T −T ∆T ∆T ∆T ∆T

in out in 12 out

q = = === (1)

th

^Rtotal ^Rin ^R1 ^R2 ^Rout

th th ¹¹

with R_total =∑ R_i ++ (2) i α A α A

in out th ^di

and R_i = (3) λ A

i air air

Here T_in and T_out are air temperature inside and outside; A is the area of the wall; λ_i (in W/(mK)) the thermal conductivity of the layer i; d_i the thickness of the layer i; α_in , α_out (in W/(m²K) the heat transfer coefficients at the inside and the outside surface of the wall).

Building thermography is looking for leaks of insulation, i.e. changes of the thermal conductivity of the wall. Such leaks should be found from the measured surface temperature distribution, i.e. the thermal signature. However, the thermal signature is also influenced by the inside and outside heat transfer coefficients α_in andα_out . Moreover the thermal signature can be dramatically decreased if the thermal resistance Rout drops with increasing heat transfer coefficientα_out due to increased wind speed.

Figure 1. Heat transfer through a plane composite wall. (a) Temperature distribution, (b) Equivalent thermal circuit

The outside heat transfer coefficient α_out is strongly influenced by the wind speed. A lot of experiments have

been done to determine the heat transfer coefficient. As reported in [3] the heat transfer coefficient is increasing linearly with the wind speed. But the comparison of different measurements shows a strong variation of the determined slope of this increase from 0.6 to 6 W/(m²K) per 1 m/s increase. Additionally it was found that the heat transfer coefficient increases with the temperature difference between the body surface and the surrounding air due to the free convection. For zero wind speed heat transfer coefficients between 1 and 10 W/(m²K) have been determined experimentally [3]. The strong variation of the experimental results for the heat transfer coefficient at the boundary between the solid and the air suggests an influence of other unconsidered parameters, such as, surface structure. The theoretical calculation of the heat transfer coefficients is very complex. In most cases there is a mix of free convection (caused by the temperature difference between the solid surface and the surrounding air) and forced convection (caused by the motion of the air). Assuming especially shaped surfaces, such as cylinders, plane, etc., approximations for the heat transfer can be calculated, see [4].

In the present paper some experimental results are presented to demonstrate the influence of changing heat transfer coefficient on thermal imaging results and to provide an estimate of the outside heat transfer coefficient and its dependence on wind speed.

Fig. 2 depicts the heat transfer rate through a wall as a function of the outside heat transfer coefficient

α_out on and the results of the temperature measurement of the inside and outside wall surface temperature.

As an example we assume a 24 cm single layer concrete or clinker brick wall with thermal conductivity of 1.4 W/(mK) and A = 1 m², an inside air temperature of 20^oC and an outside air temperature of 0^oC. For the inside heat transfer coefficient αi a value of 7.69 W/(m²K) following the German Norm DIN 4108 is used [5].

Figure 2. Influence of the wind speed dependent outside heat transfer coefficient αout on the heat transfer rate q (for 1 m² area) and the wall surface temperatures for a single layer wall with λ = 1.4 W/(mK)

As expected the outside surface temperature of the wall drops much more rapidly with increasingα_out than

the inside wall temperature. Moreover the strong cooling effect due to the forced convection on the outside of the wall with increasing wind speed decreases the thermal signature (caused by different thermal insulation due to different thermal conductivities λ) at the outside wall significantly, see Fig.3. In contrast the thermal signature of the inside wall is increased due to an increasing wind speed, i.e. the dependence of inside wall temperature on thermal conductivity of the wall λ is increased with increasing wind speed. Therefore thermal imaging should always be done from the inside of the building, if possible.

A heat transfer coefficient of 30 W/(m²K) can be expected for a wind speed of ~ 4 - 10 m/s with a linear wind

Figure 3. Inside (a) and outside (b) surface temperature of the wall as a function of outside heat transfer coefficient and thermal conductivity of the wall material (wall thickness 24 cm, inside air temperature 20^oC. outside air temperature 0^oC). The lines inside the curves depict the dependencies shown in Fig. 2. Temperature scale for inside wall temperature is inverted for better visualization. The colors mark a temperature range of 1K each.

EXPERIMENTAL SETUP FOR LABORATORY EXPERIMENTS

For the laboratory experiments a model of a house wall (~ 1m x 0.8 m) was used, see Fig. 4.

front side back side

Figure 4. House wall model. Different thermal conductivities of the wall were modeled by attaching different insulation materials as well as materials of different thickness.

For the model a thin wood plate was used as a base plate. On the front side a homogeneous wall surface was created using real plaster for buildings. On the back side different materials such as metal, wood and Styrofoam were used to achieve different thermal conductivities. This plate is heated up to get a thermal flux through the wall. This house wall model is placed in front of a heating plate, see Fig. 5. The surface temperature distribution, shown in Fig. 5, is determined by the different thermal conductivities of the materials used for the model. The thermogram looks like a typical one for timber-framed buildings, where the structure is hidden behind the plaster.

Figure 5. House wall model in front of the heating plate and a typical thermogram, illustrating the different thermal conductivities of the wall insulation materials

The influence of the air flow on the surface temperatures up to wind speeds of 7.3 m/s was analyzed using a room temperature air fan. The wind speed was measured using a calibrated sensor, shown in Fig. 6. For wind speed dependent heat flux measurements (heat flux is given by the heat transfer rate q divided by the area A) a calibrated heat flux plate was applied, see Fig. 6. Such heat flux plates detect the heat flow through it by the temperature difference between its back and front side, measured by thermocouples. Its signal is directly given in W/m².

Figure 6. Experimental setup for analysis of wind speed dependence of surface temperatures and heat flux

INFLUENCE OF WIND SPEED ON HEAT FLUX AND SURFACE TEMPERATURE DISTRIBUTION

For the determination of the heat flux as a function of wind speed the heat flux plate was first mounted directly on top of the heating plate. The heat flux plate itself also represents a thermal insulation with a thermal resistance. For a second experiment a 0.6 cm plywood board was placed between the heating plate and the heat flux plate to simulate a wall with an increased thermal resistance. Fig. 7 shows the results of the heat flux measurements as a function of wind speed. As expected (Fig. 2a) the heat flux shows a saturation behavior at higher wind speed because the outside heat transfer coefficient increases with wind speed. According to

equations (1) and (2) the larger α , the smaller its influence on ^th and hence on the heat flux. At

out ^Rtotalhigher wind speeds the inner heat transfer coefficient and the thermal resistance of the heat flux plate are limiting the heat flux. Using the plywood board the heat flux rate is decreased and the saturation effect occurs at lower wind speeds due to the increased thermal resistance due to the board.

Figure 7. Wind speed dependence of measured total heat flux (left) and heat flux corrected for radiative heat transfer (right). Approximation of the measured heat flux with dαv = 7.1 Ws/(m³K) and αv=0 = 1.3 W/(m²K) and dαv = 8.2 Ws/(m³K) and αv=0 = 0.6 W/(m²K) respectively (lines in the right diagram)

From this measurement the heat transfer coefficient and its variation with wind speed can be calculated. With the known temperature difference between the heating plate and the air (∆T = 10 K) the thermal resistance

th th

R_v=0 can be calculated from the measured heat flux rate at zero wind speed ( α_in is included in R_v=0 and ()in the following):

α_out =αv

∆T

q() v=0 = ₁ (4)

th

R +

v=0

α A

v=0

according to the equivalent thermal resistance model (see Fig. 1). Obviously

⎜⎟

⎞⎟⎟⎟ ⎠

⎛⎜⎜⎜ ⎝

1

T

∆

1

th

R

−

(5)

=

q (v =0)

0

v=

α

A

0

v=

A

For the approximation of the wind speed dependence two parameters have to be used. First the heat transfer coefficient at zero wind speed α_v=0 and second the slope of the heat transfer coefficient as a function of

dα

v

wind speed d_αv = . For arbitrary wind speed v , Eq. 4 gives

dv q()v ∆T

(6)

=

A

⎞⎟⎟⎟ ⎠

⎛⎜⎜⎜ ⎝

⎜⎟

∆T 1

1

−

+

q(v =0)

()

v

α

α

0

v=

A

with

α()=α + v

v_v=0d_αv (7)

The solid lines in Fig. 7 show the results of this fit. If only the heat flux plate is used the dependence can be fitted (least-squares fitting of the data) with α_v=0 = (1.3 + 0.1) W/(m²K) and d_αv = (7.1 + 0.3) Ws/(m³K). If

the plywood board is applied additionally the fit parameters are α_v=0 = (0.6 + 0.1) W/(m²K) and d_αv = (8.2

+ 0.9) Ws/(m³K). This indicates that the heat transfer coefficient is increasing with the temperature difference between the solid surface and the surrounding air. For zero wind speed the temperature of the heat flux plate surface is 6 degrees higher than for the composite system plywood board + heat flux plate according to the lower thermal resistance (at vwind = 0 for single heat flux plate Tsurface = 36.5^oC and for plywood board + heat flux plate Tsurface = 30.5^oC). In the former case the free convection cooling at the surface is more efficient, i.e. the thermal resistance is lower or the heat transfer coefficient is higher.

The parameters α_v=0 = 1.3 W/(m²K) and d_αv = 7.1 Ws/(m³K) determined for the use of the heat flux plate

alone can be used to fit the measured surface temperatures dependent on the wind speed according to

out air

()=T +^{q()v 1} (8)

Tv

surface out

A α(v)

Results are depicted in Fig. 8. The calculated curve reflects the measured values. While not exact, it gives a good approximation of the wind speed dependence of the surface temperatures.

Figure 8. Surface temperature of heat flux plate as a function of wind speed (solid line - theoretical fit, see text)

For a demonstration of the wind speed effect for a practical thermography problem the house wall model was used. The thermograms in Fig. 9 (top) depict a part of the wall at zero wind speed (left image) and at maximum wind speed of 7.3 m/s (right image). The temperatures of two spots (Spot01 – good insulation of the wall, Spot02 – bad insulation of the wall) have been measured during increasing the wind speed from 0 m/s to 7.3 m/s. The results are shown in the left diagram of Fig. 9 (bottom). With increasing wind speed the spot temperatures are decreasing as expected due to forced convection. The temperature difference between the two spots is decreased, see right diagram in Fig. 9. This demonstrates the decrease in the thermal signature with increasing wind speed.

Figure 9. Decrease of thermal signature with increasing wind speed from 0 to 7.3 m/s (nonlinear scale) Top: IR images of house wall model, left vwind = 0 m/s; right vwind = 7.3 m/s Bottom: Spot temperature measurements, left SP01-good insulation and SP02-bad insulation; right

difference of spot temperatures as a measure for the thermal signature

WINDCHILL EFFECT

The wind chill temperature is the apparent temperature felt on exposed skin due to the combination of air temperature and wind speed. Humans do not sense the temperature of the air but sense heat flow due to the temperature difference between the skin temperature and the temperature of the surrounding air. When there

is wind, the thermal resistance of the boundary layer (increasing α_out ) between the skin and the air

becomes smaller, the heat loss is higher and the temperature of the skin is closer to the air temperature. Therefore we feel colder if it is windy. This effect is similar to the discussed effect above. But the definition of the wind chill index [7] also includes the human temperature perception. Therefore this index cannot be applied here.

EVAPORATIVE COOLING

Evaporative cooling occurs whenever a gas flows over a liquid surface [3]. This effect is well known and has been used for cooling for a long time. “In the Arizona desert in the 1920s, people would often sleep outside on screened-in sleeping porches during the summer. On hot nights, bed sheets or blankets soaked in water would be hung inside of the screens. Whirling electric fans would pull the night air through the moist cloth to cool the room.” [6]. Evaporative cooling is a very common form of cooling buildings for thermal comfort since it is relatively cheap and requires less energy than many other forms of cooling.

All solids and liquids have a tendency to evaporate to a gaseous form, and all gases have a tendency to condense back. At any given temperature, for a particular substance such as water, there is a partial pressure at which the water vapor is in dynamic equilibrium with liquid water. With increasing wind speed the number of water molecules of the liquid water which experience collisions with the gas molecules is increasing. These collisions increase their energy and they are able to overcome their surface binding energy of the liquid. This results in an increasing evaporation effect. The energy necessary for the evaporation of the liquid comes from the internal energy of the liquid. Therefore the liquid must cool down. This effect must be taken into account for all temperature measurements of objects with moist surfaces where the measured temperature depends on wind speed.

To investigate this effect, laboratory experiments with the house wall model were carried out, see Fig. 10.

moistened surface at a wind dry surface moistened surface without wind speed of 7.3 m/s

Figure 10. Thermograms of the house wall model showing the effect of evaporative cooling

First the dry surface of the house wall was analyzed. Temperature differences due to different heat insulation quality are clearly seen as a thermal signature. After moistening the surface the thermal signature of the wall is changed. The thermogram shows a more homogeneous temperature distribution. This effect is caused by the evaporation cooling. The water evaporation is increased at higher temperatures. This causes a higher cooling effect at these areas, resulting in a more homogeneous temperature distribution. An additional air flow over the wall is increasing the evaporation effect. This results in a further cooling down of the wall surface by 5 to 6 degrees at a wind speed of 7.3 m/s.

During the laboratory experiments analyzing the influence of evaporation cooling on the results of thermography, the idea was born to use this effect consciously to check if a cold spot at a wall is dry or moist. Fig. 11 depicts the result of this experiment. At the wall in the lab some areas were moistened and others were only cooled using some pieces of ice within a plastic bag in order to avoid the moistening of those areas.

Cold spots without airflow

Experimental setup

(left: moist areas; right: dry areas)

Spots with an air flow of 7.3 m/s after 2 seconds Spots with an air flow of 7.3 m/s after 11 seconds

A water temperature for moistening was used to get the same surface temperatures of the moist and the dry but cool areas. From the initial thermogram (see Fig. 11 top right) alone it was not possible to decide which area is moist and which area is dry. If an air flow is applied the evaporation cooling of the water at the moist areas is increased resulting in a cooling down of these areas by 3-4 degrees, see Fig. 11 (bottom) and Fig.

12. The dry areas are heated by the air flow. With this experiment a qualitative analysis of walls to find moist areas with thermography becomes possible.

SUMMARY

A variety of experiments to analyze the effect of wind speed on the heat transfer coefficient at a solid-air boundary and the evaporative cooling effect have been carried out. The wind speed dependence of the heat transfer coefficient was experimentally determined and the consequences for thermography inside and outside of buildings have been discussed. The demonstrated strong decrease of the thermal signature of the outside wall with increasing wind speed is an important result with regard to outside thermal imaging and suggests that inside thermal imaging is preferable. In all cases where vWind > 0 either internal thermography should be used or an analysis has to be carried out similar to the results reported in this work. The influence of evaporative cooling on the thermal signature was demonstrated. A method using the evaporative cooling process for the detection of moist surfaces with thermal imaging was proposed and experimentally demonstrated.

REFERENCES

[1] Madding, R.P.; Leonard, K.; Orlove, G.; “Important measurements that support IR surveys in substations”, Inframation 2002 Proceedings Vol3, p. 19-25, ITC 035A 2002-08-01

[2] Madding, R.P.; Lyon, B. R.; “ Wind effects on electrical hot spots – some experimental data”, Thermosense XXII, Proc. of SPIE Vol. 4020, p. 80-84 (2000)

[3] Incropera, F. P.; DeWitt, D. P.; “Fundamentals of Heat and Mass Transfer”, John Wiley & Sons 1996, ISBN 0-471-30460-3

[4] Feist, W.; Thermische Gebäudesimulation; Verlag C.F. Müller, Heidelberg 1994

[5] German Norm DIN 4108 (1994)

[6] http://www.consumerenergycenter.org/home/heating_cooling/evaporative.html

[7] Oscevski, R.; Bluestein, M.; “The New Wind Chill Equivalent Temperature”, Bulletin of the American Meteorological Society, Oct. 2005, p. 1453-1458

ABOUT THE AUTHORS

Klaus-Peter Möllmann studied physics in Halle and Berlin and receiving his PhD in 1983, and attended Habilitation, graduating in 1989 receiving his degree in solid state physics in general, and the development of HgCdTe infrared detectors specifically. Since 1994 he has been a professor of physics at the University of Applied Sciences, in Brandenburg, Germany. He has worked in infrared thermal imaging, pyrometry, thin film technology and MEMS technology and is a Certified level II Thermographer.

Frank Pinno studied physics in Potsdam, Germany where he received his PhD (1991) in solid state physics. Since 1994, he has been employed as a scientific assistant (physics) at the University of Applied Sciences, in Brandenburg, Germany, working in the field of infrared thermal imaging and projects in applied sciences. Frank is a certified Level II Thermographer.

Michael Vollmer studied physics in Heidelberg, Germany, receiving a PhD (1986) and Habilitation (1991) in optical spectroscopy of metal clusters. Since 1994 he has been a professor of physics at the University of Applied Sciences in Brandenburg, Germany, working in the fields of infrared thermal imaging, spectroscopy, atmospheric optics, and didactics of physics. He is a certified Level II Thermographer.