Numerical Methods

Abstract

The analytical methods outlined in Chaps. 2 and 3 presume that the material properties and heat transfer coefficients are constant. That is, however, not possible in most cases in fire protection engineering as the temperature then varies within a wide range and therefore both material properties and boundary conditions vary considerably. Phase changes or latent heat due to water vaporization or chemical reactions of materials (see Sect. 14.1 on concrete) must in many cases be considered to achieve adequate results. Furthermore in particular radiation heat transfer coefficients vary considerably with temperature. As shown in Sect. 4.1 it increases with the third power of the temperature level. In addition geometries being considered are not as simple as assumed above. Often they are in two or three dimensions, and then analytical methods can seldom be used for practical temperature analyses. Therefore numerical methods involving computer codes are frequently used in fire protection engineering. In some cases in particular for 0-dimension problems (lumped-heat-capacity) relatively simple so-called spreadsheet codes such as Excel may be used. For problems with more complex geometries and boundary conditions computer codes based on finite difference or finite elements methods are needed. Several computer codes based on these methods are commercially available, see Sect. 7.3.2. The superposition technique as presented in Sect. 7.2 may be seen as a combination of a numerical and an analytical method.