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

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 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.