Approximating the solution of a linear heat transfer problem for concrete subjected to one-sided heating under standard fire conditions

Abstract

To estimate the fire resistance limit of reinforced concrete structures, it is essential to understand the temperature distribution within the concrete cross-section under standard fire conditions. Existing approximate analytical methods rely on the classical solution of the heat transfer equation assuming a constant surface temperature. The authors developed a degree approximation of the standard fire temperature curve. This approximation enables an approximate analytical solution to the heat transfer problem with a varying surface temperature corresponding to standard fire conditions. The aim of this work was to derive a convenient formula for heat transfer engineering calculations applicable to concrete with arbitrary thermophysical properties. The derived formula accurately predicts the temperature at any point within the concrete at a given time. The authors’ solution was compared with the high-precision numerical simulations (ANSYS, MATLAB) for various concrete types. Because the proposed approximation does not involve special functions, its implementation does not require any specialized software. The accuracy, simplicity, and versatility of this formula make it suitable for use in fire resistance engineering calculations to determine the time-dependent temperature distribution within concrete under standard fire conditions.