Note
When exposed to significant heat, gypsum board undergoes calcination, the depth of which is of great importance in fire investigations; the present work seeks to perform global sensitivity analysis through the Sobol method, or the variance-based sensitivity analysis method, in order to determine the effects of differences between estimated and real material properties. An in-house computational model has been developed to solve the one-dimensional, transient scalar transport equation for mass, species, momentum, and energy conservation. Previous work has been performed to validate and refine this model; however, variations in the transport mode parameters and gypsum board material properties, such as the thermal and mass convection coefficients, emissivity, or porosity, have the potential to cause meaningful variations in the model output. First-order indices are presented to show the global sensitivity of the individual parameters. Total indices are also calculated to account for higher-order interactions involving 2 or more parameters. A Monte Carlo integration scheme with 150000 trials is utilized to approximate the variances caused by changes in the input parameters, with an allowance of 5% variation. Local sensitivity analysis has also been performed as a benchmark for the sensitivity of the model with a 1% change in the transport parameters and gypsum material properties. Looking at the average temperature throughout the gypsum board, both the local and global sensitivity analyses show a strong effect from the porosity. The emissivity and thermal convection coefficient also have comparable effects on the average temperature within the gypsum board. Due to the nature of the random sampling in the Monte Carlo integration, the variance results are highly dependent on the number of samples that were used. This can lead to significant differences in the calculated global sensitivity. However, these effects have been reduced through the use of Sobol sequences. (Published Abstract Provided)
