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A robust convection cover material for selective radiative cooling applications
Solar Energy Materials & Solar Cells 95 (2011) 2778–2785
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A robust convection cover material for selective radiative cooling applications S.N. Bathgate n, S.G. Bosi 1 Applied and Plasma Physics, School of Physics, University of Sydney, NSW 2006, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 July 2009 Received in revised form 27 May 2010 Accepted 12 May 2011 Available online 28 June 2011
The enhanced cooling of exposed surfaces by radiative heat loss to the cold sky was investigated using a variety of commonly available materials. Zinc sulphide was identified as a durable substance suitable for the construction of convection covers for radiative cooling radiators. With respect to polyethylene, the most commonly used convection cover to date, the new material is mechanically stronger, impervious to damage by solar ultraviolet and in practical thicknesses is more transparent in the 8–14 mm waveband. Use of this window material with a previously proposed selective radiator material, a form of anodised aluminium that reflects radiation at wavelengths shorter than 8 mm allows for the economical production of an effective selective radiator system. Measurements were made on simple radiator plates and convection covers. & 2011 Elsevier B.V. All rights reserved.
Keywords: Radiative Cooling Selective Radiator Convection Cover
1. Introduction 1.1. Properties of the atmosphere The formation of frost by emission of infrared radiation from the ground to the cold night sky during a clear night is a common example of the loss of heat to the sky by radiative cooling. While ground temperatures in the early evening may be above the freezing point, the effective temperature of the high atmosphere may be as cold as 40 1C. Objects at a higher temperature (such as the ground) lose heat to the cold sky by radiative exchange. Although the ground is covered by air at a similar temperature, the complex nature of the atmosphere means that the sky does not behave as a simple black body and has a number of low absorption windows that are transparent to infrared radiation. The most important window for radiative cooling lies between the wavelengths of 8 and 14 mm. It is through this window that most of the energy transfer associated with radiative cooling occurs (Fig. 1). While radiative cooling is most effective during the night, heat can also be lost to the sky during the day providing the radiator surface is shaded from the sun.
The effectiveness of radiative cooling can be enhanced by technical improvements. Two in particular are important. The first is the use of selective surfaces that are designed to radiate energy in the 8–14 mm band of the infrared and reflect radiation outside those wavelengths. Selective surfaces that are matched to this atmospheric window are, in this application, more effective radiators than a black body if a depression of the radiator’s temperature below ambient is required. The second is the use of infrared transparent convection covers that insulate the radiator surface from the surrounding atmosphere. With an infrared transparent convection cover, it is possible for the radiator surface to cool to temperatures below ambient. The rate of radiative heat loss to the sky (and hence cooling of the radiator plate) is equal to the difference between the power emitted by the radiator and the power absorbed by the radiator from the sky. For example, Berdahl et al. [2] report that in a typical cooling experiment, the thermal sky irradiance may be 350 W/m2 while the radiator emits 420 W/m2, a difference of 70 W/m2 being the available cooling power. Any parasitic thermal conduction from the ambient to the radiator would reduce the available cooling power. 1.2. Radiative heat loss to the clear sky
n
Corresponding author. Tel.: þ61 413944734. E-mail addresses: [email protected] (S.N. Bathgate), [email protected] (S.G. Bosi). 1 Present address: Radiation Oncology Department, Prince of Wales Hospital, Randwick NSW 2031, Australia. Tel.: þ 61 2 93822515. 0927-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2011.05.027
The possibility of cooling by heat loss to the cold sky employing selective radiators has been understood since the work of ˚ ¨ Angstr om [3]. Little further work was published until that of Head [4]. Since that time selective radiation cooling has been investigated sporadically ([2,5–11] and others) and although some
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where Tr and Ts are, respectively, the absolute temperatures of the radiator surface and the sky, u(l,T) is Planck’s black body radiance integrated over a hemisphere, S(l) is the sky hemispherical spectral emittance, a(l) is the radiator hemispherical spectral emittance (absorptance) and A is the absorber area. This calculation assumes the radiator couples to the sky over a full hemisphere and is large enough in area to ignore edge or aperture effects. Parasitic heat gain by the radiator from its surroundings reduces the attainable effective cooling power Pc and the experiments reported below show that for the simple design of radiator reported herein, it was the dominant factor in the effectiveness of the radiative cooling system and has to be minimised by insulation. 1.3. Radiator surfaces
Fig. 1. Spectral radiance of the atmosphere measured at Coco Beach, Florida, by Bell et al. [1] showing the radiance of the 8–14 mm window at various angles from the zenith compared to the radiance of a black body at 298 K (solid black curve).
effective small scale systems have been constructed, to date no large scale use has been made of the technology. Bell et al. [1] carried out a study of the radiative properties of the atmosphere and defined the resource for radiative cooling. They measured the spectral emittance of the atmosphere between 1 and 20 mm from the zenith to the horizon and documented the energy flux that reaches the ground from the atmosphere. A black body maintained at a temperature of 31071 K was used as a radiometric reference standard for the measurements. Measurements were made at Cocoa Beach in Florida and at two sites in Colorado—Denver (1800 m) and Pikes Peak (4260 m). Similar recordings were made at each of these sites and it was found that the emission from the zenith declined as altitude increased. The measurements shown in Fig. 1 illustrate the departure of the atmospheric emission spectrum from that of an ideal black body. Between 8 and 14 mm, the radiant flux intensity is significantly less than for a black body at the equivalent temperature, in this case 298 K. Under a clear sky, there will be a net loss of energy by a radiator at ground level to the colder upper atmosphere. This ‘‘net radiative cooling power’’ is dependent on
the temperature of the radiator; the emissivity of the radiator; the inclination of the radiator surface from the zenith; the radiant flux emitted by the atmosphere and the humidity (water vapour absorbs radiation in the 8–14 mm band).
Taking these factors into consideration, the net radiative cooling power of a radiator (Pnet) is the difference between the power radiated by the radiator at its operating temperature minus the power absorbed by the radiator from the sky: Pnet ¼ Prad 2Pabs
Pc ¼ Pnet 2sDTss
ð3Þ
DTss can be increased by
reducing the non-radiative heat flow coefficient s by increas
ing the insulation around the radiator and placing an infrared transparent convection cover over the radiator; increasing the radiative heat loss Prad by modifying the surface emissivity and reducing the cooling load Pc.
1.4. Convection covers Although a number of materials exist that are suitable for use as radiator surfaces, materials that are suitable for use as convection covers are much harder to identify and to date, polyethylene film has been the only material employed as proof-of-concept, despite its vulnerability to rapid degradation by solar ultraviolet. A number of investigators have attempted to improve the durability of polyethylene by either incorporating ultraviolet resistant pigments into the film or by impregnating the surface with similar materials; however none have reported that these measures have greatly improved the long term durability. In particular, measurements of polyethylene durability made by Hamza et al. [12] in Egypt (an arid region where radiative cooling could have utility) demonstrated conclusively that polyethylene film failed completely over period of a few months. The failure to identify a suitable cover material has been a major stumbling block for the development of this technology.
ð1Þ
The radiated power (Prad) is calculated by integrating the emission spectrum of a black body at the temperature T of the radiator weighted by the hemispherical spectral emittance (¼hemispherical spectral absorptance) of the radiator surface a(l). The absorbed power (Pabs) is calculated by integrating the emission spectrum of the sky weighted by the hemispherical spectral absorptance of the radiator surface versus wavelength: Z 1 Z 1 Pnet ¼ A uðl,Tr ÞaðlÞdlA uðl,Ts ÞaðlÞSðlÞdl ð2Þ 0
Consider the radiator under steady-state conditions (i.e. negligible rate of temperature change). The steady-state temperature difference DTss between the radiator surface and the surrounding atmosphere is determined by the difference between the net radiative cooling power to the sky, Pnet, and the parasitic heat flow sDTss between the radiator and the surrounding environment. s is the linear heat transfer coefficient in W/m2/K and signifies the nonradiative heat inflow to the radiator surface. Both convection and true conduction are here rolled together into the coefficient s. At steady-state, the effective cooling power Pc of the radiator is given by
0
1.5. Potential infrared transparent cover materials A number of materials are transparent or partially transparent in the 8–14-mm infrared window. However, their suitability for use as a convection cover varies widely (Table 1). Zinc sulphide is transparent to infrared in the 8–14 mm waveband. The transmittance measurements reported here were performed on a Shimadzu IR-470 spectrophotometer using a slab of material without any attempt to suppress the surface reflectance. Reflectance is high for the high refractive index material ZnS and
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Table 1 Some properties of potential convection cover materials, including infrared transmittance in the 8–14 mm waveband, which was measured on a Shimadzu IR-470 spectrophotometer. Material
Mean transmittance 8–14 mm
Data source
Toxicity
Solar damage
Fabrication/cost
Polyethylene (CH2–CH2)n Zinc sulphide (ZnS) Zinc selenide (ZnSe) Tefzel (C–F polymer) Silicon
73% (100 mm thick) 64% (4 mm thick) 70% (7.1 mm thick) E10% (200 mm thick) 47% (0.6 mm thick)
Measured Measured [13] Measured [20]
Non-toxic Low Harmful by skin contact Non-toxic Non-toxic
Yes No No No No
Low cost High purity has high cost High cost Low cost High cost
Table 2 Power radiated from selective radiator surfaces at ambient temperature (ambient ¼298 K), radiator surfaces 5 K below ambient and radiator surfaces 10 K below ambient. Material
Reference
Net radiative power Prad at 298 K (W/m2)
Net radiative power Prad at 293 K (W/m2)
Net radiative power Prad at 288 K (W/m2)
Ideal selective radiator Black body Pot belly black paint (a high infrared emission black paint) Silicon oxide Silicon oxy-nitride Silicon nitride Anodised aluminiumb Anodised aluminiumc Anodised aluminium þ magnesium oxide
Calculateda Calculateda Measured [7] [18] [17] Measured Measured Calculateda
74.8 74.1 69.3 32.5 61.8 63.8 66.6 55.1 62.3
61.7 48.8 47.1 27.5 46.4 48.8 48.9 41.0 45.3
49.2 24.9 26.1 22.7 33.5 34.7 31.9 27.3 29.5
a b c
Calculated emissivity using Eq. (2). A sky temperature of 298 K was assumed. See Fig. 4 below 180 s anodised radiator surface. Anocoil—an aluminium reflector for light fittings.
accounts for roughly three-quarters of the deficit in transmittance. This can easily be reduced by the use of a suitable anti-reflection coating and would be expected to result in a significant improvement in cooling performance. ZnS is currently only available as a relatively expensive high purity window for scientific and military applications. The raw material ZnS powder is cheap and it is possible that a less costly, lower quality grade of ZnS could be used to produce practical convection covers for radiative cooling. Yashina [14] describes the optical and mechanical properties of poly-crystalline zinc sulphide prepared by different methods. Commonly, hot-pressed zinc sulphide is manufactured from powdered zinc sulphide, which is pressed between graphite faced anvils for 0.5–1.5 h at pressures of 50–60 MPa and temperatures of 925–950 1C. 1.6. Calculation of properties of radiator materials A limited number of materials have been investigated as potential selective radiator surfaces [5,7,15–18]. These materials have a performance superior to a black body where the radiator temperature drops below ambient although all of the surfaces tried so far fall short of the performance of an ideal selective radiator. The problem lies in obtaining a material that has a sharp transition between reflection and absorption and has maximum emission in the 8–14 mm waveband and maximum reflection outside that band. Calculated performances for various radiator surfaces assuming an ideal 100% transmittance convection cover and ignoring the effects of convection and conduction are listed in Table 2 for an ambient temperature of 298 K. The data for sky radiance in W/m2/sr were integrated to produce the hemispherical sky emission and these data were used in calculating the heat loss from radiator surfaces using Eq. (2). The sky radiance data were obtained from Bell et al. [1]. The radiator emissivity data were digitised from plots found in papers by Granqvist and Hjortsberg [7], Berdahl [16], Eriksson, Jiang and Granqvist [17] and Diatezua, Thiry and Caudano [18]. The data in Table 2 demonstrate the effectiveness of a selective surface when the radiator temperature falls below the ambient temperature. For example, an ideal selective radiator has
approximately twice the heat loss rate of a black body when the radiator temperature falls to ten degrees below an ambient temperature of 298 K. The sky temperature is assumed to be the same as ambient temperature—in general sky temperature will differ from the ambient temperature. Of all the materials considered, silicon nitride has the best performance at reduced temperatures while these figures suggest that anodised aluminium may be a practical and inexpensive selective radiator surface. It should be borne in mind that the calculations in Table 2 assume a radiator large enough to ignore edge or aperture effects, a condition probably not matched by the measurements listed.
1.7. Heat transfer models and calculations Landro and McCormick [6] developed a model that used the net radiation method of De Micco and Aldao [19] to calculate the fluxes between the radiator surface, the convection cover and the sky (Fig. 2 in Landro and McCormick [6]). Landro and McCormick [6] define the heat fluxes in the wavelength interval dl as
incoming radiation to the cover dqi,c; outgoing radiation from the cover dqo,c; incoming radiation to the radiator dqi,r and outgoing radiation from the radiator dqo,r.
Combining equations for the heat fluxes in the wavelength interval dl with the radiative heat loss from the radiator and with configuration factor¼1 (i.e. the radiator and the cover are of equal area, parallel and aligned) gives equation 4 in Landro and McCormick [6]. This equation was evaluated numerically using the transmittance of the polyethylene cover tc(y) from Catalanotti et al. [5] and values for es (sky emissivity) that were derived from the measurements of Bell et al. [1] for Cocoa Beach. Bell et al. [1] calculated es by taking the ratio of the measured spectral
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directional sky radiance and the black body radiance of a reference object at 300 K. Landro and McCormick [6] did not publish the temperature of their radiator (Tr), however it was possible to use the model to calculate the effects of varying directional sky emissivity es(l,y), the refectivity of the cover rc, ambient temperature Tr and radiator temperature T0. The model is sensitive to the directional sky emissivity. This means the model depends on accurately characterising the sky in which the radiator would operate. Because of the difficulty in obtaining the original tabulated data in Bell et al. [1], these data were digitised from a scan of Fig. 1 in Landro and McCormick [6]. To gauge the sensitivity of the model to the error inherent in the process of digitising this printed graph, these sky data were re-scaled by a pessimistic 710% and the resulting change in heat loss noted. A sensitivity analysis of the model confirmed that the most significant influence on heat loss was the directional sky emissivity es(l,y). It was found that an increase in heat loss of around þ30% resulted from a scaled 10% reduction in es(l,y) and decrease in heat loss of around 20% was found for a scaled 10% increase in es(l,y) for a black body radiator at 318 K. Changing the cover reflectivity by 710% produced a change in heat loss by 79% under the same conditions, showing, as expected, a linear relationship between cover reflectivity and heat loss. Landro and McCormick [6] have assumed that sky emissivity is independent of temperature. This seems a reasonable assumption for clear, dry air given the relatively small range of temperature variation under normal atmospheric conditions. Berdahl, Martin and Sakkal [2] state that the approximations used by Landro and McCormick [6] for the reflectance of the cover and radiator (using hemispherical values) and setting the cover temperature equal to ambient (if the cover emissivity is neglected) does not introduce serious errors. That the predictions generated by this model are highly dependent on the local sky emissivity at the time of measurement, suggests that real time sky emissivity data are required to accurately model the heat loss from an experimental radiator.
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Note that although the zinc sulphide plate is 40 times thicker than polyethylene (4 mm vs. 100 mm), the transmittances of the covers between 8 and 14 mm are similar (Figs. 2 and 3), with zinc sulphide showing an average transmittance of 64% between 8 and 14 mm and an average transmittanceE0.0 at wavelengths415 mm. This means that it would not be practical to use thicker polyethylene covers to improve weathering because the reduction in transmittance of the thicker material would defeat the purpose of the cover. However, a thinner ZnS plate may be viable. 2.2. Anodised aluminium as a selective radiator surface In this work, an investigation into the spectroscopic properties of anodised aluminium was undertaken following the work of Miller and Bradley [15] who reported that bright anodised aluminium showed promise as an inexpensive selective radiator. Measurements were made of the reflectance of the anodised surface of a similar material (1150 grade aluminium) and it was found that a useful radiator surface could be produced (see Fig. 4 below). The anodising conditions are as follows:
anodising voltage¼13 V DC; anodising current¼500 A DC; sulphuric acid concentration¼10% (by volume) and aluminium concentration 5–15 g/l.
The reflectance between 3 and 20 mm of the anodised aluminium declined gradually with increasing anodising time until at
2. Experimental 2.1. Measurements of properties of cover materials In this work, zinc sulphide (ZnS) was investigated as an alternative cover material and as shown in Fig. 3, it is sufficiently transparent in the 8–14 mm range to be useful.
Fig. 3. Measured transmittance of polished hot-pressed 4 mm thick zinc sulphide.
Fig. 2. Measured infrared transmittance of 100 mm polyethylene film (solid) plotted with atmospheric spectral radiance from the zenith (dotted) from Bell et al. [1] showing that the transmittance of polyethylene is well matched to the 8–14 mm atmospheric window.
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Fig. 5. Measured reflectance of high infrared emission black paint (pot belly black) shows a reflectance of approximately 10% between 6 and14 mm . Fig. 4. Measured reflectance of 1150 grade anodised aluminium showing a marked transition in reflectance at 180 s anodising time.
Table 3 Mean reflectance of anodised aluminium between 8 and 14 mm compared with the average reflectance between 3 and 8 mm . Anodising time (s)
Mean reflectance (%) 8–14 mm
Mean reflectance (%) 3–8 mm
30 90 150 180
86.0 75.4 67.4 12.1
73.4 66.3 59.6 52.0
180 s when the reflectance beyond 7 mm declined sharply (Fig. 4). The reflectance spectrum of the 180 s anodised test piece approaches the properties of a selective radiator with average reflectance between 8 and 14 mm E12% and average reflectance below 8 mm4 51%. The mean reflectance of anodised aluminium between 8 and 14 mm relative to the mean reflectance between 3 and 8 mm decreases with longer anodising times, suggesting that the thickness of the anodised layer is a critical variable in determining the reflective properties of the surface (Table 3). Longer anodising times (up to 12 min) produced surfaces with a reflectance similar to that of the 180 s anodising time test piece (Fig. 4). 2.3. Non-selective radiator surfaces Pot belly black paint, a high infrared emission black paint surface coating intended to be a high emittance black surface for use on wood-fired stoves and heaters, was used as an approximation to a black body radiator surface for experimental measurements. The following normal incidence plot of total reflectance (Fig. 5) was made using a Digilab FTS 7000 series FTIR spectrometer fitted with a PIKE integrating sphere and shows the low reflectance of this kind of high emission paint between 8 and 14 mm Above 5 mm, the measured reflectance of pot belly black was roughly 10%. Calculations using Eq. (2) (assuming an ideal Lambertian angular dependence) show that the infrared emission from pot belly black paint in that waveband is 90% of the emission from a black body radiating in the same waveband at 298 K and 97% of the emission from a black body at 288 K. 2.4. Experimental apparatus Radiator test boxes were constructed from 50 mm thick polystyrene foam arranged as 100 mm thick walls and a 50 mm thick
Fig. 6. Test boxes used to measure properties of radiator surfaces and convection covers.
base (see Fig. 6 below). The radiators were 100 mm2 aluminium plates. The radiator cavities were lined with aluminium foil to make the walls reflective to minimise edge effects so as to approximate an infinite radiator. A 330 O, 5 W resistor was attached with screws and thermally conducting paste to the underside of each of the radiator plates to provide a source of heat. Polyethylene or zinc sulphide convection covers were placed over the open tops of the boxes. The small differences between the temperatures of the radiators and ambient temperature required a precision of 70.1 K in the temperature measuring apparatus in order to make useful comparisons between radiators. For this reason, LM335 precision temperature sensors that produced an output of 10 mV/K were used as temperature sensors. The LM335 sensors were mounted between the polystyrene base and the radiator plate and were kept in thermal contact with the radiator plate with thermal conducting paste. The ambient temperature and the temperatures of two radiator plates were measured simultaneously. The analogue output of the temperature sensors was converted to a 12 bit digital value by an ICL7109 analogue to digital converter that gave a resolution of 1 in 4096 over a 4.096 V range. This gave a limit of measurement of 1 mV (equivalent to 0.1 K). All of the LM335 sensors were initially calibrated together in a distilled water ice bath (273.1 K) and in a boiling distilled water bath (373.1 K). Following this two-point calibration the accuracy of the measurements using the LM335 sensors was determined to be within 71 K. This difference between the outputs of the
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Table 4 Sources of error in the measuring circuit. Error
Type
Value (K)
Source
Number on Fig. 7
Long term stability of LM336 voltage reference Thermal stability of the LM336 Errors in the LM335 temperature probes Noise in the circuit components Errors in the 7109 A–D Variations in the radiator heater supply voltage Offsets in the LM335 probes Digitising resolution of the 7109 A–D Offsets of LM335 probes in thermal contact
Random Systematic Random Random Random Random Systematic Systematic Systematic
7 0.005 7 0.09 7 0.1 7 0.01 7 0.01 7 0.01 7 0.08@323, 7 0.18@273 7 0.1 7 0.5
Internal physical changes Thermal and electrical noise Thermal and electrical noise Thermal and electrical noise Thermal and electrical noise Thermal and electrical noise Non linearity of the internal circuit Internal circuit design Calibration
6 6 3 4 5 1 3 5 2
2.7. Measurements
Fig. 7. Potential sources of error in the measuring circuit and in the radiator heater power supply circuit.
probes was found to be an offset that could be subtracted and the result was that the precision of the temperatures measured by the probes was within 70.1 K, equivalent to the digitising error of the analogue to digital converter. As a test of the stability of the temperature measuring equipment, after 70 days all the probes were placed in thermal contact and allowed to track ambient temperature for several days. The variation in measurements between the probes was found to be still less than 0.1 K. Because temperature differences were the most important aspect of these measurements, the precision of 0.1 K was more significant than the accuracy of 1.0 K. 2.5. Sources of error in the experimental measuring circuit The largest errors were due to a drift in the outputs of the temperature probes and in the voltage reference that was connected to the analogue to digital converter. There was also a drift in the voltage regulator supplying power to the radiator heaters. The sum of all these sources of error was less than 0.1 K and within the digitisation resolution of the analogue to digital converter (Table 4 and Fig. 7). 2.6. Heat loss and gain in radiator test boxes Before radiative cooling measurements were made, the combined thermal conductance s of the walls, bases and tops of the boxes (and the enclosed air) was determined. The radiator plates were heated using their attached 330 O, 5 W resistors while a sheet of aluminium foil was used in place of the convection cover to act as a reflecting cover of minimal thermal mass to prevent heat being lost by radiation from the top of the box while heat loss to ambient by conduction and convection was measured. The temperature difference between ambient and the inside of the boxes versus power delivered was used to calculate the combined thermal conductance s (i.e. linear heat transfer coefficient).
Measurements of heat loss from the radiator test boxes with two different convection covers (100 mm polyethylene and 4 mm zinc sulphide) and two different radiator surfaces (anodised aluminium and pot belly black paint) were conducted on nights in Sydney, Australia, during February, March, April and May 2006. Ambient temperature and radiator temperatures were recorded continuously and the sun down and sun up times were used as the start and finish times for analysing radiator performances. As far as it was possible to determine from satellite cloud pictures and local weather reports, measurements were conducted on nights that were largely cloud-free although it was not possible to monitor this all night. Heat loss was calculated from the recorded temperatures, using the thermal conductance of the test boxes determined previously to calculate the parasitic heat flow. The following analysis assumes steady-state conditions, such that a term QT0 (where Q is thermal capacity and T0 is cooling rate) is omitted from the heat balance equation (Eq. (3)). The thermal capacity Q of the test boxes was estimated using published material properties and a range of night-time cooling rates T0 were taken from our measurements. QT0 was calculated and found to be well under 1% of the measured net radiative cooling power confirming the validity of our assumption. Measurements were performed in two modes: passive and active. In passive mode, the boxes were allowed to radiate overnight without the input of electrical heating power. During this time the temperature difference between ambient and the radiator surface was monitored. The system was assumed to be very near steady-state, in which case the effective cooling power of the system is zero and so the net radiative cooling power of the radiator plate simply equals the rate of parasitic heat gain from the surroundings (deduced from DT and s). The total parasitic heat gain between the exact times of sunset and sunrise (and hence total energy radiated by the plate) was calculated from the area under the temperature/time curve. That is, the temperature difference DT between the radiator surface and ambient was recorded and integrated versus time. This integral value was multiplied by the linear heat transfer coefficient s to yield the total energy transfer. In active mode, the radiators were heated electrically using the 330 O, 5 W resistors in order to simulate the performance of a practical cooling system. Again the energy balance was assumed to be at steady-state; so the net radiative cooling power of the radiator plate equalled the power delivered electrically to the radiator plate minus the parasitic heat loss. The passive mode measurements were used to determine the lowest attainable temperatures. The experiments were conducted under the following conditions:
Radiator cases sealed and weatherproofed to keep insides as dry as possible.
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Radiator surfaces: pot belly black paint or anodised
aluminium. Heat input: 42.270.7 W/m2 (330 O resistor supplied by 11.870.1 V regulated supply). Radiators were operated with fixed power input or with no power input. Convection covers: 100 mm polyethylene or 4 mm ZnS. Location: an exposed flat roof with a clear view of the sky and without nearby surrounding buildings, structures or trees. Weather: generally clear and mild to warm (Southern Spring). Time of experiments: sunset to sunrise.
2.8. Results Fig. 8 shows the simultaneous temperatures of two heated anodised aluminium radiator plates (active mode) covered by polyethylene and zinc sulphide for a typical experiment conducted between sunset and sunrise. The ambient temperature (Tambient) and the temperature of the radiators (Tpolyethylene and TZnS) are plotted for one night. Similarly, Fig. 9 shows the simultaneous temperatures of two unheated anodised aluminium radiator plates (passive mode) covered by zinc sulphide and polyethylene for a typical experiment conducted between sunset and sunrise. The measurements shown in Fig. 9 demonstrate stagnation temperatures of up to 6 K below ambient. The averaged results from five separate experiments (active mode) are shown in Tables 5 and 6 and from two separate experiments (passive mode) are shown in Tables 7 and 8. Each
Table 5 Comparative performances of the convection covers of heated anodised aluminium radiators (active mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers. Measurements (sunset to sunrise)
Zinc sulphide 2
Total net radiative heat loss (Wh/m ) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
Polyethylene
430 7 10 32.5 7 0.5 49.9 7 0.5 288.4 7 0.2
4207 10 32.2 7 0.5 50.27 0.5
289.4 7 0.2
289.2 7 0.2
Table 6 Comparative performances of the convection covers of heated pot belly high infrared emission black paint radiators (active mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers. Measurements (sunset to sunrise)
Zinc sulphide
Polyethylene
Total net radiative heat loss (Wh/m2) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
340 7 10 29.6 7 0.5 44.5 7 0.5 295.3 7 0.2
355 7 10 31.3 7 0.5 45.07 0.5 295.7 7 0.2
295.4 7 0.2
295.9 7 0.2
Table 7 Comparative performances of the convection covers of unheated anodised aluminium radiators (passive mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers.
Fig. 8. A typical measurement in active mode. Ambient temperature (Tambient) and the temperatures of heated anodised aluminium radiators (TZnS and Tpolyethylene) under zinc sulphide and polyethylene covers over one night in April 2006.
Measurements (sunset to sunrise)
Zinc sulphide
Polyethylene
Total net radiative heat loss (Wh/m2) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
470 7 10 33.9 7 0.5 49.0 7 0.5 283.0 7 0.2
5807 10 41.9 7 0.5 51.8 7 0.5 283.07 0.2
282.5 7 0.2
282.6 7 0.2
experiment was of several days’ duration and measurements of heat loss from zinc sulphide and polyethylene covered radiators were conducted simultaneously.
3. Discussion
Fig. 9. A typical measurement in passive mode. Ambient temperature (Tambient) and the temperatures of unheated anodised aluminium radiators (TZnS and Tpolyethylene) under zinc sulphide and polyethylene covers over one night in March 2006.
The main purpose of the investigation was to evaluate a novel convection cover for a radiative cooling apparatus using selective and non-selective radiator surfaces and compare its performance against polyethylene. It is not purported that the radiator surfaces chosen are optimised or high performance or that the radiator design is optimal. Previously published results of measurements of the properties of anodised aluminium [15] suggested that this material could make useful selective radiators. Unfortunately, it was not possible to exactly reproduce these earlier results because of the difficulty in re-creating the exact deposition conditions and in obtaining the same grade of aluminium. However, partly selective radiator surfaces with
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Table 8 Comparative performances of the convection covers of unheated pot belly high infrared emission black paint radiators (passive mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers. Measurements (sunset to sunrise)
Zinc sulphide 2
Total net radiative heat loss (Wh/m ) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
Polyethylene 260 710 22.8 70.5
2757 10 23.77 0.5 37.47 0.5 292.2 7 0.2
292.0 70.2
296.1 7 0.2
296.1 70.2
2785
4. Conclusions Radiative cooling using available materials promises to have practical application. Inexpensive materials that are suitable for use as partly selective radiators are readily available although more selective radiator surfaces (better performing and/or cheaper) need to be developed. The proof-of-concept convection cover, polyethylene, is not sufficiently robust to be a practical material. However zinc sulphide performs thermally nearly as well as polyethylene, but has been found to be a highly durable and suitable material, with the caveat that a less expensive method for manufacturing large zinc sulphide tiles needs to be developed.
References useful properties were able to be made from high purity aluminium by a typical local commercial anodiser. These anodised surfaces were still found to be more effective radiators than black body surfaces and measurements demonstrated that it was possible to use simple and inexpensive materials to construct useful selective radiators that are durable and easy to fabricate. Despite the utility of anodised aluminium as a partly selective radiator surface, calculations show that this material and those examined by other investigators are significantly less effective (approximately 2/3 as effective) as would be an ideal selective radiator and still leave considerable room for improvement. It is likely that optimal radiators with superior performance could be constructed using the proposed convection cover. The most useful general measurement of performance is the average radiative power (or total radiative heat loss divided by total measurement time) since that defines the usable cooling power of the system and determines the area required for a given desired cooling load. The results listed in Table 5 for heated anodised aluminium radiators, in Table 6 for heated high infrared emission ‘‘pot belly’’ black paint radiators, in Table 7 for unheated anodised aluminium radiators and in Table 8 for high infrared emission ‘‘pot belly’’ black paint radiators demonstrate that zinc sulphide and polyethylene covered radiators have comparable thermal performances despite the zinc sulphide tiles being 40 times as thick as the polyethylene sheet. The margins of error for net radiative heat loss, peak radiative power, average radiative power and lowest achieved radiator temperature overlapped for both types of cover with the exception of unheated anodised aluminium radiators. Zinc sulphide, although presently only available in an expensive optical grade, was found to be, as 4 mm thick tiles, impervious to environmental effects, in particular to degradation by solar ultraviolet radiation. It is possible that since the optical and mechanical requirements for a convection cover are less rigorous than those for scientific or military infrared optics applications, a lower optical/ mechanical quality (and lower cost) grade of zinc sulphide could be developed. A reduction in thickness could also reduce costs. The performance of zinc sulphide may be able to be improved by a reduction of thickness and the addition of anti-reflection coatings. For instance, calculations suggest a 10% improvement in transmittance at a wavelength of 12 mm for a reduction in thickness from 5.0 to 2.5 mm. There is however no evidence that any methods are available that can improve the durability of polyethylene, the only other identified practical convection cover material.
[1] E.E. Bell, L. Eisner, J. Young, R.A. Oetjen, Spectral radiance of sky and terrain at wavelengths between 1 and 20 microns, II. Sky measurements, J. Opt. Soc. Am. A 50 (12) (1960) 1313–1320. [2] P. Berdahl, M. Martin, F. Sakkal, Thermal performance of radiative cooling panels, Int. J. Heat Mass Transfer 26 (6) (1982) 871–880. ˚ ¨ [3] A. Angstr om, A study of the radiation of the atmosphere, Smith. Misc. Coll. 65 (3) (1915) 6–159. [4] A.K. Head, Method and means for refrigeration by selective radiation, Australian Patent No. 239364, 1959. [5] S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, G. Troise, The radiative cooling of selective surfaces, Sol. Energy 17 (1975) 83–89. [6] B. Landro, P.G. McCormick, Effect of surface characteristics and atmospheric conditions on radiative heat loss to a clear sky, Int. J. Heat Mass Transfer 23 (1979) 613–620. [7] C.G. Granqvist, A. Hjortsberg, Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films, J. Appl. Phys. 52 (6) (1981) 4205–4220. [8] N.A. Nilsson, T.S. Eriksson, C.G. Granqvist, Infrared transparent convection shields for radiative cooling: initial results on corrugated polyethylene foils, Sol. Energy Mater. Sol. Cells 12 (1985) 327–333. [9] M.J. Torbjorn, G.A. Nilsson, C.G. Granqvist, A solar reflecting material for radiative cooling applications: ZnS pigmented polyethylene, Sol. Energy Mater. Sol. Cells 28 (1992) 175–193. [10] A.H.H. Ali, H. Saito, I.M.S. Taha, K. Kishnami, I.M. Ismail, Effect of aging, thickness and color on both the radiative properties of polyethylene films and performance of the nocturnal cooling unit, Energy Convers. Manage 39 (1/2) (1998) 87–93. [11] M.A. Al-Nimr, Z. Kodah, B. Nassar, A theoretical and experimental investigation of a radiative cooling system, Sol. Energy 63 (1998) 367–373. [12] Hamza A.H. Ali, H. Saito, I.M.S. Taha, K. Kishinami, I.M. Ismail, Effects of aging, thickness and colour on both the radiative properties of polyethylene films and performance of the nocturnal cooling unit, Energy Convers. Manage. 39 (1/2) (1996) 87–93. [13] D.C. Harris, Materials for Infrared Windows and Domes: Properties and Performance, SPIE—The International Society for Optical Engineering, 1999 (p. 32). [14] E.V. Yashina, Preparation and properties of poly-crystalline ZnS for IR Applications, Inorg. Mater. 39 (7) (2002) 663–668. [15] W.C. Miller, J.O. Bradley, Radiative cooling with selective surfaces in a desert climate, in: Proceedings of the 4th National Passive Solar Conference, Kansas City, MO, 1979, pp. 480–482. [16] P. Berdahl, Radiative cooling with MgO and/or LiF layers, Appl. Opt. 23 (1984) 370–373. [17] T.S. Eriksson, S.-J. Jiang, C.G. Grandqvist, Surface coatings for radiative cooling applications: silicon dioxide and silicon nitride mad by reactive rf-sputtering, Sol. Energy Mater. Sol. Cells 12 (1985) 319–325. [18] M.D. Diatezua, P.A. Thiry, R. Caudano, Characterisation of silicon oxynitride multilayered systems for passive radiative cooling application, Vacuum 46 (1995) 1121–1124. [19] C. De Micco, C.M. Aldao, On the net radiation method for heat transfer, Eur. J. Phys. 24 (2002) 81–89. [20] R. Hull (Ed.), Properties of crystalline silicon, EMIS Data Reviews Series No. 20, INSPEC, IEE, London, UK, 1999, ISBN 0 85296 933 3, in: D.E. Aspnes (Chapter Ed.), Optical Properties of Si, p. 677.
Contents lists available at ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
A robust convection cover material for selective radiative cooling applications S.N. Bathgate n, S.G. Bosi 1 Applied and Plasma Physics, School of Physics, University of Sydney, NSW 2006, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 July 2009 Received in revised form 27 May 2010 Accepted 12 May 2011 Available online 28 June 2011
The enhanced cooling of exposed surfaces by radiative heat loss to the cold sky was investigated using a variety of commonly available materials. Zinc sulphide was identified as a durable substance suitable for the construction of convection covers for radiative cooling radiators. With respect to polyethylene, the most commonly used convection cover to date, the new material is mechanically stronger, impervious to damage by solar ultraviolet and in practical thicknesses is more transparent in the 8–14 mm waveband. Use of this window material with a previously proposed selective radiator material, a form of anodised aluminium that reflects radiation at wavelengths shorter than 8 mm allows for the economical production of an effective selective radiator system. Measurements were made on simple radiator plates and convection covers. & 2011 Elsevier B.V. All rights reserved.
Keywords: Radiative Cooling Selective Radiator Convection Cover
1. Introduction 1.1. Properties of the atmosphere The formation of frost by emission of infrared radiation from the ground to the cold night sky during a clear night is a common example of the loss of heat to the sky by radiative cooling. While ground temperatures in the early evening may be above the freezing point, the effective temperature of the high atmosphere may be as cold as 40 1C. Objects at a higher temperature (such as the ground) lose heat to the cold sky by radiative exchange. Although the ground is covered by air at a similar temperature, the complex nature of the atmosphere means that the sky does not behave as a simple black body and has a number of low absorption windows that are transparent to infrared radiation. The most important window for radiative cooling lies between the wavelengths of 8 and 14 mm. It is through this window that most of the energy transfer associated with radiative cooling occurs (Fig. 1). While radiative cooling is most effective during the night, heat can also be lost to the sky during the day providing the radiator surface is shaded from the sun.
The effectiveness of radiative cooling can be enhanced by technical improvements. Two in particular are important. The first is the use of selective surfaces that are designed to radiate energy in the 8–14 mm band of the infrared and reflect radiation outside those wavelengths. Selective surfaces that are matched to this atmospheric window are, in this application, more effective radiators than a black body if a depression of the radiator’s temperature below ambient is required. The second is the use of infrared transparent convection covers that insulate the radiator surface from the surrounding atmosphere. With an infrared transparent convection cover, it is possible for the radiator surface to cool to temperatures below ambient. The rate of radiative heat loss to the sky (and hence cooling of the radiator plate) is equal to the difference between the power emitted by the radiator and the power absorbed by the radiator from the sky. For example, Berdahl et al. [2] report that in a typical cooling experiment, the thermal sky irradiance may be 350 W/m2 while the radiator emits 420 W/m2, a difference of 70 W/m2 being the available cooling power. Any parasitic thermal conduction from the ambient to the radiator would reduce the available cooling power. 1.2. Radiative heat loss to the clear sky
n
Corresponding author. Tel.: þ61 413944734. E-mail addresses: [email protected] (S.N. Bathgate), [email protected] (S.G. Bosi). 1 Present address: Radiation Oncology Department, Prince of Wales Hospital, Randwick NSW 2031, Australia. Tel.: þ 61 2 93822515. 0927-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2011.05.027
The possibility of cooling by heat loss to the cold sky employing selective radiators has been understood since the work of ˚ ¨ Angstr om [3]. Little further work was published until that of Head [4]. Since that time selective radiation cooling has been investigated sporadically ([2,5–11] and others) and although some
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where Tr and Ts are, respectively, the absolute temperatures of the radiator surface and the sky, u(l,T) is Planck’s black body radiance integrated over a hemisphere, S(l) is the sky hemispherical spectral emittance, a(l) is the radiator hemispherical spectral emittance (absorptance) and A is the absorber area. This calculation assumes the radiator couples to the sky over a full hemisphere and is large enough in area to ignore edge or aperture effects. Parasitic heat gain by the radiator from its surroundings reduces the attainable effective cooling power Pc and the experiments reported below show that for the simple design of radiator reported herein, it was the dominant factor in the effectiveness of the radiative cooling system and has to be minimised by insulation. 1.3. Radiator surfaces
Fig. 1. Spectral radiance of the atmosphere measured at Coco Beach, Florida, by Bell et al. [1] showing the radiance of the 8–14 mm window at various angles from the zenith compared to the radiance of a black body at 298 K (solid black curve).
effective small scale systems have been constructed, to date no large scale use has been made of the technology. Bell et al. [1] carried out a study of the radiative properties of the atmosphere and defined the resource for radiative cooling. They measured the spectral emittance of the atmosphere between 1 and 20 mm from the zenith to the horizon and documented the energy flux that reaches the ground from the atmosphere. A black body maintained at a temperature of 31071 K was used as a radiometric reference standard for the measurements. Measurements were made at Cocoa Beach in Florida and at two sites in Colorado—Denver (1800 m) and Pikes Peak (4260 m). Similar recordings were made at each of these sites and it was found that the emission from the zenith declined as altitude increased. The measurements shown in Fig. 1 illustrate the departure of the atmospheric emission spectrum from that of an ideal black body. Between 8 and 14 mm, the radiant flux intensity is significantly less than for a black body at the equivalent temperature, in this case 298 K. Under a clear sky, there will be a net loss of energy by a radiator at ground level to the colder upper atmosphere. This ‘‘net radiative cooling power’’ is dependent on
the temperature of the radiator; the emissivity of the radiator; the inclination of the radiator surface from the zenith; the radiant flux emitted by the atmosphere and the humidity (water vapour absorbs radiation in the 8–14 mm band).
Taking these factors into consideration, the net radiative cooling power of a radiator (Pnet) is the difference between the power radiated by the radiator at its operating temperature minus the power absorbed by the radiator from the sky: Pnet ¼ Prad 2Pabs
Pc ¼ Pnet 2sDTss
ð3Þ
DTss can be increased by
reducing the non-radiative heat flow coefficient s by increas
ing the insulation around the radiator and placing an infrared transparent convection cover over the radiator; increasing the radiative heat loss Prad by modifying the surface emissivity and reducing the cooling load Pc.
1.4. Convection covers Although a number of materials exist that are suitable for use as radiator surfaces, materials that are suitable for use as convection covers are much harder to identify and to date, polyethylene film has been the only material employed as proof-of-concept, despite its vulnerability to rapid degradation by solar ultraviolet. A number of investigators have attempted to improve the durability of polyethylene by either incorporating ultraviolet resistant pigments into the film or by impregnating the surface with similar materials; however none have reported that these measures have greatly improved the long term durability. In particular, measurements of polyethylene durability made by Hamza et al. [12] in Egypt (an arid region where radiative cooling could have utility) demonstrated conclusively that polyethylene film failed completely over period of a few months. The failure to identify a suitable cover material has been a major stumbling block for the development of this technology.
ð1Þ
The radiated power (Prad) is calculated by integrating the emission spectrum of a black body at the temperature T of the radiator weighted by the hemispherical spectral emittance (¼hemispherical spectral absorptance) of the radiator surface a(l). The absorbed power (Pabs) is calculated by integrating the emission spectrum of the sky weighted by the hemispherical spectral absorptance of the radiator surface versus wavelength: Z 1 Z 1 Pnet ¼ A uðl,Tr ÞaðlÞdlA uðl,Ts ÞaðlÞSðlÞdl ð2Þ 0
Consider the radiator under steady-state conditions (i.e. negligible rate of temperature change). The steady-state temperature difference DTss between the radiator surface and the surrounding atmosphere is determined by the difference between the net radiative cooling power to the sky, Pnet, and the parasitic heat flow sDTss between the radiator and the surrounding environment. s is the linear heat transfer coefficient in W/m2/K and signifies the nonradiative heat inflow to the radiator surface. Both convection and true conduction are here rolled together into the coefficient s. At steady-state, the effective cooling power Pc of the radiator is given by
0
1.5. Potential infrared transparent cover materials A number of materials are transparent or partially transparent in the 8–14-mm infrared window. However, their suitability for use as a convection cover varies widely (Table 1). Zinc sulphide is transparent to infrared in the 8–14 mm waveband. The transmittance measurements reported here were performed on a Shimadzu IR-470 spectrophotometer using a slab of material without any attempt to suppress the surface reflectance. Reflectance is high for the high refractive index material ZnS and
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Table 1 Some properties of potential convection cover materials, including infrared transmittance in the 8–14 mm waveband, which was measured on a Shimadzu IR-470 spectrophotometer. Material
Mean transmittance 8–14 mm
Data source
Toxicity
Solar damage
Fabrication/cost
Polyethylene (CH2–CH2)n Zinc sulphide (ZnS) Zinc selenide (ZnSe) Tefzel (C–F polymer) Silicon
73% (100 mm thick) 64% (4 mm thick) 70% (7.1 mm thick) E10% (200 mm thick) 47% (0.6 mm thick)
Measured Measured [13] Measured [20]
Non-toxic Low Harmful by skin contact Non-toxic Non-toxic
Yes No No No No
Low cost High purity has high cost High cost Low cost High cost
Table 2 Power radiated from selective radiator surfaces at ambient temperature (ambient ¼298 K), radiator surfaces 5 K below ambient and radiator surfaces 10 K below ambient. Material
Reference
Net radiative power Prad at 298 K (W/m2)
Net radiative power Prad at 293 K (W/m2)
Net radiative power Prad at 288 K (W/m2)
Ideal selective radiator Black body Pot belly black paint (a high infrared emission black paint) Silicon oxide Silicon oxy-nitride Silicon nitride Anodised aluminiumb Anodised aluminiumc Anodised aluminium þ magnesium oxide
Calculateda Calculateda Measured [7] [18] [17] Measured Measured Calculateda
74.8 74.1 69.3 32.5 61.8 63.8 66.6 55.1 62.3
61.7 48.8 47.1 27.5 46.4 48.8 48.9 41.0 45.3
49.2 24.9 26.1 22.7 33.5 34.7 31.9 27.3 29.5
a b c
Calculated emissivity using Eq. (2). A sky temperature of 298 K was assumed. See Fig. 4 below 180 s anodised radiator surface. Anocoil—an aluminium reflector for light fittings.
accounts for roughly three-quarters of the deficit in transmittance. This can easily be reduced by the use of a suitable anti-reflection coating and would be expected to result in a significant improvement in cooling performance. ZnS is currently only available as a relatively expensive high purity window for scientific and military applications. The raw material ZnS powder is cheap and it is possible that a less costly, lower quality grade of ZnS could be used to produce practical convection covers for radiative cooling. Yashina [14] describes the optical and mechanical properties of poly-crystalline zinc sulphide prepared by different methods. Commonly, hot-pressed zinc sulphide is manufactured from powdered zinc sulphide, which is pressed between graphite faced anvils for 0.5–1.5 h at pressures of 50–60 MPa and temperatures of 925–950 1C. 1.6. Calculation of properties of radiator materials A limited number of materials have been investigated as potential selective radiator surfaces [5,7,15–18]. These materials have a performance superior to a black body where the radiator temperature drops below ambient although all of the surfaces tried so far fall short of the performance of an ideal selective radiator. The problem lies in obtaining a material that has a sharp transition between reflection and absorption and has maximum emission in the 8–14 mm waveband and maximum reflection outside that band. Calculated performances for various radiator surfaces assuming an ideal 100% transmittance convection cover and ignoring the effects of convection and conduction are listed in Table 2 for an ambient temperature of 298 K. The data for sky radiance in W/m2/sr were integrated to produce the hemispherical sky emission and these data were used in calculating the heat loss from radiator surfaces using Eq. (2). The sky radiance data were obtained from Bell et al. [1]. The radiator emissivity data were digitised from plots found in papers by Granqvist and Hjortsberg [7], Berdahl [16], Eriksson, Jiang and Granqvist [17] and Diatezua, Thiry and Caudano [18]. The data in Table 2 demonstrate the effectiveness of a selective surface when the radiator temperature falls below the ambient temperature. For example, an ideal selective radiator has
approximately twice the heat loss rate of a black body when the radiator temperature falls to ten degrees below an ambient temperature of 298 K. The sky temperature is assumed to be the same as ambient temperature—in general sky temperature will differ from the ambient temperature. Of all the materials considered, silicon nitride has the best performance at reduced temperatures while these figures suggest that anodised aluminium may be a practical and inexpensive selective radiator surface. It should be borne in mind that the calculations in Table 2 assume a radiator large enough to ignore edge or aperture effects, a condition probably not matched by the measurements listed.
1.7. Heat transfer models and calculations Landro and McCormick [6] developed a model that used the net radiation method of De Micco and Aldao [19] to calculate the fluxes between the radiator surface, the convection cover and the sky (Fig. 2 in Landro and McCormick [6]). Landro and McCormick [6] define the heat fluxes in the wavelength interval dl as
incoming radiation to the cover dqi,c; outgoing radiation from the cover dqo,c; incoming radiation to the radiator dqi,r and outgoing radiation from the radiator dqo,r.
Combining equations for the heat fluxes in the wavelength interval dl with the radiative heat loss from the radiator and with configuration factor¼1 (i.e. the radiator and the cover are of equal area, parallel and aligned) gives equation 4 in Landro and McCormick [6]. This equation was evaluated numerically using the transmittance of the polyethylene cover tc(y) from Catalanotti et al. [5] and values for es (sky emissivity) that were derived from the measurements of Bell et al. [1] for Cocoa Beach. Bell et al. [1] calculated es by taking the ratio of the measured spectral
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directional sky radiance and the black body radiance of a reference object at 300 K. Landro and McCormick [6] did not publish the temperature of their radiator (Tr), however it was possible to use the model to calculate the effects of varying directional sky emissivity es(l,y), the refectivity of the cover rc, ambient temperature Tr and radiator temperature T0. The model is sensitive to the directional sky emissivity. This means the model depends on accurately characterising the sky in which the radiator would operate. Because of the difficulty in obtaining the original tabulated data in Bell et al. [1], these data were digitised from a scan of Fig. 1 in Landro and McCormick [6]. To gauge the sensitivity of the model to the error inherent in the process of digitising this printed graph, these sky data were re-scaled by a pessimistic 710% and the resulting change in heat loss noted. A sensitivity analysis of the model confirmed that the most significant influence on heat loss was the directional sky emissivity es(l,y). It was found that an increase in heat loss of around þ30% resulted from a scaled 10% reduction in es(l,y) and decrease in heat loss of around 20% was found for a scaled 10% increase in es(l,y) for a black body radiator at 318 K. Changing the cover reflectivity by 710% produced a change in heat loss by 79% under the same conditions, showing, as expected, a linear relationship between cover reflectivity and heat loss. Landro and McCormick [6] have assumed that sky emissivity is independent of temperature. This seems a reasonable assumption for clear, dry air given the relatively small range of temperature variation under normal atmospheric conditions. Berdahl, Martin and Sakkal [2] state that the approximations used by Landro and McCormick [6] for the reflectance of the cover and radiator (using hemispherical values) and setting the cover temperature equal to ambient (if the cover emissivity is neglected) does not introduce serious errors. That the predictions generated by this model are highly dependent on the local sky emissivity at the time of measurement, suggests that real time sky emissivity data are required to accurately model the heat loss from an experimental radiator.
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Note that although the zinc sulphide plate is 40 times thicker than polyethylene (4 mm vs. 100 mm), the transmittances of the covers between 8 and 14 mm are similar (Figs. 2 and 3), with zinc sulphide showing an average transmittance of 64% between 8 and 14 mm and an average transmittanceE0.0 at wavelengths415 mm. This means that it would not be practical to use thicker polyethylene covers to improve weathering because the reduction in transmittance of the thicker material would defeat the purpose of the cover. However, a thinner ZnS plate may be viable. 2.2. Anodised aluminium as a selective radiator surface In this work, an investigation into the spectroscopic properties of anodised aluminium was undertaken following the work of Miller and Bradley [15] who reported that bright anodised aluminium showed promise as an inexpensive selective radiator. Measurements were made of the reflectance of the anodised surface of a similar material (1150 grade aluminium) and it was found that a useful radiator surface could be produced (see Fig. 4 below). The anodising conditions are as follows:
anodising voltage¼13 V DC; anodising current¼500 A DC; sulphuric acid concentration¼10% (by volume) and aluminium concentration 5–15 g/l.
The reflectance between 3 and 20 mm of the anodised aluminium declined gradually with increasing anodising time until at
2. Experimental 2.1. Measurements of properties of cover materials In this work, zinc sulphide (ZnS) was investigated as an alternative cover material and as shown in Fig. 3, it is sufficiently transparent in the 8–14 mm range to be useful.
Fig. 3. Measured transmittance of polished hot-pressed 4 mm thick zinc sulphide.
Fig. 2. Measured infrared transmittance of 100 mm polyethylene film (solid) plotted with atmospheric spectral radiance from the zenith (dotted) from Bell et al. [1] showing that the transmittance of polyethylene is well matched to the 8–14 mm atmospheric window.
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Fig. 5. Measured reflectance of high infrared emission black paint (pot belly black) shows a reflectance of approximately 10% between 6 and14 mm . Fig. 4. Measured reflectance of 1150 grade anodised aluminium showing a marked transition in reflectance at 180 s anodising time.
Table 3 Mean reflectance of anodised aluminium between 8 and 14 mm compared with the average reflectance between 3 and 8 mm . Anodising time (s)
Mean reflectance (%) 8–14 mm
Mean reflectance (%) 3–8 mm
30 90 150 180
86.0 75.4 67.4 12.1
73.4 66.3 59.6 52.0
180 s when the reflectance beyond 7 mm declined sharply (Fig. 4). The reflectance spectrum of the 180 s anodised test piece approaches the properties of a selective radiator with average reflectance between 8 and 14 mm E12% and average reflectance below 8 mm4 51%. The mean reflectance of anodised aluminium between 8 and 14 mm relative to the mean reflectance between 3 and 8 mm decreases with longer anodising times, suggesting that the thickness of the anodised layer is a critical variable in determining the reflective properties of the surface (Table 3). Longer anodising times (up to 12 min) produced surfaces with a reflectance similar to that of the 180 s anodising time test piece (Fig. 4). 2.3. Non-selective radiator surfaces Pot belly black paint, a high infrared emission black paint surface coating intended to be a high emittance black surface for use on wood-fired stoves and heaters, was used as an approximation to a black body radiator surface for experimental measurements. The following normal incidence plot of total reflectance (Fig. 5) was made using a Digilab FTS 7000 series FTIR spectrometer fitted with a PIKE integrating sphere and shows the low reflectance of this kind of high emission paint between 8 and 14 mm Above 5 mm, the measured reflectance of pot belly black was roughly 10%. Calculations using Eq. (2) (assuming an ideal Lambertian angular dependence) show that the infrared emission from pot belly black paint in that waveband is 90% of the emission from a black body radiating in the same waveband at 298 K and 97% of the emission from a black body at 288 K. 2.4. Experimental apparatus Radiator test boxes were constructed from 50 mm thick polystyrene foam arranged as 100 mm thick walls and a 50 mm thick
Fig. 6. Test boxes used to measure properties of radiator surfaces and convection covers.
base (see Fig. 6 below). The radiators were 100 mm2 aluminium plates. The radiator cavities were lined with aluminium foil to make the walls reflective to minimise edge effects so as to approximate an infinite radiator. A 330 O, 5 W resistor was attached with screws and thermally conducting paste to the underside of each of the radiator plates to provide a source of heat. Polyethylene or zinc sulphide convection covers were placed over the open tops of the boxes. The small differences between the temperatures of the radiators and ambient temperature required a precision of 70.1 K in the temperature measuring apparatus in order to make useful comparisons between radiators. For this reason, LM335 precision temperature sensors that produced an output of 10 mV/K were used as temperature sensors. The LM335 sensors were mounted between the polystyrene base and the radiator plate and were kept in thermal contact with the radiator plate with thermal conducting paste. The ambient temperature and the temperatures of two radiator plates were measured simultaneously. The analogue output of the temperature sensors was converted to a 12 bit digital value by an ICL7109 analogue to digital converter that gave a resolution of 1 in 4096 over a 4.096 V range. This gave a limit of measurement of 1 mV (equivalent to 0.1 K). All of the LM335 sensors were initially calibrated together in a distilled water ice bath (273.1 K) and in a boiling distilled water bath (373.1 K). Following this two-point calibration the accuracy of the measurements using the LM335 sensors was determined to be within 71 K. This difference between the outputs of the
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Table 4 Sources of error in the measuring circuit. Error
Type
Value (K)
Source
Number on Fig. 7
Long term stability of LM336 voltage reference Thermal stability of the LM336 Errors in the LM335 temperature probes Noise in the circuit components Errors in the 7109 A–D Variations in the radiator heater supply voltage Offsets in the LM335 probes Digitising resolution of the 7109 A–D Offsets of LM335 probes in thermal contact
Random Systematic Random Random Random Random Systematic Systematic Systematic
7 0.005 7 0.09 7 0.1 7 0.01 7 0.01 7 0.01 7 0.08@323, 7 0.18@273 7 0.1 7 0.5
Internal physical changes Thermal and electrical noise Thermal and electrical noise Thermal and electrical noise Thermal and electrical noise Thermal and electrical noise Non linearity of the internal circuit Internal circuit design Calibration
6 6 3 4 5 1 3 5 2
2.7. Measurements
Fig. 7. Potential sources of error in the measuring circuit and in the radiator heater power supply circuit.
probes was found to be an offset that could be subtracted and the result was that the precision of the temperatures measured by the probes was within 70.1 K, equivalent to the digitising error of the analogue to digital converter. As a test of the stability of the temperature measuring equipment, after 70 days all the probes were placed in thermal contact and allowed to track ambient temperature for several days. The variation in measurements between the probes was found to be still less than 0.1 K. Because temperature differences were the most important aspect of these measurements, the precision of 0.1 K was more significant than the accuracy of 1.0 K. 2.5. Sources of error in the experimental measuring circuit The largest errors were due to a drift in the outputs of the temperature probes and in the voltage reference that was connected to the analogue to digital converter. There was also a drift in the voltage regulator supplying power to the radiator heaters. The sum of all these sources of error was less than 0.1 K and within the digitisation resolution of the analogue to digital converter (Table 4 and Fig. 7). 2.6. Heat loss and gain in radiator test boxes Before radiative cooling measurements were made, the combined thermal conductance s of the walls, bases and tops of the boxes (and the enclosed air) was determined. The radiator plates were heated using their attached 330 O, 5 W resistors while a sheet of aluminium foil was used in place of the convection cover to act as a reflecting cover of minimal thermal mass to prevent heat being lost by radiation from the top of the box while heat loss to ambient by conduction and convection was measured. The temperature difference between ambient and the inside of the boxes versus power delivered was used to calculate the combined thermal conductance s (i.e. linear heat transfer coefficient).
Measurements of heat loss from the radiator test boxes with two different convection covers (100 mm polyethylene and 4 mm zinc sulphide) and two different radiator surfaces (anodised aluminium and pot belly black paint) were conducted on nights in Sydney, Australia, during February, March, April and May 2006. Ambient temperature and radiator temperatures were recorded continuously and the sun down and sun up times were used as the start and finish times for analysing radiator performances. As far as it was possible to determine from satellite cloud pictures and local weather reports, measurements were conducted on nights that were largely cloud-free although it was not possible to monitor this all night. Heat loss was calculated from the recorded temperatures, using the thermal conductance of the test boxes determined previously to calculate the parasitic heat flow. The following analysis assumes steady-state conditions, such that a term QT0 (where Q is thermal capacity and T0 is cooling rate) is omitted from the heat balance equation (Eq. (3)). The thermal capacity Q of the test boxes was estimated using published material properties and a range of night-time cooling rates T0 were taken from our measurements. QT0 was calculated and found to be well under 1% of the measured net radiative cooling power confirming the validity of our assumption. Measurements were performed in two modes: passive and active. In passive mode, the boxes were allowed to radiate overnight without the input of electrical heating power. During this time the temperature difference between ambient and the radiator surface was monitored. The system was assumed to be very near steady-state, in which case the effective cooling power of the system is zero and so the net radiative cooling power of the radiator plate simply equals the rate of parasitic heat gain from the surroundings (deduced from DT and s). The total parasitic heat gain between the exact times of sunset and sunrise (and hence total energy radiated by the plate) was calculated from the area under the temperature/time curve. That is, the temperature difference DT between the radiator surface and ambient was recorded and integrated versus time. This integral value was multiplied by the linear heat transfer coefficient s to yield the total energy transfer. In active mode, the radiators were heated electrically using the 330 O, 5 W resistors in order to simulate the performance of a practical cooling system. Again the energy balance was assumed to be at steady-state; so the net radiative cooling power of the radiator plate equalled the power delivered electrically to the radiator plate minus the parasitic heat loss. The passive mode measurements were used to determine the lowest attainable temperatures. The experiments were conducted under the following conditions:
Radiator cases sealed and weatherproofed to keep insides as dry as possible.
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Radiator surfaces: pot belly black paint or anodised
aluminium. Heat input: 42.270.7 W/m2 (330 O resistor supplied by 11.870.1 V regulated supply). Radiators were operated with fixed power input or with no power input. Convection covers: 100 mm polyethylene or 4 mm ZnS. Location: an exposed flat roof with a clear view of the sky and without nearby surrounding buildings, structures or trees. Weather: generally clear and mild to warm (Southern Spring). Time of experiments: sunset to sunrise.
2.8. Results Fig. 8 shows the simultaneous temperatures of two heated anodised aluminium radiator plates (active mode) covered by polyethylene and zinc sulphide for a typical experiment conducted between sunset and sunrise. The ambient temperature (Tambient) and the temperature of the radiators (Tpolyethylene and TZnS) are plotted for one night. Similarly, Fig. 9 shows the simultaneous temperatures of two unheated anodised aluminium radiator plates (passive mode) covered by zinc sulphide and polyethylene for a typical experiment conducted between sunset and sunrise. The measurements shown in Fig. 9 demonstrate stagnation temperatures of up to 6 K below ambient. The averaged results from five separate experiments (active mode) are shown in Tables 5 and 6 and from two separate experiments (passive mode) are shown in Tables 7 and 8. Each
Table 5 Comparative performances of the convection covers of heated anodised aluminium radiators (active mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers. Measurements (sunset to sunrise)
Zinc sulphide 2
Total net radiative heat loss (Wh/m ) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
Polyethylene
430 7 10 32.5 7 0.5 49.9 7 0.5 288.4 7 0.2
4207 10 32.2 7 0.5 50.27 0.5
289.4 7 0.2
289.2 7 0.2
Table 6 Comparative performances of the convection covers of heated pot belly high infrared emission black paint radiators (active mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers. Measurements (sunset to sunrise)
Zinc sulphide
Polyethylene
Total net radiative heat loss (Wh/m2) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
340 7 10 29.6 7 0.5 44.5 7 0.5 295.3 7 0.2
355 7 10 31.3 7 0.5 45.07 0.5 295.7 7 0.2
295.4 7 0.2
295.9 7 0.2
Table 7 Comparative performances of the convection covers of unheated anodised aluminium radiators (passive mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers.
Fig. 8. A typical measurement in active mode. Ambient temperature (Tambient) and the temperatures of heated anodised aluminium radiators (TZnS and Tpolyethylene) under zinc sulphide and polyethylene covers over one night in April 2006.
Measurements (sunset to sunrise)
Zinc sulphide
Polyethylene
Total net radiative heat loss (Wh/m2) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
470 7 10 33.9 7 0.5 49.0 7 0.5 283.0 7 0.2
5807 10 41.9 7 0.5 51.8 7 0.5 283.07 0.2
282.5 7 0.2
282.6 7 0.2
experiment was of several days’ duration and measurements of heat loss from zinc sulphide and polyethylene covered radiators were conducted simultaneously.
3. Discussion
Fig. 9. A typical measurement in passive mode. Ambient temperature (Tambient) and the temperatures of unheated anodised aluminium radiators (TZnS and Tpolyethylene) under zinc sulphide and polyethylene covers over one night in March 2006.
The main purpose of the investigation was to evaluate a novel convection cover for a radiative cooling apparatus using selective and non-selective radiator surfaces and compare its performance against polyethylene. It is not purported that the radiator surfaces chosen are optimised or high performance or that the radiator design is optimal. Previously published results of measurements of the properties of anodised aluminium [15] suggested that this material could make useful selective radiators. Unfortunately, it was not possible to exactly reproduce these earlier results because of the difficulty in re-creating the exact deposition conditions and in obtaining the same grade of aluminium. However, partly selective radiator surfaces with
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Table 8 Comparative performances of the convection covers of unheated pot belly high infrared emission black paint radiators (passive mode). Total net radiative heat loss (Wh/m2), average radiative power (W/m2), peak radiative power (W/m2), radiator temperature at peak radiative power (K) and ambient temperature at peak radiative power (K) are compared for zinc sulphide and polyethylene convection covers. Measurements (sunset to sunrise)
Zinc sulphide 2
Total net radiative heat loss (Wh/m ) Average net radiative power (W/m2) Peak net radiative power (W/m2) Radiator temperature at peak radiative power (K) Ambient temperature at peak radiative power (K)
Polyethylene 260 710 22.8 70.5
2757 10 23.77 0.5 37.47 0.5 292.2 7 0.2
292.0 70.2
296.1 7 0.2
296.1 70.2
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4. Conclusions Radiative cooling using available materials promises to have practical application. Inexpensive materials that are suitable for use as partly selective radiators are readily available although more selective radiator surfaces (better performing and/or cheaper) need to be developed. The proof-of-concept convection cover, polyethylene, is not sufficiently robust to be a practical material. However zinc sulphide performs thermally nearly as well as polyethylene, but has been found to be a highly durable and suitable material, with the caveat that a less expensive method for manufacturing large zinc sulphide tiles needs to be developed.
References useful properties were able to be made from high purity aluminium by a typical local commercial anodiser. These anodised surfaces were still found to be more effective radiators than black body surfaces and measurements demonstrated that it was possible to use simple and inexpensive materials to construct useful selective radiators that are durable and easy to fabricate. Despite the utility of anodised aluminium as a partly selective radiator surface, calculations show that this material and those examined by other investigators are significantly less effective (approximately 2/3 as effective) as would be an ideal selective radiator and still leave considerable room for improvement. It is likely that optimal radiators with superior performance could be constructed using the proposed convection cover. The most useful general measurement of performance is the average radiative power (or total radiative heat loss divided by total measurement time) since that defines the usable cooling power of the system and determines the area required for a given desired cooling load. The results listed in Table 5 for heated anodised aluminium radiators, in Table 6 for heated high infrared emission ‘‘pot belly’’ black paint radiators, in Table 7 for unheated anodised aluminium radiators and in Table 8 for high infrared emission ‘‘pot belly’’ black paint radiators demonstrate that zinc sulphide and polyethylene covered radiators have comparable thermal performances despite the zinc sulphide tiles being 40 times as thick as the polyethylene sheet. The margins of error for net radiative heat loss, peak radiative power, average radiative power and lowest achieved radiator temperature overlapped for both types of cover with the exception of unheated anodised aluminium radiators. Zinc sulphide, although presently only available in an expensive optical grade, was found to be, as 4 mm thick tiles, impervious to environmental effects, in particular to degradation by solar ultraviolet radiation. It is possible that since the optical and mechanical requirements for a convection cover are less rigorous than those for scientific or military infrared optics applications, a lower optical/ mechanical quality (and lower cost) grade of zinc sulphide could be developed. A reduction in thickness could also reduce costs. The performance of zinc sulphide may be able to be improved by a reduction of thickness and the addition of anti-reflection coatings. For instance, calculations suggest a 10% improvement in transmittance at a wavelength of 12 mm for a reduction in thickness from 5.0 to 2.5 mm. There is however no evidence that any methods are available that can improve the durability of polyethylene, the only other identified practical convection cover material.
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