Sensitivity of the Human Comfort Equation and of Free Convection in a Vertical Enclosure as Examples of the Use of Global Sensitivity to Evaluate Parameter Interactions

Many models of engineering and scientific systems involve interactions between and among the parameters, stimuli, and physical properties. The determination of the adequacy of models for predictions and for designing experiments generally involves sensitivity studies. Good designs mandate that the experiments be sensitive to the parameters sought with little interaction between them because such interaction generally confuses the estimation and reduces the precision of the estimates. For design purposes, analysts frequently want to evaluate the sensitivities of the predicted responses to specific variables, but if the variables interact it is often difficult to separate the effects. Global sensitivity is a technique by which one can evaluate the magnitude of the interactions between multiple variables. In this paper, the global sensitivity approach is applied to the human comfort equation and to free convection in a rectangular enclosure. It is found that when occupants are uncomfortable, there is little interaction and that one can predict the effects of changing several environmental conditions at once by adding the separate effects. But when occupants are comfortable, there is a large interaction and the effects cannot be treated separately. Free convective heat transfer in an enclosure is a function of the Rayleigh number Ra and the aspect ratio $H/W$⁠, and the flow field changes from unicellular to multicellular as Ra increases. There is a strong interaction for $H/W≤2$ but little for $H/W≥2$⁠.