A large range of heat transfer problems within the field of buildings physics can be analyzed using these tools. There are, however, many things to keep in mind when modelling a problem, such as how to choose the numerical mesh, the proper boundary conditions, numerical accuracy, numerical stability, etc. The second aim of the thesis is to provide advice and guidelines how to deal with various problems that occur in building physics applications. To this aim, a large part is devoted to specific problems.



The third aim of the thesis is... (More)
The first aim of this doctoral work has been to develop a new generation of computer programs for transient and steady-state heat conduction in two and three dimensions.



A large range of heat transfer problems within the field of buildings physics can be analyzed using these tools. There are, however, many things to keep in mind when modelling a problem, such as how to choose the numerical mesh, the proper boundary conditions, numerical accuracy, numerical stability, etc. The second aim of the thesis is to provide advice and guidelines how to deal with various problems that occur in building physics applications. To this aim, a large part is devoted to specific problems.



The third aim of the thesis is to address a number of particular topics and problems: Numerical accuracy, successive over-relaxation, methods to increase accuracy by combining results from calculations using different numerical meshes, solution of large three-dimensional problems, solution of problems with large difference in thermal conductivity (steel versus insulation), heat conduction coupled to radiation in cavities, how to obtain a proper U-value for a foundation with floor heating, etc.



The robust method of explicit finite differences is used. This method closely follows the physical equations. The mathematical equations for two- and three-dimensional heat conduction and the numerical formulation are presented. The numerical error for different meshes is studied and compared with analytical solutions. The effectiveness of the method of successive over-relaxation is demonstrated, while the gain using "successive subdivision'' is modest. Results from calculations with two or three different meshes may be used to estimate more accurate results. The gain using this technique can be quite substantial.



The problem of thermal radiation in a cavity coupled to heat conduction and ventilation is analyzed in detail. The presented equations are well suited for an iterative computer solution procedure, which turns out to be robust and very rapid. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Prof. Johannesson, Gudni, KTH
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Byggnadsteknik, Building construction, civil engineering, building physics, thermal radiation, numerical modelling, Heat conduction, computer programs
in
Report TVBH
volume
1008
pages
188 pages
publisher
Byggnadsfysik LTH, Lunds Tekniska Högskola
defense location
Sektionen för väg- och vattenbyggnad, John Ericssons väg 1, Hörsal V:A, Tekniska fakulteten vid Lunds universitet
defense date
1996-06-05 13:15
external identifiers
  • other:TVBH-1008
ISSN
0349-4950
ISBN
ISBN 91-88722-05-8
language
English
LU publication?
yes
id
f395d13d-2e1d-449f-9c15-0dc2a64de552 (old id 17728)
date added to LUP
2007-05-24 09:06:37
date last changed
2016-09-19 08:44:55
@phdthesis{f395d13d-2e1d-449f-9c15-0dc2a64de552,
  abstract     = {The first aim of this doctoral work has been to develop a new generation of computer programs for transient and steady-state heat conduction in two and three dimensions.<br/><br>
<br/><br>
A large range of heat transfer problems within the field of buildings physics can be analyzed using these tools. There are, however, many things to keep in mind when modelling a problem, such as how to choose the numerical mesh, the proper boundary conditions, numerical accuracy, numerical stability, etc. The second aim of the thesis is to provide advice and guidelines how to deal with various problems that occur in building physics applications. To this aim, a large part is devoted to specific problems.<br/><br>
<br/><br>
The third aim of the thesis is to address a number of particular topics and problems: Numerical accuracy, successive over-relaxation, methods to increase accuracy by combining results from calculations using different numerical meshes, solution of large three-dimensional problems, solution of problems with large difference in thermal conductivity (steel versus insulation), heat conduction coupled to radiation in cavities, how to obtain a proper U-value for a foundation with floor heating, etc.<br/><br>
<br/><br>
The robust method of explicit finite differences is used. This method closely follows the physical equations. The mathematical equations for two- and three-dimensional heat conduction and the numerical formulation are presented. The numerical error for different meshes is studied and compared with analytical solutions. The effectiveness of the method of successive over-relaxation is demonstrated, while the gain using "successive subdivision'' is modest. Results from calculations with two or three different meshes may be used to estimate more accurate results. The gain using this technique can be quite substantial.<br/><br>
<br/><br>
The problem of thermal radiation in a cavity coupled to heat conduction and ventilation is analyzed in detail. The presented equations are well suited for an iterative computer solution procedure, which turns out to be robust and very rapid.},
  author       = {Blomberg, Thomas},
  isbn         = {ISBN 91-88722-05-8},
  issn         = {0349-4950},
  keyword      = {Byggnadsteknik,Building construction,civil engineering,building physics,thermal radiation,numerical modelling,Heat conduction,computer programs},
  language     = {eng},
  pages        = {188},
  publisher    = {Byggnadsfysik LTH, Lunds Tekniska Högskola},
  school       = {Lund University},
  series       = {Report TVBH},
  title        = {Heat conduction in two and three dimensions : computer modelling of building physics applications},
  volume       = {1008},
  year         = {1996},
}