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Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

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Abstract

Fanger’s predicted mean vote (PMV) equation is the result of the combined quantitative effects of the air temperature, mean radiant temperature, air velocity, humidity activity level and clothing thermal resistance. PMV is a mathematical model of thermal comfort which was developed by Fanger. The uncertainty budget of the PMV equation was developed according to GUM in this study. An example is given for the uncertainty model of PMV in the exemplification section of the study. Sensitivity coefficients were derived from the PMV equation. Uncertainty budgets can be seen in the tables. A mathematical model of the sensitivity coefficients of \(T_{\mathrm{a}}\), \(h_{\mathrm{c}}\), \(T_{\mathrm{mrt}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) is given in this study. And the uncertainty budgets for \(h_{\mathrm{c}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) are given in this study.

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Abbreviations

PMV :

Predicted mean vote

M :

Metabolic rate production, units of \(\hbox {kcal}{\cdot }\hbox {h}^{-1}\)

\(A_{\mathrm{DU}}\) :

Surface area of human body, units of \(\hbox {m}^{2}\)

\(\eta \) :

Mechanical efficiency

\(P_{\mathrm{a}}\) :

Water vapor pressure, units of mmHg

\(T_{\mathrm{a}}\) :

Air temperature, units of \(^{\circ }\hbox {C}\)

\(f_{\mathrm{cl}}\) :

Clothing area factor: the ratio of the surface area of the clothed body to the surface area of the naked body

\(T_{\mathrm{cl}}\) :

Surface temperature of clothing, units of \(^{\circ }\hbox {C}\)

\(T_{\mathrm{mrt}}\) :

Mean radiant temperature, units of \(^{\circ }\hbox {C}\)

\(h_{\mathrm{c}}\) :

Convective heat-transfer coefficient, units of \((\hbox {kcal}{\cdot }\hbox {m}^{-2}{\cdot }\hbox {h}^{-1}{\cdot } {}^{\circ }\hbox {C}^{-1})\)

\(I_{\mathrm{cl}}\) :

Thermal resistance of clothing, units of clo \((1\hbox { clo}= 0.155\, \hbox {m}^{2}{\cdot }\hbox {K}{\cdot }\hbox {W}^{-1})\)

\(\nu \) :

Relative air velocity, units of \(\hbox {m}{\cdot }\hbox {s}^{-1}\)

\(C_{PMV,T\mathrm{a}}\) :

Sensitivity coefficient of air temperature which is related to the uncertainty of PMV

\(C_{PMV,h\mathrm{c}}\) :

Sensitivity coefficient of convective heat- transfer coefficient which is related to the uncertainty of PMV

\(C_{PMV,P\mathrm{a}}\) :

Sensitivity coefficient of air vapor pressure which is related to the uncertainty of PMV

\(C_{PMV,T\mathrm{cl}}\) :

Sensitivity coefficient of surface temperature of clothing which is related to the uncertainty of PMV

\(C_{PMV,T\mathrm{mrt}}\) :

Sensitivity coefficient of mean radiant temperature of clothing which is related to the uncertainty of PMV

\(C_{h\mathrm{c},\upnu }\) :

Sensitivity coefficient of air velocity which is related to the uncertainty of convective heat-transfer coefficient

\(C_{h\mathrm{c},T\mathrm{a}}\) :

Sensitivity coefficient of air temperature which is related to the uncertainty of convective heat-transfer coefficient

\(C_{h\mathrm{c},T\mathrm{cl}}\) :

Sensitivity coefficient of surface temperature of clothing which is related to the uncertainty of convective heat-transfer coefficient

\(C_{T\mathrm{cl},T\mathrm{a}}\) :

Sensitivity coefficient of air temperature which is related to the uncertainty of surface temperature of clothing

\(C_{T\mathrm{c}l,T\mathrm{mrt}}\) :

Sensitivity coefficient of mean radiant temperature which is related to the uncertainty of surface temperature of clothing

\(C_{T\mathrm{cl},h\mathrm{c}}\) :

Sensitivity coefficient of convective heat-transfer coefficient which is related to the uncertainty of surface temperature of clothing

\(C_{P\mathrm{a},\mathrm{w}}\) :

Sensitivity coefficient of air humidity which is related to the uncertainty of air vapor pressure

\(C_{P\mathrm{a},P\mathrm{g}}\) :

Sensitivity coefficient of saturated vapor pressure which is related to the uncertainty of air vapor pressure

\(u(T_{\mathrm{a}})\) :

Air-temperature measurement uncertainty \((k = 1)\)

\(u(h_{\mathrm{c}})\) :

Uncertainty of convective heat-transfer coefficient \((k = 1)\)

\(u(T_{\mathrm{mrt}})\) :

Mean radiant temperature measurement uncertainty \((k = 1)\)

\(u(T_{\mathrm{cl}})\) :

Uncertainty of surface temperature of clothing \((k = 1)\)

\(u(P_{\mathrm{a}})\) :

Uncertainty of air vapor pressure \((k = 1)\)

\(u(\nu )\) :

Relative air velocity measurement uncertainty \((k = 1)\)

u(w):

Air humidity measurement uncertainty \((k = 1)\)

\(u(P_{\mathrm{g}})\) :

Uncertainty of saturated vapor pressure \((k = 1)\)

PPD :

Predicted percentage dissatisfied, units of %

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yildiz Technical University, Istanbul, Turkey

    Can Ekici

  2. Gebze Calibration Directorate, Turkish Standard Institution, Ankara, Turkey

    Can Ekici

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Ekici, C. Measurement Uncertainty Budget of the PMV Thermal Comfort Equation. Int J Thermophys 37, 48 (2016). https://doi.org/10.1007/s10765-015-2011-3

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