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Research Papers: Natural and Mixed Convection

# 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

[+] Author and Article Information
A. F. Emery

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600emery@u.washington.edu

M.-H. H. Wu, A. M. Mescher

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600

Sobol considered only uniform probability distributions of $xi$, but the method is easily generalized.

J. Heat Transfer 132(1), 012501 (Oct 22, 2009) (10 pages) doi:10.1115/1.3194759 History: Received August 25, 2007; Revised May 18, 2009; Published October 22, 2009

## Abstract

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 $H/W≥2$.

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## Figures

Figure 1

(a) Skin temperature as a function of metabolic rate. (b) Evaporative heat loss as a function of metabolic rate.

Figure 2

Comparison of predicted and observed thermal sensations in air conditioned and naturally ventilated buildings (adapted from Ref. 5)

Figure 3

(a) PPD(Icl,V) for PPD evaluated at the comfort conditions for M=1 met, rh=50%. (b) f12(Icl,V) for PPD evaluated at the comfort conditions for M=1 met, rh=50%.

Figure 4

dPPD/dTa for M=1 met, rh=50%

Figure 5

(a) PMV response surfaces for Trm=Ta, V=0.5 m/s, and Icl=1 clo. (b) PPD response surfaces for Trm=Ta, V=0.5 m/s, and Icl=1 clo.

Figure 6

(a) Response surface of average Nu for nominal values of H/W=1 and Ra= 103. (b) Response surface of average Nu for nominal values of H/W=1 and Ra= 5×104. (c) Response surface of average Nu for nominal values of H/W=2 and Ra=5×104.

Figure 7

(a) Streamlines for Ra=104. (b) Streamlines for Ra=71,430. (c) Streamlines for Ra=1,128,570.

Figure 8

Second order Interactions for average Nu and maximum stream function

Figure 9

(a) Nu versus Ra from simulations for H/W=1. (b) Nu versus Ra from simulations for H/W=2.

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