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In this paper a new simple calculation method for compartment temperatures is derived. The method is applicable to post-flashover ventilation controlled fires. A parameter termed the ultimate compartment fire temperature is defined as the temperature obtained when thermal equilibrium is reached and thick compartment boundaries cannot absorb any more heat from the fire gases. This temperature depends only on the product of the heat of combustion and the combustion efficiency over the specific heat capacity of air. It is, however, independent of the air mass flow rate, and of the fire compartment geometry and the thermal properties of the compartment boundary materials. These parameters on the other hand govern the rate at which the fire temperature is increasing towards the ultimate temperature. It is shown how the fire temperature development as a function of time in some idealized cases may be calculated by a simple analytical closed form formula.
The fire temperature developments of two types of compartment boundaries are presented, semi-infinitely thick and thin structures. It is also shown that for the semi-infinite case, the solution resembles the standard ISO 834/EN 1363-1 curve and the parametric fire curves according to Eurocode 1, EN 1991-1-2.