ELASTOMER- METAL- ABSORBER - DEVELOPMENT AND APPLICATION Bernd Bartelsen, Gunter Rockendorf Institut für Solarenergieforschung GmbH, Am Ohrberg, D-386 Emmerthal, Germany, Tel. +49 ()55/ 999-522, Fax -5 Norbert Vennemann Fachhochschule Osnabrück, Albrechtstr. 3, D-4976 Osnabrück, Germany, Tel. +49 ()54/ 969-294, Fax -2999 Rainer Tepe, Klaus Lorenz Solar Energy Research Centre - Dalarna University College, S-7888 Borlänge, Sweden, Tel. +46 ()23/ 778-73, Fax -7 Gottfried Purkarthofer Arbeitsgemeinschaft Erneuerbare Energie, A-82 Gleisdorf, Austria, Tel. +43 ()32/ 5886-6, Fax -8 $EVWUDFW - A new principle of a solar collector, that consists in appropriately shaped metal form plates as absorber and clipped in elastomer fluid pipes, the so called elastomer-metal-absorber, will be presented. The advantages are its freeze resistance, the seawater suitability and new possibilities for cost reducing collector installation and system techniques. The design parameters including a detailed analysis of the thermal resistance between absorber and fluid will be discussed, where special regard is given to the development of an appropriate elastomer material with high thermal conductivity as one of the key items. The first development steps have shown, that absorbers with a high thermal performance may be constructed. Finally, the idea to apply the principle of the elastomer-metalabsorber to metal roofs and façades will be presented. This idea is followed up within a development project.,752'8&7,2 The idea of a combined absorber with a metal absorber sheet for the absorption of the solar radiation and a flexible elastomer fluid pipe for the transport of the solar heat has been developed. Elastomer-Metal-Absorber: clip profile Figure : elastomer-metal-absorber construction. absorber elastomer tube As shown in figure, a round shaped clip profile is integrated into a metal plate, which has an absorption layer for solar thermal conversion. In this profile an elastomer tube for the heat removal is clipped in. The application of this elastomer-metal-absorber in solar thermal collectors offers the following potential advantages and essential possibilities: Due to its inherent freeze resistance, operation without an antifreeze additive is possible. System installation without heat exchanger in the solar loop may be discussed. Operation with a corrosive fluid is possible, e.g. direct flow with sea or brackish water. New and simplified techniques for the collector and system installation can be developed. The most promising application results from the new installation possibilities for the collector and the system. It is intended to integrate this new collector concept into roofs and façades made out of metal form sheet elements. This idea will be presented in the following. Furthermore the elastomer-metal-absorber concept seems to be an attractive collector for the solar desalination of brackish and sea water, as the collector may be operated directly with corrosive liquids without cost intensive corrosion protected heat exchangers. The desalination process should be designed to operate on a low temperature level (e.g. around 7 C). The use of elastomer tubes in collectors requires appropriate absorber constructions. Different constructions have been developed and investigated with regard to the internal heat transfer resistance in combination with freeze-thaw-cycles. These absorbers have been integrated in solar collector prototypes, and thus the thermal performance and the reliability have been examined. A high thermal efficiency may only be achieved with a low heat transfer resistance of the complete construction. In order to minimize this thermal resistance between absorber and fluid, the low thermal conductivity of standard elastomer material has to be improved. Therefore different elastomer mixtures with significantly higher thermal conductivities and acceptable mechanical properties have been developed and investigated. In the following, the results of the development and analysis work will be presented, future applications will be discussed. &2//(&725'(6,* It is evident, that the low thermal conductivity of normal elastomer material results in a high thermal resistance between absorber and fluid, which lowers the thermal performance of a collector with this design. For this reason, a theoretical study of the absorber heat transfer had to be performed first. The results of appropriate numerical calculations have led to the following conclusions: A direct contact of the metal absorber fin with the elastomer tube is necessary, no additional adhesive or contact material should be used. The thermal conductivity of standard black elastomer material (around.25 W/mK) should be increased to a value of around.7 to. W/mK. The contact area between the absorber fin and elastomer tube must be large, the wall thickness of the tube should be small and finally, the diameter of the tube should be large.
The last two requirements are in contradiction to the necessary strength of the elastomer tube at operation pressure. Of special importance for a high thermal performance is the contact between the metal absorber and the elastomer tube. Therefore, during the first development steps, different absorber stripe constructions as well as different collector prototypes have been investigated with special regard to the heat transfer characteristics, the thermal performance and the reliability. Figure 2 shows five different constructions of realized absorber shapes, which have been investigated up to now. profile "A" profile "B" clip profile elastomer tube absorber $$/<6,62),7(5$/7+(5$/5(6,67$&( The efficiency of a solar collector mainly depends on the quality of the absorber. Beside the absorption and the emission of the coating, the capability to transfer the heat from the absorber to the fluid is important. Figure 3 shows the thermal resistance network of a typical absorber stripe. X solar radiation Xs W/2 d t D absorber (T abs ) base (T base ) tube, outside (T ) t, out tube, inside (T ) t, in fluid (T ) m U fin U base U tube U conv. U int profile "C" profile "D" profile "E" Figure 2: Different design types of the elastomer-metal-absorber. Type "A" is a typically soldered or welded absorber construction which has been used for the first experiments. Type "B" is an absorber construction out of roll bended aluminium sheets. The clip profile, which embraces the elastomer tube, is integrated in the sheet, thus no welding or soldering is necessary. Type "C" and type "D" are aluminium roll shaped constructions, which are used as absorber in typical thermal collectors. Normally a copper fluid tube instead of the elastomer tube will be used in the clip profile. Type "E" is a specially developed absorber construction out of roll bended aluminium sheets. This clip profile is an improvement of the types "A" to "D" and takes the capabilities of a roll-form machine for mm thick aluminium sheets into account. These different constructions have been used as absorbers in collector prototypes for the measurement of the thermal performance and as single absorber stripes for the investigation of the internal heat transfer capability. Figure 3: Simplified thermal steady state model of absorber stripes. The heat has to pass four single resistances on its way to the fluid. These are the resistance of the absorber fin and of the base connection, the tube wall resistance and the convective resistance between tube and fluid. The serial connection of these single resistances is equivalent to the total resistance between the absorber and the fluid, (/U int ). For the elastomer-metal-absorber the internal thermal resistance resp. the internal heat transfer capability depends on: fin resistance - characterised by the tube distance W, the base diameter D, the fin thickness s f and the fin conductivity k f. connection between fin and tube - characterized by the connection technique and its production quality. tube resistance - characterised by the conductivity of the elastomer k t, the tube diameter d t, the wall thickness of the tube s t and the contact area between the clip profile and the tube, i.e. the contact angle ϕ. convection between the inner tube wall and the fluid - characterized by the convective heat transfer coefficient α fluid, which is a function of the fluid, its flow velocity and its temperature and the inner tube diameter and surface. In metal absorbers, the resistance of the tube wall (/U tube ) is normally neglectable because of the high conductivity of the metal fluid tube. However, in the case of the elastomer-metalabsorber, the tube resistance is very important for the total resistance of the absorber construction. It may be summarized, that the internal heat transfer resistance depends on the construction parameters of the absorber sheet and the fluid tube, the connection technique between the absorber sheet and the fluid tube, its production quality and of the operation parameters. The dependency of the internal thermal resistance of these different construction parameters has been determined by calculations, for which the following base case parameters of the elastomer-metal-absorber have been used:
W D fin tube conv. s f k f [W/mK] d t,i s t ϕ [ ] α fluid [W/m²] 7 2 9 2 27 2 Table : Base case parameters for the calculation of the internal thermal resistance of the elastomer-metal-absorber. Figure 4 presents results of U int -calculations carried out for different tube distances W, in figure 5 the tube diameter to wall thickness ratio is varied. In both figures, the parameter is the thermal conductivity of the elastomer material. internal heat transfer capability U int [W/m²K] 5 5 elastomer conductivity [W/mK] k t =,25 k t=, k t=,75 k t=,5 k t =,25 5 5 2 tube distance W Figure 4: Internal heat transfer capability U int versus tube distance, parameter is the thermal conductivity of the elastomer material. internal heat transfer capability U int [W/m²K] 5 5 4 6 8 ratio tube diameter / wall thickness (d /s ) t,m t elastomer conductivity [W/mK] k t =,25 k t=, k t=,75 k t=,5 k t =,25 Figure 5: Internal heat transfer capability U int versus the ratio of mean tube diameter to the tube wall thickness, parameter is the thermal conductivity of the elastomer material. As figure 4 and 5 show, the internal heat transfer capability of the elastomer-metal-absorber is mainly determined by the low conductivity of the elastomer material, which leads to a high thermal resistance of the tube. This tube resistance becomes even more important, if the amount of collected heat transported over this resistance increases. Therefore the second parameter of major importance is the tube distance. Furthermore, the tube diameter resp. the thickness of the tube as well as the contact area between the clip profile and the tube have a clear influence on the internal heat transfer resistance of the construction and therefore on the efficiency of the collector. As the collector efficiency factor F and thus the conversion factor η depend on the ratio F = U int U loss + int ----------------------------, () U the U int -value should be maximized by optimization of the complete absorber construction. For a nonselective single glazed collector U int should be higher than 5 W/m 2 K (U loss = 5.5 W/m 2 K, F =.9) and for an unglazed absorber a value of more than 7 W/m 2 K is desired (U loss = 5 W/m 2 K, F =.82). These relatively high U int -values may only be achieved with a thermal conductivity of the elastomer of at least.6 W/mK, if a realistic tube distance of more than 8 mm is assumed. The other alternative, to reduce the tube wall thickness, has clear boundaries: A long term reliability requires a wall thickness of at least.5 mm. Therefore the thermal conductivity of standard black elastomer material (k t =.25 W/mK) has to be increased significantly. '(9(/23(72)7+((/$672(5$7(5,$/ The department of material technology of the University of Applied Science in Osnabrück has developed an elastomer material based on ethylene-propylene-dien-terpolymer (EPDM) for the application in the elastomer-metal-absorber. Main part of the development was to increase the low thermal conductivity of typical elastomer material with a simultaneous improvement of the mechanical strength. In addition to typically used well conductive filling materials like carbon black, particles out of aluminium and graphite have been applied during the development steps. The EPDM mixture is varied with different types of carbon black with high electrical conductivity, two kinds of aluminium particles and various kinds of graphite powder. The measured thermal conductivity and the tensile strength of some of the elastomer mixtures are presented in figure 6. thermal conductivity [W/mK],8,6,4,2 thermal conductivity tensile strength V- V- V-2 M-4 M-7 M-3 D-4 mixture Figure 6: Thermal conductivity and tensile strength of different elastomer mixtures. 2 6 2 8 4 tensile strength [N/mm²]
The mixture indication starting with a "V" labels the first series with only one single additive, the indication "M" is for laboratory mixtures with two conductive filling materials and the indication "D" stands for elastomer mixtures produced by using an industrial mixing device. For the elastomer mixtures in figure 6 the following filling materials have been used: "V-" pure polymer "V-" addition of phr ) aluminium particles "V-2" addition of 4 phr carbon black "M-4" addition of 4 phr carbon and 8 phr aluminium "M-7" addition of 3 phr carbon and 8 phr graphite "M-3" addition of phr carbon and 9 phr graphite "D-4" addition of carbon and graphite The pure polymer without filling materials shows a thermal conductivity of about.2 W/mK. Aluminium as single filling material like in mixture V- improves only the thermal conductivity. If a conductive carbon black is added to the mixture (V-2), the tensile strength is raised more than six times and the thermal conductivity is doubled. The mixtures M-4 and M-7 contain two filling materials. Beside the conductive carbon black an aluminium or a graphite powder is added to the polymer. The thermal conductivity is raised up to around.8 W/mK, four times the value of the pure polymer, and the tensile strength is at a high level, too. For the efficiency measurement of the first improved prototypes, the elastomer mixtures M-5 (similar to M-4) and M-7, with a good thermal conductivity and a good tensile strength, have been used. From these new elastomer mixtures, tubes have been extruded and integrated into the test collectors. Due to the high carbon black content, the materials M-5, M-7 and M-3 have a very high viscosity during the mixing process and the extruded tubes show a high hardness and a low flexibility. Furthermore, the tube surface has a significant roughness. The conclusion of this first elastomer development step is, that high thermal conductivity and tensile strength values have been achieved, but the material is not appropriate for an industrial production process and does not result in the desired properties of elastomer tubes. The second EPDM development step therefore focuses on the improvement of the production parameters and the final elastomer material data like hardness, stress relaxation, torsion pendelum and ageing resistance. For this purpose, the content of carbon black has been reduced and the other components have been adjusted with regard to the special requirements. First result is the mixture D-4, the first sample produced in an industrial mixer, which shows a clear progress and already meets some of the requirements. However, further efforts are necessary for the optimization of the elastomer material for the use as fluid tube in the elastomer-metal-absorber, especially with regard to the production parameters, costs and long-term reliability. This work is going on. One problem is inherent with the application of EPDM as tube material. The temperature resistance is restricted to a short term maximum temperature below 6 C, as the elastomer presents a. "phr" means "per hundred rubber", i.e. the number of weight parts of the filling material which will be added to hundred weight part of the basis polymer material. clearly decreasing strength with increasing temperatures and an accelerated degradation at such high temperatures. This has two consequences: The stagnation temperature has to be reduced to a value below 6 C. Therefore the heat loss coefficient must be higher than of commercial high performance flat plate collectors, which come up to more than 2 C at W/m 2, 3 C air temperature and low air speed. The heat loss coefficient a (according to ISO 986-, referred to mean fluid temperature) must be higher than or equal to 4.5 W/m 2 K. The system design has to avoid the simultaneous occurrence of high pressure and high temperature, which is the case for typical closed loop solar systems. (;3(5,(7627+(5$/3523(57,(6 During the development steps of the elastomer-metal-absorber, the internal thermal conductivity between solar absorber and fluid, the U int -value, has been determined by numerical calculations, measurements at single absorber stripes and measurements at complete solar absorbers during the performance test procedure of test collectors. Table 2 presents some of the most important results. profile clip profile elastomer tube U int type ϕ d f,i k t d t,a s t calcul. measur. [ ] [W/mK] [W/m²K] [W/m²K] A 285 2,,25 2, 2, 9,3 2,7 A 285 2,,78,7,5 58, 39,7 A 25 3,2,78 3,2,5 55,5 47,3 B 255 3,,78 3,2,5 57,4 52, B 255 3,,75 3,2,5 55, 52,5 C 29,,78,7,5 57,7 55,3 D 26 3,,75 3,2,5 6,5 5,2 D 27 2,2,7-2,2,5 5-6 58,7 E 275 2,2, 2,8 2, 6,5 - Table 2: Heat transfer capability U int of different elastomer-metalabsorber constructions, measured and calculated values, tube distance is constant (W = 5 mm, except second line from bottom: W = 35 mm). The five types of absorber profiles presented in figure 2 have been investigated with different construction and material parameters. The calculated and measured internal heat transfer capability of the construction depends, like discussed in chapter 3, on the conductivity of the elastomer k t, the tube diameter d t, the thickness of the tube s t and on the contact angle of the clip profile. The tube distance is the same for each construction (W = 5 mm) and the base diameter D is varied only in a small range. With the fin and tube construction parameters, the internal heat transfer capability has been calculated. These theoretical values may be compared with the experimental results. Up to now, the internal heat transfer capability has been increased from 2 W/m²K to 6 W/m²K, resulting in a collector efficiency factor which raised from.78 up to.92 for typical nonselective collectors (U loss = 5.5 W/m 2 K). That means, that the realistic aim of 6 W/m²K has already been achieved, an objective for the future is 75 W/m²K.
If the construction type C (see table 2, U int =57.7W/m 2 K) would have been equipped with a metal fluid tube instead of the elastomer tube, the collector efficiency factor would be.95 instead of.9. The difference of.4 is the price for an absorber construction with elastomer fluid tubes. Also with future optimized constructions (U int =75 W/m 2 K) this difference will be around.3. Table 2 shows, that some calculated values fit rather well to the measured ones, others show significantly lower measured values. The main reason is the thermal contact between the tube and the metal profile. As some of the tubes showed a low flexibility, the contact to the absorber has been reduced, as the uneven and hard tube wall does not touch the whole embracing metal area. Therefore, the flexibility is an important quantity. For this reason, the fluid pressure normally has a positive influence on U int and it could furthermore be remarked, that a heating-up under pressure also improves the thermal contact. Another important influence may also be derived from table 2. If the outer diameter of the tube is too small in comparison to the clip profile, the measured value of U int are significantly lower than the calculated ones. Therefore, the outer diameter of the tube should be around.5 mm larger than the profile circle. Here the production tolerance has to be taken into account. Up to now, five different test collectors with an integrated elastomer-metal-absorbers have been constructed and investigated. For the collector frame, insulation and cover components of a standard flat plate collector have been used. Figure 7 shows two of the test collectors in front of the institute s building. The first test collector had a copper absorber plate with soldered clip profiles in form of the type A construction. With this collector, the base case investigations and the first measurements with the improved elastomer tubes have been performed. For the base case investigations, the absorber was equipped with a conventional rubber tube (low thermal conductivity of around.25 W/mK) and a black painted surface (EMA-). For the second base case collector (EMA-2) an adhesive selective foil has been used instead of the black painted surface. The first improved test collector (EMA-3) contains the same absorber construction, but the rubber tube has been replaced by a tube made out of the improved elastomer (similar to mixture M-4, figure 5). Again an adhesive selective foil has been applied. The second improved test collector (EMA-4) was produced with a type B absorber construction (roll bended absorber sheets) and an improved elastomer tube with a larger diameter. The absorber coating is again the adhesive selective foil. The diagram in figure 8 presents the measured efficiency curves of the improved test collectors EMA-3 and EMA-4 in comparison to a typical selective flat plate collector as well as to the selectively coated base case test collector. η [-],8,6,4 typical collector prototype EMA-2 typical EPDM prototype EMA-3 mixture M-5 prototype EMA-4 mixture M-7,2 2 3 4 5 6 7 fluid temperature [ C] Figure 8: Efficiency curves of different test collectors compared with a typical selective flat plate collector, test conditions: irradiance level 8 W/m 2, ambient temperature 2 C, air speed 3 m/s, according ISO 986-, referring to mean fluid temperature and aperture area. Figure 7: Test collectors in front of the institute s building. The resulting low conversion factor of.67 of the base case collector with a selective surface (EMA-2) is caused by the high thermal resistance of the rubber hose. For the first test collector with an improved elastomer tube (elastomer mixture M-5) and a selective absorber coating the conversion factor was raised up to.78. The conversion factor of the second improved test collector reached.8. The differences of this prototype EMA-4 is the use of a more flexible elastomer tube made out of mixture M-7 and the use of an other absorber construction, profile "B". These improvements during the first development steps have shown, that the proposed elastomer-metal-absorber construction gives a thermal performance close to that of typical flat plate collectors with selective metal absorbers.
However, the conversion factor of an absorber construction with an elastomer tube will remain at least 3 % smaller in comparison to the same construction with a metal fluid pipe. As the reliability of the absorber is the most important condition for any future applications, first reliability investigations have been carried out on the elastomer tube, the absorber construction and the collector prototypes. Burst pressure, long term stability at high temperature and pressure and the torsion vibration properties have been investigated on the tubes, freezethaw-cycles have been performed with different types of absorber stripes and exposition tests on a complete collector prototype have been carried out. The results showed, that the existing problems should be solvable. $33/,&$7,2$6)$d$'($'522)(/((7 Industrially produced roofs and façades often consist of corrugated metal form sheets made out of steel or aluminium. These roof or façade constructions are widely used for industrial, public or residential buildings. The elastomer-metal-absorber concept will transform these metal form sheets into uncovered or transparently covered roof and façade absorbers by integrating an appropriate clip profile into the form sheets during the production process. The elastomer tube can then easily be clipped into these profiles after the installation of the roof or façade. Figure 9 shows the conversion of a typical metal form sheet (presented here as insulated sandwich plate) into an unglazed or transparently covered solar collector. steel or aluminium form sheets (as insulated plate) form sheets with integrated clip profiles form sheets with integrated elastomer tubes form sheets with elastomer tubes and transparent covers Figure 9: Steps from a metal roof and façade element to a solar collector. The first step of the conversion is the integration of the clip profile into the metal form sheet during the roll form process. The form sheet is covered with a paint of high solar absorptivity, with or without selective properties. The sheet will be mounted on the roof or façade by normal roofing or metal processing companies. The optical and technical properties will be the same like for normal metal roofs. The second step is the integration of the elastomer tubes into the form sheets. The elastomer tubes will be connected via the manifold tubes to the solar system. Thus, an uncovered absorber results with only little extra costs, where the technical properties of the metal roof or façade remain unchanged. As an additional option for systems with higher demand temperatures a transparent cover may be added, using single glass panes or transparent plastic covers. By this way also low cost glazed collectors may be produced, which are specially suited for large systems. The idea of this building integrated collector type has the following advantages: Metal form sheets are a common and well proved technology. The transformation into the elastomer-metal-absorber does not affect the reliability of the original roof resp. façade. The additional effort to transform metal roofs into unglazed absorbers seems to be very low, on the other hand, the metal roof and façade elements gain by their new property as active solar absorber further attractivity. The extension to glazed collector roofs for higher demand temperature is possible. The integration may be performed with a high aesthetical quality and architectural acceptance. Typical examples for a future application of this concept are buildings with a high demand of low temperature heat, e.g. swimming-bath and sports halls, hospitals etc. for glazed collector constructions and outdoor swimming-pools and heat-pump systems for the unglazed absorber type. Domestic hot water and residential room heating purposes may also be taken into account. Due to the very low additional costs expected for the transformation of the metal building envelope into a glazed or unglazed solar collector, this concept has the potential to result in new solar applications with a high economic benefit. '(9(/23(7352-(&767$7(2)7+($57 Despite of the encouraging results of the first development steps, this absorber type is not available up to now. Open questions are mainly the production and installation technology, the long term reliability and the long term thermal performance. A research and development project, funded by the European Commission, has started to develop and investigate the integrated elastomer-metal-absorber in roof and façade metal form sheet elements and possible heat use applications. The main tasks within this cooperation between industrial partners coming from various activity fields and research institutions are: further improvement of the elastomer material with special regard to heat conductivity, mechanical strength and durability, as well as the production of appropriate elastomer tubes, development of absorber constructions with focus on production parameters, thermal performance and reliability, construction and assessment of test collectors, determination of thermal performance and reliability characteristics, development of different solar system concepts, assessment of collectors in test systems, comparison and extrapolation. The first results of this project are encouraging: An improved elastomer mixture with special regard to the industrial produceability has been developed, from which first prototypes of an appropriate elastomer tube have been produced in an industrial extrusion machine. The construction of the form sheet elements for the integration into metal-roofs has been performed, the tools for the roll form machine are ready and the first absorber form sheet elements are in production. A simulation tool for the elastomer-metal-absorber has been developed, first different heat use concepts have been worked out and simulated. However, still a couple of problems exist which have to be solved on the way to an industrial product with high performance and reliability.
Some items to be worked out are in the fields of: assessment of the absorptive surface and its stability, design of the hydraulic system and the manifolds, development of the connection technique between tubes and manifold, and system operation and security technique, with special regard to the fact, that water will be used as heat transfer fluid. It has to be pointed out here, that at the moment it is planned to transform the whole roof area into an elastomer-metal-absorber, i.e. the normal application are large collector areas. For the specific problems arising from this aspect, the development has to go on over intermediate stages like medium sized pilot and demonstration plants. &2&/86,2$'287/22. The principle of the elastomer-metal-absorber with its clip profile contact opens up new possibilities with regard to the heat transfer fluid, the collector and system design and the architectural integration. The development steps have shown that the proposed elastomer-metal-absorber construction already has a thermal performance close to that of typical flat plate collectors, with only a slightly lower conversion factor. The essential results up to now are the increase of the thermal conductivity of the elastomer material from.25 W/mK up to. W/mK, which in combination with an optimized absorber construction leads to an internal heat transfer coefficient of at least 6 W/m 2 K, a value comparable to standard flat plate collectors. The existing reliability problems seem to be soluble, the first results of the actual development project are encouraging. The special attraction of this building integrated design is given for the following reasons: high expected cost reduction for unglazed absorbers or glazed collectors, significant reduction of energetic amortisation periods, well suited solution for repair or recycling, enlargement of the solar market by new manufacturers and solar systems, especially in large commercial and public buildings, as well as in residential buildings, and improvement of architectural acceptance by the high degree of building integration. Acknowledgements-The work is funded partially by the European Commission, within the project Façade and Roof Integrated Solar Collectors with a Combination of Elastomer Tubes and Metal Form Sheet Elements, contract no. JOE3-CT98-236, organized in the framework of the Non-Nuclear Energy Research and Technological Development Programme JOULE III. 2(&/$785( a linear collector heat loss coefficient, referred to T m (W/m²K) α fluid convective heat transfer coefficient between the inner tube wall and the fluid (W/m²) D base diameter (projection width of visible tube surface) (mm) d f diameter of the clip profile (mm) d t tube diameter (mm) d t,i inner tube diameter (mm) d t,m arithmetic mean of outer and inner tube diameter (mm) F collector efficiency factor (-) G Solar irradiance (W/m²) η collector thermal efficiency, referred to T m (-) k f thermal conductivity of the fin material (W/mK) k t thermal conductivity of elastomer tube material (W/mK) ϕ contact angle of the clip profile ( ) s f thickness of the fin (mm) s t wall thickness of the tube (mm) T abs mean temperature on the absorber fin ( C) T base temperature on the absorber base ( C) T m mean temperature of heat transfer fluid ( C) T t,out temperature on the outer surface of the tube ( C) T t,in temperature on the inner surface of the tube ( C) U fin internal heat transfer conductivity of the fin (W/m²K) U base internal heat transfer conductivity of the base (W/m²K) U tube internal heat transfer conductivity of the tube (W/m²K) U conv convective heat transfer conductivity between tube wall and fluid (W/m²K) U int internal heat transfer conductivity of absorber construction (W/m²K) U loss overall heat loss coefficient of the collector, referred to T m (W/m²K) W tube distance (mm) 5()(5(&(6 Bartelsen B., Rockendorf G. and Vennemann N. (996) Development of an Elastomer-Metal-Absorber for Thermal Solar Collectors. In Proceedings of the EuroSun 96, 6-2 September, Freiburg, Germany, pp. 495-499, DGS-Sonnenenergie Verlag GmbH, München. Rockendorf G., Falk S.,Wetzel W. (996) Bedeutung und Bestimmung des Kollektorwirkungsgradfaktors bei Sonnenkollektoren; 6. Symposium thermische Solarenergie, 8- May, Staffelstein, Germany, pp. 96-2, OTTI e.v., Regensburg. Duffie J.A. and Beckmann W.A. (99) Solar Engineering of Thermal Processes; 2n d edn, pp. 268-276, Wiley-Interscience Publication; New York. Bökamp K., Vennemann N., Wallach J., Bartelsen B. and Rockendorf G. (997) EPDM Compounds with Improved Thermal Conductivity for Thermal Solar Collectors. In Proceedings of the International Rubber Conference, 3 June - 3 July, Nürnberg, Germany.