Laser-Scanning-Based Method for Estimating the Distribution of the Convective-Heat-Transfer Coefficient on Full-Scale Building Walls

Abstract

We propose a method for estimating the convective-heat-transfer coefficient (CHTC) distribution on building walls by using the water-evaporation method involving filter paper and three-dimensional laser scanning, and demonstrates consistency with the gravimetric evaporation method. The theory and method are established based on the convective heat- and mass-transfer analogy and a near-infrared laser-scanning system. The equations to remotely estimate the CHTC distribution are obtained empirically, and the proposed method is applied to the walls of a penthouse during winter. The spatial distribution of the surface reflection intensity that determines the evaporation rate is successfully retrieved with 0.2–0.3% accuracy from a measurement distance of 5 m. The comparison of evaporation rates with a gravimetric measurement does not show a statistically significant bias. The results show that the crucial factors for the precision of the CHTC estimation are errors in the laser-scanning system and their amplification when dividing the evaporation rate by the vapour pressure deficit to obtain the convective-mass-transfer coefficient. The estimated CHTC distributions on the target walls have approximately ≤ 2–3 W m⁻² K⁻¹ errors in the 95% confidence interval after applying spatial and/or temporal averaging. Although the error in the convective-heat-transfer coefficient is larger in winter during minimal vapour pressure deficits, it is generally well explained in the range of the random error in laser scanning. The correlation between the spatially-averaged convective-heat-transfer coefficient and near-wall wind speed is comparable to existing methods (R = 0.71–0.79), and the regression relation agrees with that obtained in previous studies performed in similar conditions.

Appendix: Sensitivity of the Convective-Heat-Transfer Coefficient to Temperature Error

The effect of temperature error on $e_{\text{s}}^{*}$ can be evaluated analytically by using the so-called August–Roche–Magnus relation

$$ e_{\text{s}}^{*} \left( {T_{\text{s}} } \right) = a{ \exp }\left( {\frac{{bT_{\text{s}} }}{{T_{\text{s}} + c}}} \right), $$

(9)

where $T_{\text{s}}$ is in °C, $e_{\text{s}}^{*}$ is the saturation vapour pressure [kPa], and a = 0.611 [kPa], $b = 17.5$ [°C], and c = 249.93 [°C] are typical atmospheric pressures (Campbell and Norman 1998). By using Eq. 9, the sensitivity (relative error) of the value of $e_{\text{s}}^{*}$ to the temperature error can be expressed as

$$ \frac{{\Delta e_{\text{s}}^{*} }}{{e_{\text{s}}^{*} }} = \Delta T_{\text{s}} \left[ {\frac{{ - bT_{\text{s}} }}{{\left( {c + T_{\text{s}} } \right)^{2} }} + \frac{b}{{c + T_{\text{s}} }}} \right], $$

(10)

where $\left| { - T_{\text{s}} /\left( {c + T_{\text{s}} } \right)} \right| \ll 1$ results in

$$ \frac{{\Delta e_{\text{s}}^{*} }}{{e_{\text{s}}^{*} }} = \frac{b}{{c + T_{\text{s}} }}\Delta T_{\text{s}} . $$

(11)

When $T_{\text{s}}$ = 5–8 °C, which is a typical value in our measurement, Eq. 11 leads to $\Delta e_{\text{s}}^{*} /e_{\text{s}}^{*} \approx 0.07\Delta T_{\text{s}}$. Assuming that the atmospheric relative humidity is 50% (which is the typical value here and that of a sunny day in Japan) and $T_{\text{s}} \approx T_{\text{a}}$ (this seems a tolerable assumption for a shaded building wall), the sensitivity of the vapour pressure deficit is doubled and leads to a CHTC sensitivity $\Delta h_{\text{c}} /h_{\text{c}} \approx 0.14\Delta T_{\text{s}}$.