Boundary Conditions in Fire Protection Engineering

Abstract

A summary of the three kinds of boundary conditions as outlined in Sect. 1.1.3 is shown in Table 4.1. The third kind of BC sometimes called natural BC is by far the most important and common boundary condition in fire protection engineering, while the first and second kinds of BCs can rarely be specified. The third kind of BC may be divided into three subgroups, (a), (b) and (c). The subgroup (b) and (c) are particularly suitable for fire engineering applications. Subgroup (a) is applied when the heat transfer coefficient may be assumed constant as assumed in Chaps. 2 and 3. T g is then the surrounding gas temperature. In fire protection engineering it is, however, generally not accurate enough to assume a constant heat transfer coefficient as in particular heat transfer by radiation is highly non-linear, i.e. the heat transfer coefficient varies with the surface temperature. Therefore the subgroups (3b) and (3c) are the most commonly applied. They consist of a radiation term and a convection term with the corresponding emissivity e and convection heat transfer coefficient h, respectively. The subgroup (3b) presupposes a uniform temperature T f , i.e. the radiation temperature and the gas temperature are equal. This is assumed, for example, when applying time–temperature design curves according to standards such as ISO 834 or EN 1363-1 for evaluating the fire resistance of structures, see Chap. 12. The subgroup (3c) is a more general version of (3b) as it allows for different gas T g and radiation T r temperatures, so-called mixed boundary conditions. Alternatively \( \sigma \cdot {T}_r^4 \) may be replaced by an equivalent specified incident radiation \( {\overset{.}{q}}_{inc}^{{\prime\prime} } \) according to the identity \( {\overset{.}{q}}_{inc}^{{\prime\prime}}\equiv \sigma \cdot {T}_r^4 \) (Eq. 1.17). As shown in Sect. 4.4 all boundary conditions of subgroup 3 may be written as type 3a. That means momentarily a single effective temperature named the adiabatic surface temperature (AST) with a value between the radiation and gas temperatures as well as a corresponding total heat transfer coefficient can always be defined, see Sect. 4.4.