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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.solener.2010.07.012 Byline: Y.B. Tao, Y.L. He Keywords: Parabolic solar collector tube; Mixed convection; Coupled heat transfer; Local Nusselt number Abstract: A unified two-dimensional numerical model was developed for the coupled heat transfer process in parabolic solar collector tube, which includes nature convection, forced convection, heat conduction and fluid-solid conjugate problem. The effects of Rayleigh number (Ra), tube diameter ratio and thermal conductivity of the tube wall on the heat transfer and fluid flow performance were numerically analyzed. The distributions of flow field, temperature field, local Nu and local temperature gradient were examined. The results show that when Ra is larger than 10.sup.5, the effects of nature convection must be taken into account. With the increase of tube diameter ratio, the Nusselt number in inner tube (Nu.sub.1) increases and the Nusselt number in annuli space (Nu.sub.2) decreases. With the increase of tube wall thermal conductivity, Nu.sub.1 decreases and Nu.sub.2 increases. When thermal conductivity is larger than 200W/(m K), it would have little effects on Nu and average temperatures. Due to the effect of the nature convection, along the circumferential direction (from top to down), the temperature in the cross-section decreases and the temperature gradient on inner tube surface increases at first. Then, the temperature and temperature gradients would present a converse variation at I[cedilla] near I. The local Nu on inner tube outer surface increases along circumferential direction until it reaches a maximum value then it decreases again. Author Affiliation: State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China Article History: Received 22 September 2009; Revised 17 July 2010; Accepted 20 July 2010 Article Note: (miscellaneous) Communicated by: Associate Editor Brian Norton

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.solener.2010.06.016 Byline: B. StojanoviA, D. Hallberg, J. Akander Keywords: Unglazed solar collector; Roof integrated; Duct; Modelling; Fin-theory; Benchmarking Abstract: This paper presents the thermal modelling of an unglazed solar collector (USC) flat panel, with the aim of producing a detailed yet swift thermal steady-state model. The model is analytical, one-dimensional (1D) and derived by a fin-theory approach. It represents the thermal performance of an arbitrary duct with applied boundary conditions equal to those of a flat panel collector. The derived model is meant to be used for efficient optimisation and design of USC flat panels (or similar applications), as well as detailed thermal analysis of temperature fields and heat transfer distributions/variations at steady-state conditions; without requiring a large amount of computational power and time. Detailed surface temperatures are necessary features for durability studies of the surface coating, hence the effect of coating degradation on USC and system performance. The model accuracy and proficiency has been benchmarked against a detailed three-dimensional Finite Difference Model (3D FDM) and two simpler 1D analytical models. Results from the benchmarking test show that the fin-theory model has excellent capabilities of calculating energy performances and fluid temperature profiles, as well as detailed material temperature fields and heat transfer distributions/variations (at steady-state conditions), while still being suitable for component analysis in junction to system simulations as the model is analytical. The accuracy of the model is high in comparison to the 3D FDM (the prime benchmark), as long as the fin-theory assumption prevails (no 'or negligible' temperature gradient in the fin perpendicularly to the fin length). Comparison with the other models also shows that when the USC duct material has a high thermal conductivity, the cross-sectional material temperature adopts an isothermal state (for the assessed USC duct geometry), which makes the 1D isothermal model valid. When the USC duct material has a low thermal conductivity, the heat transfer course of events adopts a 1D heat flow that reassembles the conditions of the 1D simple model (for the assessed USC duct geometry); 1D heat flow through the top and bottom fins/sheets as the duct wall reassembles a state of adiabatic condition. Author Affiliation: Building Materials Technology, KTH Research School, Centre for Built Environment, University of Gavle, SE-801 76 Gavle, Sweden Article History: Received 12 November 2008; Revised 28 January 2010; Accepted 15 June 2010 Article Note: (miscellaneous) Communicated by: Associate Editor Brian Norton

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.solener.2008.10.021 Byline: Yoann Raffenel (a)(b), Enrico Fabrizio (b)(c), Joseph Virgone (d)(e), Eric Blanco (a), Marco Filippi (c) Keywords: Solar heating systems; Solar combisystems; Initial sizing; TRNSYS Abstract: The sizing of the solar installation of an individual dwelling is a problem which can be solved in many ways. The approach described in this paper is a simplified procedure of considerable interest. It requires only a small quantity of data and can be computed in a short time. The performance of this procedure was evaluated by a more complex sizing method based on detailed simulation. The simplified procedure was applied to the case of an individual dwelling using a solar collector field to produce domestic hot water and space heating. The building and the solar installation have then been modelled with the software TRNSYS 16 and their behaviour was simulated during a whole year. The results obtained are particularly close to the ones expected by the simplified sizing procedure. Author Affiliation: (a) Laboratoire AMPERE, UMR 5005, Ecole Centrale de Lyon, Bat. H9, 36 Avenue Guy de Collongue, 69134 Ecully, France (b) Centre de Thermique de Lyon (CETHIL),UMR 5008, INSA de Lyon, Domaine Scientifique de la Doua, Bat. Freyssinet, 40 Rue des Arts, 69621 Villeurbanne, France (c) Dipartimento di Energetica (DENER), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (d) IUT A Lyon 1, Universite de Lyon, 43 Bd du 11 Novembre 1918, 69622 VILLEURBANNE Cedex, France (e) Laboratoire sciences de l'habitat, Ecole nationale des travaux publics de l'Etat, Rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France Article History: Received 14 February 2008; Revised 12 September 2008; Accepted 19 October 2008 Article Note: (miscellaneous) Communicated by: Associate editor C. Estrada-Gasca

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.solener.2008.10.009 Byline: Elsa Andersen, Simon Furbo Keywords: Measured weather data; Solar radiation variations; Solar heating systems; Solar collectors; Thermal performance; Utilized part of solar radiation Abstract: The thermal performances of solar collectors and solar combi systems with different solar fractions are studied under the influence of the Danish design reference year, DRY data file, and measured weather data from a solar radiation measurement station situated at the Technical University of Denmark in Kgs. Lyngby. The data from DRY data file are used for any location in Denmark. The thermal performances of the solar heating systems are calculated by means of validated computer models. The measured yearly solar radiation varies by approximately 23% in the period from 1990 until 2002, and the investigations show that it is not possible to predict the yearly solar radiation on a tilted surface based on the yearly global radiation. The annual thermal performance of solar combi systems cannot with reasonable approximation be fitted to a linear function of the annual total radiation on the solar collector or the annual global radiation. Solar combi systems with high efficient solar collectors are more influenced by weather variations from one year to another than systems with low efficient solar collectors. The annual thermal performance of solar collectors cannot be predicted from the global radiation, but both the annual thermal performance and the annual utilized solar energy can with a reasonable approximation be fitted to a linear function of the yearly solar radiation on the collector for both flat plate and evacuated tubular solar collectors. Also evacuated tubular solar collectors utilize less sunny years with large parts of diffuse radiation relatively better than flat plate collectors. Author Affiliation: Department of Civil Engineering, Technical University of Denmark, Building 118, DK-2800 Kgs. Lyngby, Denmark Article History: Received 24 May 2007; Revised 1 October 2008; Accepted 3 October 2008 Article Note: (miscellaneous) Communicated by: Associate Editor Yogi Goswami

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.solener.2008.08.013 Byline: T.N. Anderson (a), M. Duke (a), G.L. Morrison (b), J.K. Carson (a) Keywords: Photovoltaics; Solar thermal; Photovoltaic/thermal; BIPVT Abstract: The idea of combining photovoltaic and solar thermal collectors (PVT collectors) to provide electrical and heat energy is an area that has, until recently, received only limited attention. Although PVTs are not as prevalent as solar thermal systems, the integration of photovoltaic and solar thermal collectors into the walls or roofing structure of a building could provide greater opportunity for the use of renewable solar energy technologies. In this study, the design of a novel building integrated photovoltaic/thermal (BIPVT) solar collector was theoretically analysed through the use of a modified Hottel-Whillier model and was validated with experimental data from testing on a prototype BIPVT collector. The results showed that key design parameters such as the fin efficiency, the thermal conductivity between the PV cells and their supporting structure, and the lamination method had a significant influence on both the electrical and thermal efficiency of the BIPVT. Furthermore, it was shown that the BIPVT could be made of lower cost materials, such as pre-coated colour steel, without significant decreases in efficiency. Finally, it was shown that by integrating the BIPVT into the building rather than onto the building could result in a lower cost system. This was illustrated by the finding that insulating the rear of the BIPVT may be unnecessary when it is integrated into a roof above an enclosed air filled attic, as this air space acts as a passive insulating barrier. Author Affiliation: (a) Department of Engineering, University of Waikato, Hamilton 3240, New Zealand (b) School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia Article History: Received 21 November 2007; Revised 26 May 2008; Accepted 25 August 2008 Article Note: (dedication) Communicated by: Associate Editor Brian Norton

The electrical power generated by a polycrystalline silicon photovoltaic (PV) module mounted on an unglazed transpired solar collector (UTC) has been studied and compared to that of a PV module without UTC for a quantitative analysis of electrical output and its role in reducing the simple payback periods of photovoltaic electrical systems. A 75 W polycrystalline silicon PV module was fixed on an UTC in front of the ventilation fan, and effectiveness of cooling by means of the forced ventilation at the rate of 160 CFM was monitored. The temperature reduction under forced ventilation was in the range of 3-9[degrees]C with a 5% recovery in the electrical output power on a typical day of the month of February 2005. The simulated and measured electrical power outputs are in reasonable agreement with root-mean-square error of 2.40. The life cycle assessment of a hypothetical PV system located at Daejeon, South Korea and consisting of 3 kW PV modules fixed on a 50 [m.sup.2] UTC shows that with a possible reduction of 3-9[degrees]C in the operating temperatures, the system requires three 75 W fewer PV modules. The simple payback period of PV system is reduced from 23 years to 15 years when integrated into an UTC air heating system. [DOI: 10.1115/1.2212438]

The knowledge of the absorber surface temperature distribution is essential for efficient operation and further development of solar thermal high temperature receivers. However, the concentrated solar radiation makes it difficult to determine the temperature on irradiated surfaces. Contact thermometry is not appropriate and pyrometric measurements are distorted by the reflected solar radiation. The measurement in solar-blind spectral ranges offers a possible solution by eliminating the reflected solar radiation from the measurement signal. The paper shows that besides the incoming solar radiation and the absorber emittance, the bi-directional reflection properties and the temperature of the object are determining for the required selectivity of the spectral filter. Atmospheric absorption affects the solar blind pyrometric measurements in absorption bands of C[O.sub.2] and water vapor. The deviation of temperature measurement due to atmospheric absorption is quantified and the possibilities and limitations of accounting for the atmospheric absorption with models based on radiation transfer calculations are discussed. [DOI: 10.1115/1.2210499]

Promotion of the use of renewable energy, such as solar heat, for space heating and drying crops and wood is desired to prevent global warming. High-temperature collection of heat by air collectors producing as much as 50[degrees]C in winter for space heating and about 80[degrees]C in summer for exchanging heat to circulating water for hot water supply would be appropriate applications. In this study, first, a flow control system for constant outlet temperature was installed in a hot air supply system to examine the feasibility of the control system. After experiments, it was found that the control system could function satisfactory. Second, an unsteady-state analysis was made to predict the thermal performance of a flat-plate collector under a given condition of variable flow rate. The analytical model became simple by the assumptions that the heat capacity of the air in the collector and heat conduction in the flow direction through the air and the materials of the collector could be neglected. The maximum differences in outlet temperature and collector efficiency for constant flow rate between the analysis and the experiment were 1.8[degrees]C and 6% of the collector efficiency, respectively, except in the beginning of experiments. The biggest difference in the collector efficiency was 30% at 3:00 P.M., which occurred at the end of one of the experiments. The analytical results generally agreed well with the experimental results even when the flow rate and solar radiation changed greatly as time went on. Transient effects are important to predict outlet temperature for variable solar radiation intensity, wind speed, and flow rate. [DOI: 10.1115/1.2210493] Keywords: solar air collector, solar house, collector efficiency, flow control, unsteadystate analysis

High-temperature solar reforming of methane with C[O.sub.2] is investigated using a directly solar-irradiated absorber subjected to a solar mean flux level above 400 kW [m.sup.-2] (the peak flux of about 700 kW [m.sup.-2]). The new type of catalytically activated ceramic foam absorber--a Ru/Ni-Mg-O catalyzed SiC-foam absorber--was prepared, and its activity was tested in a laboratory-scale volumetric receiver-reactor with a transparent (quartz) window by using a sun-simulator Compared to conventional Rh/[Al.sub.2][O.sub.3] catalyzed SiC-foam absorber, this new catalytic absorber is more cost effective and is found to exhibit a superior reaction performance at the high solar flux or at high temperatures, especially above 950[degrees]C. This new absorber will be applied in solar receiver-reactor systems for converting concentrated high solar fluxes to chemical fuels via endothermic natural-gas reforming at high temperatures. [DOI: 10.1115/1.2210497] Keywords: solar hydrogen, solar heat, natural gas reforming, volumetric receiver, reforming catalyst

The degradation of gallic acid and imidacloprid with supported Millennium PC500 and Degussa P25 Ti[O.sub.2] is reported. Ti[O.sub.2] particles were immobilized using a titanium solsolution and direct deposition on glass supports. The film characterization was done by x-ray diffraction, scanning electron microscopy, and atomic force microscopy, and degradation of organic compounds was monitored by high-performance liquid chromatography, total organic carbon analyzer, and ion chromatography. The experiments were performed under sunlight in compound parabolic collector plants with flat supports inside the glass tubes. Photocatalytic activity of the films was compared and identified. Although sol-gel coatings had better mechanical properties, mineralization was observed to be approximately five times slower than paste-deposited films. Photoactivity of the films decreased with silver deposition due to the nature of the organic compounds. The rate constants were calculated to be between 2 x [10.sup.-1] and 6 x [10.sup.-2] mg [m.sup.2]/kJ for organic compounds, and 6 X [10.sup.-2] and 6 x [10.sup.-3] for total organic carbon. [DOI: 10.1115/1.2210494] Keywords: photocatalysis, supported catalyst, silver deposition, sol-gel film

A solar chimney power plant consists of a large greenhouse-type collector surrounding a tall chimney. The air, heated within the collector, passes through an inlet guide vane (IGV)cascade and then through a transition section to a turbine that powers a generator. The transition section contains the turbine inlet guide vanes that support the whole chimney and guides the flow entering the turbine. The primary objective of the study was to determine the loss coefficient and mean exit swirl angle of the flow passing through the collector-to-chimney transition section of a full-scale solar chimney power plant as dependent on IGV stagger angle and collector roof height. Very good agreement was found between experimental values measured in a scaled model and commercial CFD code predictions of flow angles, velocity components, and internal and wall static pressures. The agreement between measured and predicted total pressure loss coefficient was reasonable when considering how small it is. The CFD code served to extend the predictions to a proposed full-scale geometry. Semi-empirical equations were developed to predict the loss coefficient and turbine mean inlet flow angles of solar chimney power plants as dependent on collector deck height and inlet guide vane setting angle. The two empirical equations may be useful in solar chimney plant optimization studies. [DOI: 10.1115/1.2210502] Keywords: solar energy, solar chimney, solar tower, radial-to-axial flow, transition duct, loss coefficient

The dual receiver concept presented in this paper improves the adaptation of the central receiver to the steam cycle in a solar thermal power plant. By combination of an open volumetric air heater and a tubular evaporator the dual receiver concept profits from the advantages of these two concepts while their characteristic problems are avoided. The water is evaporated directly in the tubular steam generator; preheating and superheating are done in heat exchangers by using the hot air from the volumetric receiver. This paper presents a concept study that extends previous work on the 10 [MW.sub.el] level (Buck et al., 2004, 'Dual Receiver Concept for Solar Towers,' Proc. 12th Solar PACES Int. Symposium, Oct. 6-8, Oaxaca, Mexico) to a level of 100 [MW.sub.el], which is the expected power range of future plants. The results confirm the benefits of the new concept, resulting from higher thermal efficiency of the receiver and lower parasitic power consumption. The annual mean efficiency is increased from 13% to 16%. Advantageous are also the reduced thermal loads in the receiver components. [DOI: 10.1115/1.2210501]

A rigorous approach for the radiative heat transfer analysis in solar collector glazing is developed. The model allows a more accurate prediction of thermal performance of a solar collector system. The glass material is analysed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in the one-dimensional case using the Radiation Element Method by Ray Emission Model (REM by REM). This method is used to analyse the combined non-gray convective, conductive and radiative heat transfer in glass medium. The boundary surfaces of the glass are specular. The spectral dependence of the relevant radiation properties of glass (i.e. specular reflectivity, refraction angle and absorption coefficient) are taken into consideration. Both collimated and diffuse incident irradiation are applied at the boundary surfaces using the spectral solar model proposed by Bird and Riordan. The optical constants of a commercial ordinary clear glass material have been used. These optical constants (100 values) of real and imaginary parts of the complex refractive index of the glass material cover the range of interest for calculating the solar and thermal radiative heat transfer through the solar collector glass cover. The model allows the calculation of the steady-state heat flux and temperature distribution within the glass layer. The effect of both conduction and radiation in the heat transfer process is examined. It has been shown that the real and imaginary parts of the complex refractive index have a substantial effect on the layer temperature distribution. The computational time for predicting the combined heat transfer in such a system is very long for the non-gray case with 100 values of n and k. Therefore, a simplified non-gray model with 10 values of n and k and two semi-gray models have been proposed for rapid computations. A comparison of the proposed models with the reference non-gray case is presented. The result shows that 10 bandwidths could be used for rapid computation with a very high level of accuracy.

It has been suggested earlier that the incidence angle modifier [K.sub.[Tau][Alpha]] for low concentrating collectors with tubular absorbers could be factorised according to [K.sub.[Tau][Alpha]] ([[Theta].sub.[Tau]],[[Theta].sub.1]) [Alpha] [K.sub.[Tau][Alpha]]([Theta].sub.[Tau],0)[K.sub.[Tau][Alpha]] ([0,[Theta].sub.1]), where [[Theta].sub.t] and [[Theta].sub.1] are the projected incidence angles in the transversal and longitudinal projection planes, respectively. Ray-tracing calculations on low-concentrating CPC collectors with flat absorbers parallel to the cover show that a [K.sub.[Theta][Alpha]] factorisation overestimates the annual delivered energy from the collector by about 4-5%, when compared to calculations using the full incidence angle modifier. Data from outdoor testing has been used for characterization of incidence angle behaviour for a truncated CPC with a concentration of C = 1.56. Multiple linear regression analysis was used. This analysis technique makes feasible the determination of angular dependent incident angle modifiers and is an efficient tool to use for all collectors which cannot be characterised by standard equations of the incidence angle dependence.

A parameter sensitivity analysis is presented to examine the effect of different time dependent and time independent input parameters on the various output parameters of a tunnel-type directly irradiated solar agricultural dryer with integrated collector. The parameter sensitivity of the system is expressed by the sensitivity matrix, the elements of which are the relative sensitivity coefficients. The relative sensitivity coefficients have been calculated at different stages of the drying process. Results of the sensitivity analysis obtained for the drying of camomile are summarized in tabulated forms.

Within the German 1000 roof PV programme, about 2000 grid connected PV plants (1-5 [kW.sub.p]) with a total peak power of 5 [MW.sub.p] were installed on the roofs of single and two family houses. In the Federal State of Lower Saxony, ISFH has been responsible for the technical inspections and the global monitoring of 172 PV plants up until now. The annual final yields range between 430 kWh/([[kW.sub.p].sup.*]a) and 875 kWh/([[kW.sub.p].sup.*]a) with a mean value of 680 kWh/([[kW.sub.p].sup.*]a). Using the annual in-plane irradiation, we determine annual performance ratios in the range 47.5%-81% (mean 66.5%). A procedure to receive standardized performance ratios is introduced using actual peak powers of the PV modules and inverter-specific efficiencies. Typical curves of monthly values of the performance ratio are recorded. PV plants with low final yields are analyzed with respect to operational failures, partly shadowing effects, and poorness in maximum power point adaptation of some inverters. Optimization potentials are also discussed.

Alinear heat-loss model of solar collectors and a general relation of endoreversible three-heat-source heat pumps help analyze the optimal performance and derive the overall coefficient of performance of a solar-driven heat pump system containing a three-heat-source heat pump and a solar collector. The maximum overall coefficient of performance and the optimum operating temperature values of the heat system and the solar collector indicate the non-feasibility of using the heat pump system. The data from the model analysis is helpful for the optimal designing and operation of heat pump systems.

The performance and behavior of five unglazed solar collector installations, devoted to the heating of five outdoor swimming pools located in Switzerland, is studied on the basis of experimental data collected in 1988. Due to the low temperatures involved, hourly efficiencies often exceed 80%. The mean daily collector efficiency is of the order of 60% in optimal conditions and is in good agreement with the G3 simulation program.

For solar cavity-receivers operating at high temperatures, the optimum aperture size results from a compromise between maximizing radiation capture and minimizing radiation losses. When the absorbed solar energy is utilized as high temperature process heat, the energy conversion efficiency can be represented as the product of the energy absorption efficiency and the Carnot efficiency. We describe a simple, semiempirical method to determine the optimum aperture size and optimum operating temperature of a solar cavity-receiver for which its energy conversion efficiency is maximum. Such optimization strongly depends on the incident solar flux distribution at the aperture plane of the receiver. We analytically examine the case of a Gaussian distribution of the incident power flux, and we compare theoretical results with the results obtained when using an optically measured flux distribution. Using Monte-Carlo ray tracing, we further investigate the influence of sunshape on the optimal parameters of a cavity-receiver in a paraboloidal concentrator.

The CAtalytically Enhanced Solar Absorption Receiver (CAESAR) is a 100 k [W.sub.chemical] test reactor currently in operation. This type of high-temperature chemical reactor volumetrically absorbs concentrated solar energy throughout a catalytic porous absorber matrix volume, promoting heterogeneous reactions with fluid-phase reactant species flowing through the absorber. A numerical model of these reactors has been developed to provide guidance in the catalytic matrix design for CAESAR. In the CAESAR reactor, methane is reformed using carbon dioxide and a rhodium catalyst. In addition, the model is being used to evaluate both the reactor performance and test data. This paper presents the thermal and chemical characteristics of the reactor for varying incident solar flux, fluid mass flow, convective heat-transfer coefficient, solar and infrared extinction coefficients, and catalyst loading. Predicted CAESAR performance is based on a prototype absorber and anticipated operating conditions. Model results suggest the mass flux must be proportioned to the incident solar flux radial distribution to prevent unacceptably high local temperatures and to provide a reactor having more uniform exit conditions. Either the catalytic loading or geometric thickness of the absorber should be increased for conversion to approach equilibrium levels. Also, the optical density of the matrix (particularly at the sunlit side of the reactor) should be decreased to distribute solar energy more uniformly in depth and decrease matrix temperatures at the front of the absorber., The thermal and chemical characteristics of the Catalytically Enhanced Solar Absorption Receiver (CAESAR) are described for various incident solar flux, fluid mass flow, convective heat-transfer coefficient, catalyst loading and solar and infrared extinction coefficients. A protoype absorber and predicted operating conditions are used to determine CAESAR performance. Results show that mass flux must be proportional to the incident solar flux radial distribution to prevent high local temperatures and to obtain uniform exit conditions.

A coupled electric/thermal model is used for studying the combined efficiencies in a coupled photovoltaic (PV)/thermal concentrating solar collector. The studies have shown that the overall efficiency of the system is optimized by the variation in key factors such as the solar concentration factor, the band gap of the PV material and the system thermal design configuration, which has led to a maximum combined efficiency.

Byline: J.J. Navarrete-Gonzalez, J.G. Cervantes-de Gortari, E. Torres-Reyes In this paper, a thermodynamic procedure is presented to analyse energy and exergy balances of a rock bed thermal storage system. The thermal behaviour is described by means of a control volume that includes three subsystems: the solar collectors, the fluid distribution system and the storage chamber. Solar-to-thermal energy conversion was obtained by means of a solar collector at a fixed airflow rate. The final purpose of the method is to determine how well the thermodynamic modelling fits the real data obtained experimentally from the prototype under normal operating conditions.

Laminar mixed convection in the entrance region of an inclined tube with longitudinal external fins (corresponding to the basic element of a flat plate solar collector) has been studied numerically. The system is subjected to a uniform solar flux and convective losses on its top surface; it is insulated on its bottom surface. The results show that the secondary flow induced by buoyancy has a very significant effect on the axial flow and on the isotherms in both the fluid and the solid. Furthermore, due to circumferential conduction in the tube wall, more heat reaches the fluid from the bottom half of the fluid-solid interface than from its top half. The circumferentially average Nusselt number shows the usual decrease with axial distance from the tube inlet towards a constant value in the fully developed region. This constant value is considerably higher for the finned tube than the corresponding value for a bare tube. Both these values are significantly higher than one for fully developed forced convection. A parametric study shows the effects of the fin and tube materials, of the solar flux and the fin's width on the thermal performance of the collector.

We present an approach to find optimal reflector shapes for non-tracking solar collectors under practical constraints. We focus on cylindrical absorbers and reflectors with translational symmetry. Under idealized circumstances, edge ray reflectors are well known to be optimal. However, it is not clear how optimal reflectors should be shaped in order to obtain maximum utilizable energy for given operating temperatures under practical constraints like reflectivity less than unity, real radiation data, size limits, and gaps between the reflector and the absorber. For a prototype collector with a symmetric edge ray reflector and a tubular absorber, we derive from calorimetric measurements under outdoor conditions the optical efficiency as a function of the incidence angle. Using numerical optimization and raytracing, we compare truncated symmetric edge ray reflectors, truncated asymmetric edge ray reflectors and free forms parametrized by Bezier splines. We find that asymmetric edge ray reflectors are optimal. For reasonable operating conditions, truncated asymmetric edge ray reflectors allow much better land use and easily adapt to a large range of roof tilt angles with marginal changes in collector construction. Except near the equator, they should increase the yearly utilizable energy per absorber tube by several percent as compared to the prototype collector with symmetric reflectors. [C] 2000 Elsevier Science Ltd. All rights reserved.