Yu. Maydanik

Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences Amundsen st. 106, Ekaterinburg, 620016, Russia

Phone: +7 (343) 2678791. Fax: +7 (343) 2678799. E-mail: maidanik@etel. ru

Loop heat pipes (LHPs) are hermetic heat-transfer devices operating on a closed evaporation-condensation cycle with the use of capillary pressure for pumping the working fluid [1]. In accordance with this, they possess all the main advantages of conventional heat pipes, but, as distinct from the latter, have a considerably higher heat-transfer capacity, especially when operating in the “antigravity” regime, when heat is transferred from above downwards. Besides, LHPs possess a higher functional versatility, are adaptable to different operating conditions and provide great scope for various design embodiments. This is achieved at the expense of both the original design of the device and the properties of the wick — a special capillary structure used for the creation of capillary pressure. The LHP schematic diagram is given in Fig. 1.

The device contains an evaporator and a condenser — heat exchanger connected by means of smooth-walled pipe-lines with a relatively small diameter intended for separate motion of vapor and liquid. The evaporator is equipped with a wick specially configured for providing in it a sufficiently low hydraulic resistance, despite a very small pore radius of the order of 1 micron. The evaporator is joined to a compensation chamber intended for accumulating the working fluid during the operation of the device.

The most efficient working fluids for LHPs in the range of operating temperatures from 20°C to 200°C are ammonia and water. It is also possible to use some other working fluids which possess the necessary thermophysical properties and are chemically compatible with LHP structural materials, which are copper, stainless steel, nickel, titanium.

Wicks sintered from fine-grained particles are capable of creating the pressure required for pumping a working fluid for a distance up to several tens of metres along pipe-lines 6-10 mm in diameter. In operation in the “antigravity” regime the heat-transfer distance may reach 5-7 m, and its value 1-5 KW.

The device may have one or several parallel evaporators and condensers, whose design varies in accordance with the conditions of heat exchange with the heat source and the heat sink.

At present loop heat pipes are most extensively employed in thermoregulation systems of spacecrafts. Miniature LHPs are used for cooling electronics and computers. At the same time there exists a considerable potential of using these devices for the recovery of low-grade (waste) heat from different sources, and also in systems of sun heat supply. In the latter case LHPs may serve as an efficient heat-transfer link between a sun collector and a heat accumulator, which has a low
thermal resistance and does not consume any additional energy for pumping the working fluid between them.

Two PMBLDC motor/fans of different ratings (9.5 W and 20.3 W) were tested with a 10 Wp PB Solarex polycrystalline PV module at Napier University in Edinburgh. Initial tests were performed on the PV module and each of the fans separately for performance evaluation and determination of the motor/fan constants given in Eqs. 2, 3, 6 and 8. Each of the PV module-fan combinations were then installed in a slate roof section and performance was monitored

1.3 The PV module

The method used for predicting the PV module I-V characteristic as a function of irradiance and module temperature requires the measurement of the PV module reference I-V curve. Voltage and current were recorded for different selected resistive loads using two multimeters and a variable resistor. The reference data and derived constants for the 10 Wp module are shown in Table 1. Figure 2 shows a comparison between measured I-V curves and those generated by the newly developed method.

1.4 The motor/ fan

Due to the absence of motor parameters from existing manufacturer’s data, stall conditions, no-load conditions and Eq. (7) are used to evaluate motor parameters. Table 1 shows Ra, Km and Kf for both motors.

Manufacturer’s H-Q curves for the two fans are shown in Fig. 1. These curves are generated from the affinity fan laws at ю = 2000 r / min.

The fans were also tested to determine their I-V curves as shown in Fig. 2. Furthermore, measurements of speed and voltage were carried out in the roof section where the fans were installed. These measurements serve as a means to calculate the measured speed from voltage measurements across the fan. The reason such a relationship is needed is because it is possible to log voltage data into a data logger while this is not possible for speed measurements.

1.5 Roof section

The fans were fixed into a plenum centred between the rafters in a roof section which was prepared for solar preheating and ventilation testing. Irradiance, module temperature and the voltage across the fan (V) were measured for several days at 5-minute intervals. Irradiance measurements were obtained using a Kipp and Zonen pyranometer directly connected to a data logger. A k-type thermocouple placed in the middle at the back of the PV module [14] was used for temperature measurements. The voltage of the motor/fan was also logged into the data logger.

The first option proposed consists of two pairs of curved mirrors and a flat one. Figure 1 shows a sectional view of this concentrator (the flat mirror is not presented here). The bigger curved mirrors are parabolic and the smaller are elliptic and they have the following parametric equations, where the parameter т corresponds, in a polar coordinate system, to the angular coordinate of a point on a mirror. The semi angle of acceptance of the concentrator is 00, which has a value between 0 and 30° is a veiy important design parameter. The extreme value of 30° corresponds to a flat collector without MCC.

For the CPCi (truncated) mirror:

Where:

q = Tan 1

And the geometric solar concentration is:

Only a part of the beam radiation impinging on the concentrator aperture reaches the absorbers of the flat collectors. The acceptation function F (t ) is defined as the fraction of beam radiation, which reach the absorber for a given angle of incidence t.

if 0 <T<TC = — — 30o

Now, the thermal efficiency of a flat collector with the MCC is ingenuously approximate by:

(16)

where r|max, B and C have the same values that in equation 5, and the energy gathered per m2 of flat collector is now calculated from:

Qu = C Г+ F (t (t)) r (t) G (t)k (t) dt

ta

And the mean efficiency is given by:

Г + N F (t(t))r (t) G (t)k (t) dt

ta

ta + N

Г G (t) dt

ta

The calculated values for the energy gathered for flat-plate solar collectors with this MCC as compared to a the same collectors without the MCC shows that Qu increases as the acceptance half angle e0 decreases even though the overall efficiency can decrease for small values of Є0. This MCC makes a best job when high values temperature are needed. For temperatures about 80° C, for example, the rate of the flat solar collectors is as least doubled when the MCC is implemented in them.

For solar collectors whose absorbers cannot resist high temperatures, a second option is suggested. This variation consist in to substitute the parabolic mirrors with flat mirrors with the same acceptance half angle. The elliptic mirrors must be substituted by others parabolic (non-truncated) as it is shown in figure 2. The acceptation function changes, but the most significant difference consists of a geometric concentration Cg much smaller, so the benefits are reduced. But this option is still attractive for inexpensive arrays of flat-solar collectors.

For this second option, the coordinates of extreme points Pmax and Pi are the following:

And the geometric concentration is given by:

(22)

The new acceptation function is defined as:

Where

Equations 16, 17 and 18 are used to evaluate the performance of this arrays with the MCC solar concentrator for different operational temperature, acceptance half angles, reflectance of the mirrors, ambient temperature profiles, etcetera. Table 1 shows a comparison between two-flat collector arrays with and without MCC. It must be noted that the maximum values of the mean thermal efficiency and the useful heat for each temperature of operation correspond to different acceptance half angle. This occurs because the MCC increases the area of solar acceptation, but it shadows partially the absorbers of the flat collectors.

Therefore exists a trade-off between the energy collected, the mean thermal efficiency, the temperature of operation and, of course, the cost of the MCC and the flat collectors. Tables like table 1 can help to choose the most convenient option for a given application and budget. As an example, for an array of commercial solar collectors like the model used for build the table 1, a MCC with an half acceptance angle of 22° would deliver 9,75 % more useful heat if the application is at 30 ° C, but it would deliver 27% , 55,6 % or 111,6 more for operational temperatures of 70, 90 and 110 ° C, respectively. For 30° C the output energy would be slightly smaller.

CONCLUSIONS

A simple multi-compound solar concentrator intended to improve the performance of arrays of flat-plate solar collectors have been developed in two options. Both of them improve the performance of the array in an economical way cause the cost of the added MCC is a small fraction of the cost of the system but the rate can be doubled or almost triplicate, if the required temperature of application is high enough. In this paper it is not described the effect of a fifth mirror placed at the bottom side of the array, nor the increase of the angle of inclination of the collectors. These two aspects have a very important role in boosting even more the system performance and will be presented in a future paper.

REFERENCES

[1] ANSI/ASHRAE 93-1986 (1986), Methods of testing to determine the thermal performance of solar collectors, ASHRAE Standard, USA.

[2] Duffie J. A, and Beckman W. A. (1980), Solar Engineering of Thermal Processes. 2nd Ed., John Wiley & Sons, Inc., USA.

[3] Fernandez Zayas J. y Estrada-Cajigal V. (1983), Calculo de la radiacion solar instantanea en la Republica Mexicana, Series del Instituto de Ingenieria No. 472, UNAM.

■ Several varieties of centralized systems were investigated; freshwater storage systems, "storage loaded” systems (that is, double storage tank combinations with combined buffer and freshwater storage tanks) and buffer storage systems with additional freshwater unit. The storage tank buffer system with a freshwater unit and the storage loaded system with the heating element in the freshwater tank showed the same energy efficiency if the design and the system concept was optimized. Both systems have a significant advantage over the "storage loaded” system with the heating element in the buffer storage tank, but only an insignificant advantage over the freshwater storage system (which requires a larger collection area).

■ Among the centralized systems, no one system showed itself to be clearly better than the others in terms of cost. When choosing a system, it is recommended that other aspects which are less quantifiable be considered. For example, factors such as bulky design requiring more space, costly installation or more difficult adjustment and operating instructions in the case of the double storage tank systems should also be taken into account.

■ It is possible to achieve an improvement in the solar contribution (depending on the system) of between 2 and 8 % by using a stratified charging in the centralized solar storage tanks.

Organizational Aspects

The most important criteria in making the decision to convert to a centralized heating system are the aspects of ownership and responsibility. Both when the Housing Committee organize the installation of the system or when an external company is employed, the house owners are the official owners of the heating system. If the heating system is leased, then the Contractor remains the owner of it. Many building companies view the idea of leasing a heating system as a psychological impediment for prospective
house buyers, who are in effect, purchasing a house ‘without a heating system’. On the other hand, factors such as the cost of the house being reduced significantly due to the many investors in the heating system, and a much better service in terms of maintenance could be seen as a definite incentive to install such a system. It is important that the decision in favor of a centralized system or otherwise is taken as early as possible so that the correct model can be selected and the appropriate choice of heating company can be made, as well as the arrangement of the contracts. Highest priority should be given to the signing of contracts as early as possible, whether the house owners or the leasing company own the heating system. It is very important for all parties involved to have a clear agreement on issues such as ownership, guarantees and the responsibility of each party, all which must be clearly defined.

Table 1 shows an extract from the technical and economic values of comparable heating systems concepts investigated during the project /2/.

4 Conclusion

The above results show that “mini-centralized” hot water systems using solar units between 20-60 m2 collector area offer clear advantages, especially from an economic point of view. Certainly, there are a variety of environmental factors which can influence results, so that no general recommendations (or rules of thumb) can in fact be given. An appropriate concept must be devised to accommodate each individual housing requirement. The above findings from the comparison project can serve as a reliable data source when planning solar hot water systems in the future.

5 References

/1/ K. Schwarzer, C. Wemhoner, B. Hafner:

Berechnung von Solaranlagen mit CARNOTunter MATLAB-Simulink®,

10. Symposium Thermische Solarenergie, Staffelstein, 2000

/2/ K. Schwarzer, C. Faber, T. Hartz, F. Spate, C. Petersdorff, J. Backes:

Planungshilfe solare Brauchwasserversorgung in Siedlungen — zentral oder dezentral?, Ecofys GmbH, Eupener Strafte 59, 50933 Koln

Experiment No 1

Initially water was taken for the experiment in order to find the temperature increase, and kept in the Line Concentrated Solar Funnel Cooker and following observations were taken. The intensity of solar rays was only 400 W/m2. (That was on cloudy day)

Amount of water taken = 3 l Initial Temperature of water = 360C

Time duration of experiment = 5 hours

The efficiency of the Line Concentrated Solar Cooker can be calculated as follows:

Mass m = 3 kg ; Sp. Capacity Cp = 4.18 * 103 kJ/kg K; Temp Difference AT = (85-36) = 490C ; Time Duration T =150 minutes ; Intensity I =400 W/m2 ; and A = % of area covered by sunrays* total area = (0.925+0.775)/2 * 1.67=1.419 m2.

Water was taken for the experiment in order to find the temperature increase, and kept in the Line Concentrated Line Concentrated Solar Cooker and following observations were taken. The intensity of solar rays was 500 W/m2.

Amount of water taken = 3 l, Initial Temperature of water =380C

Time duration of experiment = 5 hours

Mass m = 3 Kg ; Sp. Capacity CP = 4.18 * 103 kJ/kg K; Temp Difference AT = (99-38) = 610C; Time Duration t =110 minutes ; I =500 W/m2 ; and A = % of area covered by sunrays* total area = (0.95+0.85)/2 * 1.67=1.503 m2.

Efficiency = 15.42%

Experiment No 3

As the temperature of the water rose up to 99 degree C and got converted into steam. It was decided to make a low-pressure steam generator. Hence aluminum can was taken which holds the capacity of 3 l of water and converts it in to steam when exposed to the sunrays. And steam produced can be utilized for the heating the water. An aluminum can was tightly sealed, so that steam produced and the water does not leak out. Hence the can was made to have two openings. One opening for water inlet and other for steam outlet. This can was kept in center of the Line Concentrated Solar Cooker on a bright sunshine day. The observation was a follows:

= 3 l Initial temperature of water = 300C

= 5 hours Intensity = 550 W/m2

After 90 minutes steam started getting out of the chamber. The steam continued to come out of the chamber for next 120 minutes.

After the experiment completion, the following observations were made.

Final temperature of water = 980 C

Volume of water after experiment = 2.25 l

Amount of water converted to steam = 0.75 l

Total time taken = 210 minutes.

The efficiency of the Line Concentrated Solar Cooker can be calculated as follows:

Efficiency = *100

input

Output = (mw * CP * AT) + (ms * h)

t

Input = I * A

The values of the above-mentioned variable were as follows:

Mass m = 3 Kg ; Sp. Capacity CP = 4.18 * 103 kJ/kg K; Temp Difference AT = (100-30) = 70 0C ; Time Duration t =210 minutes ; I =600 W/m2 ; and A = % of area covered by sunrays* total area = ((0.925+0.6)/2 * 1.67 = 1.27 m2.

The fossil fuels are consumed in large range daily. It is the role of the energy engineers for the development of the renewable energy sources like Line Concentrated Solar Cooker in order to compensate the fossil fuels. India is gifted with enormous amount of the renewable energy like solar energy. This has to be utilized effectively by producing some devices for capturing the energy. One of such device is the above-mentioned, which gave a tremendous performance with maximum efficiency of 27.2%. Thus such type of devices should be used for domestic purpose like cooking, heating water, pasteurization etc,. This device can be manufactured with great ease using the materials that are easily and vitally available. The material used for this device was Galvanized Iron Sheet whose cost is very low when compared to other type of cookers. Unlike other solar devices, there is no need of covering the full device with glass sheets for producing green house effect, but the green house effect can be increased by covering the can suitably with high density poly ethylene sheet which can withstand high temperatures. This device can be encouraged for usage in rural areas where electricity is not available. More over the device is cheap and economically feasible.

LITERATURE CITED

1. Garg, H. P; Prakash, J. 1997 "Solar Energy Fundamentals and Applications”, Tata McGraw Hill Publications.

2. Salaria K. S., Singh M. 1978‘Solar Cooking Appliances’ Proc National Solar Energy Convention, Bhavnagar Dec.,

3. Srinivasan et al. 1979.‘A Simple Technique for Fabrication of Parabolic concentrator’ Solar Energy, 22,

4. VITA 1971. ‘Solar Cooker Construction Manual’ 11009 BK A VITA Publication.

5. INTERNET Site http://solarcooking. org/funnel. htm on Solar Cookers.

6. Mathur S. S. & Bansal N. K. 1981, ‘Indian Institute of Technology Renewable energy Research in India, Aug.

Optical scheme for the CLON is depicted on Fig. 2 and 3. Requirements for optical scheme are:

1. rays incoming at angle ©A shall be reflected from end point of each zone to the opposite focus F2.

2. rays incoming at 0° shall be reflected by beginning point of each zone always to adjacent focus F1.

It can be shown that at suitable shape of the concentrator according to the criteria above, also other rays in the angular range defined and reflected by inner points of mirrors will always hit the receiver. Rays bounding the zone are in addition to those specified above these:

1. incomming at ©A and reflected by beginning point of zones

2. incomming at 0° and reflected by ending points of zones.

It is clear that if the receiver will be hit by rays reflected from beginning and ending points of a zone, all the rays between them will also meet surface of receiver. The same time, boundary point between two zones is always a beginning point of one of them and ending point of another. Details can be seen on fig. 3. Single reflection of this type of concentrator is satisfied by situation at © = 0° and reflection by beginning of a zone. If a ray is to be directed to the opposite corner (focus) F1 and all other rays within that zone must be with this rim ray parallel, not a single ray can be reflected before the focus F1 (on axis x), i. e. will never hit a lower placed zone (mirror).

Optical scheme shown on figures had undergo a transformation to geometry, by means of which final recursion formulas for calculation of the shape of mirrors has been derived. Number of mirrors is on selection of designer, as well as required acceptance angle (in accordance with required concentration level and tracking). Output area d defines the overall size of concentrator and do not affect to its shape. So each mirror can be then described by a pair of parameters — inclination ©i and length li, where i stands for index of current mirror. Recursion formulas for calculation of current mirror requires to know the parameters of all the lower (i. e. previous) mirrors:

Z l; COS © ;

©n = 90o — jarCtg^

Z i;s;n ©;

i=i

l = C°s(2Qn — QA — Qi) _dCOS(2Qn — Qa)

n “1 ; COs(©n -©A) COs(©n -©A)

Ending points of current mirror n can be calculated as

n

xn = Z l; cos ©

i=1

n

Уп = Zli sin0i

i=1

From equations above can be seen that it is not trivial to calculate the first zone at is has no predecessors. Length of first mirror can be obviously calculated by knowing the current (this time the first) inclination angle, but there is no prescription to calculate just the first inclination angle. It can be chosen, though it has been shown that there exist a range for selection, but concentrators with different angle ©1 and equal in all other parameters will differ in concentration factor C. Thus, in the set of solution there exist one which is supposed to be optimal. We need to find it in an optimisation process.

To optimize the concentrator according to C (also alternative for optimisation according to utilisation factor M has been laid under analysis) failed by analytic manner, thus it has been performed using numerical methods. It has been proved that such optimal solution exist and is unique. Aim of optimisation lies in maximisation of the function C = f (©1), i. e. it is necessary to find

sup {C (©1; ©a, n): ©1 є (0; 90°); ©A, n = const}

We assume that optimal inclination of the first zone will depend not only on acceptance angle ©A, but also on number of mirrors n. This means that number of mirrors must be known right before the optimisation run. From the said follows that it is not possible to add further zones later. Solution of optimisation will be searched in the form

©1 = f (©A; n), where n is taken as a parameter

In Shah, L. J. & Furbo, S. (2003) and Shah, L. J. & Furbo, S. (2004), a theoretical model for calculating the thermal performance of evacuated collectors with tubular absorbers was developed. The principle in the model was that flat plate collector performance equations were integrated over the whole absorber circumference. In this way, the transverse incident angle modifier was eliminated. The model was valid only for vertically tilted pipes.

In this section, the principle of the model will shortly be summarized. Further, the newest development that improves the model to be able to also take tilted pipes into calculation will be described.

Generally, for a solar collector without reflectors and without parts of the collector reflecting solar radiation to other parts of the collector, the performance equation can be written as:

TOC o "1-5" h z P. = P + Pd + P8I — Ploss (1) or more detailed described:

P« = Ab■-F’-(та).-K9’Rb’Gb + A. — F ’-(ха). — Kw — FcVG + A.-F’-(та).- — Fc_8^ — A. U — (Tta — T.) (2) where Ke is the incident angle modifier defined as:

Ke=1 — tan‘ (jj (3)

The incident angle modifiers for diffuse radiation, Ke, d, and ground reflected radiation, Ke, gr, are evaluated by equation 3 using 0=n/3.

To calculate the thermal performance of the evacuated tubes, the general performance equations (1) and (2) have been integrated over the whole absorber circumference. This means that the tube is divided into small "slices”, and each slice is treated as if it was a flat plate collector. In this way, the transverse incident angle modifier is eliminated. For describing the solar radiation on a tubular geometry, this method has previously been used by Pyrko J. (1984). .

SHAPE * MERGEFORMAT

Power from beam radiation on collector/tube, Pb:

The power contribution from the beam radiation can be written as:

0 <Vl-y0 <k : Pb = } F’-(xa)e-Gb-Ab-K9= F’-(xa)e-Gb-LV} K9^-d?

To To

0 <Yo-у, <k : Pb = ] F’-(xa)e-Gb-Ab-K9 ^-d? = F’-(xa)e-Gb-L-rp-} K9^-d?

Fig. 3 shows an example where a part of one tube vector N tube is shaded and a part is exposed to beam ’ ‘

radiation. In order to determine the size of the area exposed to beam radiation, the points P0 and P1 must be determined.

Since P0 is located where the solar vector and the tube vector are at right angles to each other, P0, described by the angle y0, can be determined by the scalar product of the two vectors:

S-N = |s|-|N|-cos (J = o ^ sin 6,-cos уs’cos ( “-Ps j cos уo + sin 6,-sin уs-sin у o + cos 6,-sin ( “-Ps ]’sin Yo — o =

Since the equation for Yo involves the tangens function, the equation will return two solutions. Based on information on the position of the sun, the correct solution is found.

Fig. 4: Illustration of the

Equations(15) (16) and (17) together give four equations shaded area and the area to the four unknowns: T, Y1, xn and zn. Solving for Y1 gives: exp0sed t0 beam rndiati0n.

(19)

1

v 2 s) tan (6z )-sin (ys — yf)

4 2 2 2 2

4 — ^^3 ^^"1 ^^3 K2 ^^3

From equation (18) it appears that there are two solutions for y1. Based on information on the position of Y0, the correct solution is found.

The incident angle, в, and the geometric factor, Rb:

The incident angle, 0, can be described as:

C0S(6) = sin(62)-COs(ys — У f)-COS I -2 — p, J’COS(y actual) + — y f)-sin(y„cl„1) + COs(62)-sin I jC°S(y aCMJ

Solving the performance equation:

In order to evaluate the performance of the tubular collector on a yearly basis, the above theory is implemented into a Trnsys type. All the integrals can be solved analytically, except the integral in equation (11), which is solved by using the trapezoidal formula for solving integrals numerically. 360 integration steps are used in the numerical integration. Taking the collector capacity into account, the collector outlet temperature is evaluated by:

D. G. Kroger, Dept. ofMech. Eng., University of Stellenbosch, South Africa M. Burger, Dept. ofMech. Eng., University of Stellenbosch, South Africa

The convection heat transfer coefficient between a horizontal surface and the natural environment is determined experimentally. It is shown that heat is transferred due to natural and forced convection. The results are compared to values obtained by other investigators. A good correlation is obtained between a new semi-empirical equation and experimental results.

Introduction

Consider the energy balance that is applicable to a unit area of horizontal surface that is exposed to the natural environment on a clear, dry, sunny day, as shown in figure 1, i. e.

has = h(Ts — Ta) +Є so(Ts4 — Tsky4) — kg(dT/dz)

For diffuse surfaces as is constant. According to Duffie and Beckman [1] the surfaces of most solar collectors are such that the absorptivity is some function of the beam incidence angle, which for horizontal surfaces, is the zenith angle of the sun i. e.

lba„ + laas = lba, [і + 2.0345 x 10^вг -1.99 x 10^0? + 5.324 x 1O-6^ — 4.799x 10^в‘ ]

+,A

(3)

where /h = /b + /d, /b and /d are the beam and diffuse solar radiation respectively and0zis the zenith angle.

The first term on the right-hand side of equation (1) represents the convective heat transfer between the surface and the ambient air. The objective of this study is to determine the heat transfer coefficient h.

The second term on the right-hand side of equation (1) represents the long-wave radiation between the surface and the environment. In this term, the Kelvin sky temperature can be approximated by (Swinbank [2])

Tsky = 0.0552 Ta1’5

The third term on the right-hand side of equation (1) represents the heat that is conducted into the surface or ground. If the ground is insulated, this term is negligible and the heat transfer coefficient is given by

The results of tests that were conducted on surfaces exposed to the natural environment during windy conditions are reported by Duffie and Beckman [1], Watmuff, Charters and Proctor [3], Clarke [4] and Test, Lessman and Johary [5]. It should however be noted that the tests by Test, Lessman and Johary [5] were done on an inclined surface of 40°. In general the convective heat transfer coefficients for these tests are expressed as

h = a + bvw (6)

where a and b are supposed to be constants. Examples of these correlations are shown in figure 2. A correlation by Vehrencamp [6] that differs from equation (6) is also shown as well as a dimensionless equation according to Lombaard and Kroger [7]. Note the significant discrepancies between the equations.

It is obvious that equation (6) cannot adequately express the heat transfer coefficient. Equation (6) is not dimensionless and does not make provision for changes in thermo­physical properties. Furthermore, when the wind speed vw = 0, heat that is transferred due to natural convection is not constant, but is a function of the temperature difference between the surface and the ambient air as given by Bejan [8].

Nu = cRa13

or

where Tm = (Ts + Ta)/2 is the mean air temperature.

Many laboratory experiments have been conducted to determine the heat transfer coefficient due to turbulent natural convection from a heated horizontal upward-facing surface (Fujii and Imura [9], Rohsenow et al. [10], Lloyd and Moran [11], Al-Arabi and El — Riedy [12], Clausing and Berton [13]). Values of c range between 0.13 and 0.16. In part, this range of values for c is due to the fact that the test surfaces were made up of different materials and had different sizes. In some tests uniform surface temperatures were maintained while in other cases it was claimed that the heat flux was uniform.

Lombaard and Kroger [7] conducted experiments on an insulated 1m x 1m horizontal plate exposed to the natural environment. This truly uniform "heat flux” (solar radiation) test gave a value of c = 0.227.

Al-Arabi and El-Riedy [12] refer to the work of Kraus who tested 160mm x 160mm to 260mm x 260mm heated horizontal surfaces and obtained a coefficient of c = 0.137 and Kamal and Salah who studied a horizontal rectangular plate 504mm x 200mm maintained at constant temperature and concluded that for a plate of infinite size (for which case the edge effects could be neglected) the value of the coefficient was c = 0.135. Al-Arabi and El-Riedy [12] carried out experiments on upward facing heated plates at constant temperature. They tested square plates having dimensions varying from 50mm to 450mm, circular plates ranging from 100mm to 500mm in diameter and rectangular plates of 150mm wide and lengths of 250mm to 600mm. All their mean results are well correlated by a coefficient of c = 0.155. They also conducted an experiment on a square plate to find the heat transfer coefficient in the central part of the plate, which was not influenced by edge effects. The resultant coefficient had a value of c = 0.145.

According to the studies by Al-Arabi and El-Riedy [12], it would thus appear that for an infinite plate horizontal surface at constant temperature, c = 0.14 (average of 0.135 and 0.145). According to Kroger [14] the value of the constant for uniform heat flux is я/2 times this value i. e. 0.22. This value is close to the 0.227 found by Lombaard and Kroger [7].

Kroger [14] theoretically analysed the problem of convection heat transfer on a horizontal surface exposed to the natural environment. He shows that the dimensionless convective heat transfer coefficient is given by

1/3

In this approximate semi-empirical equation the constant c has a theoretical value of 0.243. The effective friction coefficient, Cf, has to be determined experimentally under windy conditions.

Experiment

Experiments were conducted at the Solar Energy Laboratory of the University of Stellenbosch, Stellenbosch, South Africa (Latitude -33.93°, Longitude 341.15° west). The experimental apparatus consisted of a 1m x 1m polystyrene plate having a thickness of 50mm, which was surrounded by an open area covered with a large black plastic sheet as shown schematically in figure 3. The plate was put on the black sheet to simulate an infinite black surface and to minimise edge effects.

The surface temperature measurements were obtained from six type T thermocouples that were embedded on the surface of the plate. Another four type T thermocouples were placed at different heights above the solar collector, as shown in figure 3, to measure the temperature gradient above the collector.

A weather station was used to measure ambient air temperature, barometric pressure, humidity, wind speed and wind direction. The wind speed was measured at 0.15m and 1.0m above ground level. Solar radiation was measured with a Kipp & Zonen pyranometer. All data was collected in one minute intervals and averaged over ten minutes.

Examples of experimental measurements as a function of solar time on a particular day are shown graphically in figure 4, 5, 6 and 7.

6 7 8 9 10 11 12 13 14 15 16 17 18 19

Solar time

Figure 6: Measured wind speed and direction at a height of 0.15m above ground level.

Figure 7: Measured wind speed and direction at a height of 1m above ground level.

Results and discussion

As shown in figure 8 the experimental results for the dimensional heat transfer coefficient are well correlated by an expression having the same form as equation (8), i. e.

і

0.9 0.8 0.7 0.6 0.5 0.4 — 0.3 0.2 0.1 — 0

w LM9 (T. — T)_

Figure 8: Experimental results of the dimensional heat transfer coefficient.

The value of the coefficient c of 0.2128 is close to the expected value of 0.14(^/ 2) = 0.22.

The value of the effective friction factor based on a height of 1m above ground level is Cf = 0.0046.

In general the velocity distribution is close to the 1/7th power law as shown in figure 9.

Only experimental data taken during the period 10:00 to 14:00 was considered since the nature of equation (5), used to evaluate the heat transfer coefficient, is such that it becomes very sensitive to small errors in temperature measurement before and after these times, as is shown in figure 10 for an error of +1°C in surface temperature.

Conclusion

The convection heat transfer coefficient between an infinite horizontal surface and the natural environment has been studied experimentally. The experimental data is well correlated by equation (9) in the range of 0m/s < vw < 4m/s, measured 1m above ground level. The value of the effective skin friction coefficient, based on a height of 1m above ground level, is found to be Cf = 0.0046.

Subscripts

a Air or ambient g Ground m Mean

nc Natural convection

[3]

Although the dimensions of the present test fapade are smaller than required by the Norwegian building regulations, the measurements give an indication of the building-physical consequences of an integrated collector faqade. During the summer period, the collector and the wall layers underneath are cooled when the solar system is operative. The temperature in the wall layer directly behind the solar collectors was — as expected — higher for the wall without ventilated cavity. Fig. 3 and Fig. 4 show the measurements on June 27, 2003 and July 31, 2003. Here the temperature and relative humidity conditions can be compared for the wall with — and without ventilated cavity, for an active and passive solar system.

The relative humidity on surfaces should be below 80% in order to avoid degradation due to fungal attacks (Geving and Thue, 2002). The most important and simple observation from the humidity measurements is that the relative humidity in the wall without ventilated cavity was — except for very few and short peaks — laying considerably below the critical limit of 80% for the monitoring period since June 2003 (Fig. 5-Fig. 7). The relative humidity in the wall without ventilated cavity revealed an increase at low level (< 50%) during periods of days with low solar irradiation and high relative air humidity. However, the present construction secures that the relative humidity in the wall reaches the low RH-values with improving weather conditions.

01

Collector fagade without ventilated cavity (green absorbers): Compared are the temperature and the relative humidity measurements in the collector fagade from June 27 when the solar system was operative and July 31, 2003 when the system was not operative. RH_ref is the relative humidity of the ambient air.

Time [Day — Month]

Fig. 5. Measurements in September 2003. Shown are the solar irradiance, the ambient temperature, relative humidity of the ambient air (RH_ref) and the relative humidity RH_int. up, measured between thermal insulation and vapour barrier.

Time [Day — Month]

Fig. 6. Measurements in October 2003. Shown are the solar irradiance, the ambient temperature, relative humidity of the ambient air (RH_ref) and the relative humidity RH_int. up, measured between thermal insulation and vapour barrier.

An angular differential measurement method was used to test transmission efficiencies of optical fibers. The angular measuring accuracy is about 0.2°. Solar radiation was used as a parallel incident beam. The solar power fluctuation during each period of trial (usually several minutes) was measured to be less than 2%. Several transmission curves were obtained corresponding to different fiber lengths, all showing very similar transmission characteristics. A typical transmission curve for the optical fibers is given in Fig.6.

Due to the UV and IR absorption of solar spectrum, only 89% transmission efficiency was measured at the angle of 0o. The efficiency was further reduced to 50% at the rim angle of 23o. A major part of the transmission loss was caused by the imperfect total internal reflections along side surface of optical fibers. As shown in Fig.6, it was dependent on polar angles. Rays of large angles suffered from higher losses. From basic principles of optics, it is known that Fresnel reflections on the end-faces of a light guide depend also on input beam angles, which could be avoided by antireflection coating techniques in the future.