Analytical Solution for Adiabatic Surface Temperature (AST)

Abstract

In this contribution an analytical solution of the equation of an ideal surface of a perfect insulator is introduced. The new solution bases on the solution of the heat balance equation, which is fourth degree polynomial. The resulting expression for adiabatic surface temperature (AST) is discussed and verified. This solution can be easily incorporated, with negligible computational cost, inside the computational fluid dynamics solvers for fire simulations. Finally, since AST is close to the temperature measured by plate thermometers, AST is easy to measure in any arbitrary point in a computational domain. This makes it possible to validate numerical results with the temperatures measured by plate thermometers in experiments. Furthermore, an expression, which is given in the end of the article, describes the physical quantity with a closed-form solution. This may be potentially used for analyses performed for better understanding of physical process, e.g. during the experiments involving localized fires.