An opaque cloud cover model of sky short wavelength radiance

The average angular distribution of short wavelength sky radiance for clear, partly cloudy, and overcast sky conditions has been measured for the range of solar zenith angle 31° to 80°. Detailed analysis of this sky radiance data shows that the normalized sky radiance is given analytically by N(θ, φ) = CN₀(θ, φ) + [1−C]N_C(θ, φ) where N₀(θ, φ) = 0.45 +0.12 θ^* + 0.43 cosθ + 0.72e^−1.88ψ N_c(θ, φ) = [1.63 + 53.7e^−5.49ψ + 2.04 cos² ψ cosθ^*] [1− e^−0.19Secθ][1minus; e^−0.53Secθ], and θ^* is the solar zenith angle (radians), (θ, φ) is the sky radiance direction, Ψ is the scattering angle (radians) between sky and sun directions, and C is the prevailing opaque cloud cover.     

Angular distribution of overcast sky short wavelength radiance

A detailed analysis of 1438 all-sky scans of shortwave radiance (95 skypoints per scan) for overcast skies shows that angular dependence of the (suitably normalized) diffuse sky radiance can be represented by the analytical expression. N_C2(ψ)= 0.45 + 1.12θ^* + 0.43 cos θ + 0.72 exp[−1.88ψ] where Cosψ = Cos θ^*cos θ + sin θ^*cos φθ = sky zenith angle, Φ = sky azimuth angle (relative to the sun), θ^* = solar zenith angle. Both θ^* and ψ are in radians.     

Solar position algorithm for solar radiation applications

There have been many published articles describing solar position algorithms for solar radiation applications. The best uncertainty achieved in most of these articles is greater than ±0.01° in calculating the solar zenith and azimuth angles. For some, the algorithm is valid for a limited number of years varying from 15 years to a hundred years. This report is a step by step procedure for implementing an algorithm to calculate the solar zenith and azimuth angles in the period from the year −2000 to 6000, with uncertainties of ±0.0003°. The algorithm is described in a book written by Jean Meeus in 1998. This report is written in a step by step format to simplify the complicated steps described in the book, with a focus on the sun instead of the planets and stars in general. It also introduces some changes to accommodate for solar radiation applications. The changes include changing the direction of measuring azimuth angles to be measured from north and eastward instead of being measured from south and eastward, and the direction of measuring the observer’s geographical longitude to be measured as positive eastward from Greenwich meridian instead of negative. This report also includes the calculation of incidence angle for a surface that is tilted to any horizontal and vertical angle, as described by Iqbals in 1983.     

Measured shortwave sky radiance in an urban atmosphere

An extensive data set of measurements of the shortwave sky radiance at Toronto, Canada, was compiled by the authors in 1984. A pyroelectric radiometer with a half-angle field of view of 5 degrees was used to make a total of more than 100,000 sky radiance measurements. This paper presents an analysis of almost 40,000 of these measurements in the form of a set of plots showing means and percentiles of sky radiance as a function of position in the sky; atmospheric clearness index, k_t; diffuse fraction, k; and solar zenith angle, θ_z. The data show (i) that, in the circumsolar region, the highest observed values of sky radiance occur for partly cloudy sky conditions characterized by intermediate values of k and k_t, (ii) that, in the regions of the sky away from the solar position, sky radiance tends to increase monotonically both with increasing k and with increasing k_t, (iii) that there is a progressive transition with increasing k, from the horizon brightening for skies with low diffuse fractions to horizon darkening for skies with diffuse fractions approaching unity, (iv) that the shape of the sky radiance distribution is a strong function of the elevation of the sun in the sky, and (v) that the sky radiance is highly variable, with a positively skewed probability density function.     

Air mass: Analytical and empirical treatment; an improved formula for air mass

In this paper, relative air mass is defined analytically and treated empirically, and a new formula is proposed. This formula takes into account not only the zenith angle, but also the Earth's curvature, altitude and temperature. The new formula and the old one (m = 1/cos θ_z) are in good agreement for zenith angles up to 70°, but for bigger angles the new formula gives smaller values of air mass. In particular, it gives a finite value for air mass when the zenith angle is 90°. It is shown that the old formula is a special case of the new one. The values of relative air mass calculated with the new formula depend on the effective thickness of the atmosphere. Experimentally, it is found that the effective thickness of the atmosphere is linearly related to the average thickness of the atmosphere, which depends on latitude and meteorological conditions. It is concluded that for values of θ_z up to 70°, with little error, the old formula can be used, but that for larger zenith angles (especially for times near sunrise or sunset), only the new formula can give proper and meaningful results. The influence of the zenith angle, the altitude and the temperature on the relative air mass is analyzed.     

Heat transfer coefficient and friction factor correlations for rectangular solar air heater duct having transverse wedge shaped rib roughness on the absorber plate

As is well known, the heat transfer coefficient of a solar air heater duct can be increased by providing artificial roughness on the heated wall (i.e. the absorber plate). Experiments were performed to collect heat transfer and friction data for forced convection flow of air in solar air heater rectangular duct with one broad wall roughened by wedge shaped transverse integral ribs. The experiment encompassed the Reynolds number range from 3000 to 18000; relative roughness height 0.015 to 0.033; the relative roughness pitch 60.17φ^−1.0264<p/e<12.12; and rib wedge angle (φ) of 8, 10, 12 and 15°. The effect of parameters on the heat transfer coefficient and friction factor are compared with the result of smooth duct under similar flow conditions. Statistical correlations for the Nusselt number and friction factor have been developed in terms of geometrical parameters of the roughness elements and the flow Reynolds number.     

A SOLAR EJECTOR COOLING SYSTEM USING REFRIGERANT R141b

A high-performance solar ejector cooling system using R141b as the working fluid was developed. We obtain experimentally a COP of 0.5 for a single-stage ejector cooling system at a generating temperature of 90°C, condensing temperature of 28°C, and an evaporating temperature 8°C. For solar cooling application, an optimum overall COP can be obtained around 0.22 at a generating temperature of 95°C, evaporating temperature of 8°C and solar radiation at 700 W m⁻².     

Structural and electrical properties of CuGaS2 thin films by electron beam evaporation

Single phase CuGaS₂ thin film with a highest diffraction peak of (1 1 2) at a diffraction angle (2θ) of 28.8° was made at a substrate temperature of 70°C, an annealing temperature of 350°C and an annealing time of 60 min. Second highest (2 0 4) peak was shown at diffraction angle of (2θ) 49.1°. Lattice constant of a and c of that CuGaS₂ thin film was 5.37 and 10.54 Å, respectively. The greatest grain size of the thin film was about 1 μm. The (1 1 2) peak of single phase of CuGaS₂ thin film at an annealing temperature of 350°C with excess S supply appeared at a little higher about 10% than that of no excess S supply. The resistivity, mobility and hole density at room temperature of p-type CuGaS₂ thin film was 1.4 Ω cm, 15 cm²/V s and 2.9×10¹⁷ cm⁻³, respectively. It was known that carrier concentration had considerable effect than mobility on a variety of resistivity of the fabricated CuGaS₂ thin film, and the polycrystalline CuGaS₂ thin films were made at these conditions were all p-type.     

Investigation of solar radiation in Botswana and some anomalous phenomena observed

Daily global insolation on a horizontal surface in Botswana is recorded continuously at several synoptic stations and at the University of Botswana's Physics Department. Over a number of years, daily total insolation on a tilted surface (β = −30°) was recorded at the Botswana Technology Centre. Hourly, and instantaneous direct normal, global, diffuse and UV-components are continuously recorded at the University of Botswana. All these measurements are done with standard EPLAB equipment.It is found out that the instantaneous direct normal radiation at Solar noon can be as high as 1150 W·m⁻²; and that at 30 min before sunset it can be above 600 W·m⁻²; and it can also be as high as 100 W·m⁻² at sunset or sunrise moments (i.e. with half of the solar disk under the horizon).Daily direct normal solar radiation can exceed 45 MJ·m⁻². Mean daily global radiation varies from 31 MJ·m⁻² in December to 16 MJ·m⁻² in June. Such big values of daily direct normal and global radiation are explained by low humidity and low turbidity.Cases of an anomalous phenomenon which lead to an abnormally big phase shift when direct normal radiation is increasing greatly after Solar noon are observed, and discussed. It is also found that when humidity is low and visibility is high, hourly I_g values recorded with a pyranometer can be less than I_bn (cosθ_z) + I_d-values. This discrepancy could be quite common for regions where humidity and turbidity are low. The trend in the behaviour of the UV-component during the last five years is also analyzed and discussed. The conclusion is made that the ozone layer over Botswana is continuously being depleted.     

CVT-growth of AgGaSe2 single crystals: Electrical and photoluminescence properties

Single crystals of AgGaSe₂ were grown by the Chemical Vapor Transport (CVT) -method using iodine as transport agent. Growth temperatures of 770°C and concentrations of the transport agent of 1.6–1.7 mg I₂/cm³ yielded compact single crystals with a size of up to 8 X 5 X 5 mm³ and a habitus dominated by the {112}-faces. The as-grown crystals were highly insulating (σ < 10⁻⁸(Ω cm)⁻¹). Annealing of the crystals in vacuum at 700°C resulted in n-type conductivity of 2 · 10⁻¹ (Ω cm)⁻¹ with a dominant peak in the photoluminescence spectra at 4 K associated with a donor level of 164 meV. Annealing in Se-atmosphere at 600°C lead to p-type conductivity of 6 · 10⁻⁶ (Ωcm)⁻¹ within a surface layer of the AgGaSe₂ single crystals. The corresponding photoluminescence spectra and the activation energy of the electrical conductivity (between 100 K and 300 K) suggest the presence of an acceptor (V_cation) with an activation energy of 60 meV and a donor (V_Se) with an activation energy of 100 meV.     

The thermal radiance of clear skies

Measurements of the longwave radiance of the sky were made during the summer of 1979 at Tucson, Arizona; Gaithersburg, Maryland; and St. Louis, Missouri. The global longwave radiation (wavelengths greater than 3 μm) was monitored with a pyrgeometer and the distribution of this radiation in several spectral bands at five different zenith angles was monitored with a spectral radiometer. This paper presents results for the global sky radiation during clear sky conditions. The spectral radiometer was used to calibrate the pyrgeometer and to detect the presence of clouds. The results can most appropriately be summarized in terms of the correlation between the global sky emissivity _sky and surface dewpoint temperature T_dp(°C). The global sky emissivity is defined as the ratio of sky radiance to σT_a⁴, where T_a is the absolute air temperature near the ground, and σ is the Stefan-Boltzmann constant. Based on 2945 night-time measurements in all three cities we find _sky=0.741 +0.0062T_dp with a standard error of estimate of 0.031. A similar relationship with almost identical coefficients holds during daylight hours.     

A study of zenith radiance in Pamplona under different sky conditions

Zenith radiance was measured in Pamplona (Spain) during sixteen months under different sky conditions. 5th degree polynomials that relate log(L_z) with solar elevation return the best correlations both when considering the entire dataset as well as when data are split into the five sky conditions considered. Besides, we have obtained simple relations, with high correlation coefficients and low Relative Root Mean Square Difference, to predict the values of the mean zenith radiance for a type of sky from the mean zenith radiance values of one or more of the remaining four types. Lastly, we obtained month–hour equal mean zenith radiance contours for each of the five sky types considered in the study as well as for all the skies as a whole.     

Thermal behavior of buildings with curved roofs as compared with flat roofs

In this paper, a detailed finite element model dealing with heat transfer through a domed or vaulted roof is suggested based on a three-dimensional heat transfer equation and solar geometry. This model allows a comparison of the thermal behavior of curved and flat roofs in terms of heat flux and daily heat flow through them into an air-conditioned building under different climatic conditions. The results of numerical calculations show that the ratio of daily heat flow through curved roofs to that through flat ones is not affected by the curve radius, thickness and construction material of the roof, but is significantly influenced by the half rim angle θ₀ of the roofs and the ambient temperature. Compared to a flat roof, under typical hot dry climatic conditions, the daily heat flow through a domed roof of θ₀=90° is about 40% higher, whereas the daily heat flow through a south–north oriented and an east–west oriented vault of θ₀=90° is about 20 and 27% higher, respectively. The reason for this is mainly attributed to the convective heat transfer between the enlarged curved roof and ambient air. However, when θ₀<50°, heat flux and daily heat flow through a curved roof is close to that through a flat roof. The results also confirm that curved roofs are not suitable for areas with higher air temperature and intense sky diffuse radiation typical of hot humid areas.     

Luminous efficacy models and their application for calculation of photosynthetically active radiation

From a spectral radiative transfer model, an algorithm is developed for the conversion of illuminance to different measures of Photosynthetically Active Radiation (PAR) (in W m⁻² or in μEm⁻²s⁻¹). This illuminance to PAR conversion may even be used in combination with a luminous efficacy model and, thus, form a photosynthetic efficacy model. In this work, two luminous efficacy models are chosen, one empirical and one derived from the above radiative transfer model. Observed PAR energy flux and PAR photon flux from seven Nordic stations (56–70°N) and illuminance from one U.S. station (43°N) are, together with observed all-wave solar irradiance from all stations, used for verification.Observed and modelled luminous efficacies agree on the average within 1% at high solar elevation under cloudless sky, while it is indicated that the illuminance, PAR energy flux, and PAR photon flux radiometers are mutually inconsistent by some 6–16%. Even differences in cosine response between radiometer types are apparent at low solar elevation under cloudless sky. In the present climates, the global radiation efficacy is 10–12% higher under an average cloudless atmosphere than it is outside the atmosphere. By introducing an average cloud deck in this cloudless atmosphere, a further efficacy increase, slightly exceeding these 10–12%, is observed. However, observations indicate that the cloud transmittance algorithm used in the radiative transfer model significantly overestimates the global radiation efficacy increase caused by horizontally inhomogeneous cloud decks.     

Performance analysis of non-isothermal solar reactors for methanol decomposition

A procedure for analyzing the performance of non-isothermal solar reactors for methanol decomposition was developed, based on a model of thermal loss from direct steam generation collector and a comprehensive kinetic model of methanol decomposition employing BASF K3-110 catalyst. It was found that catalytic bed temperature tends towards a certain value, which depends on the chemical reaction type, radiation intensity and collector structure mainly. For a beam incidence angle of 0°, system efficiency increases from 56% at a radiation intensity of 400 W m⁻² to almost 58% at a radiation intensity of 1000 W m⁻². For a radiation intensity of 400 W m⁻², beam incidence angle of 20°, absorber length of 10 m, feed temperature of 373 K and ratio of reaction section of 0.9, the mole flow rate of feed in the range of 0.21–0.23 mol s⁻¹ results in a maximum quantity of reacted methanol of 0.146 mol s⁻¹, while a mole flow rate of feed of 0.15 mol s⁻¹ leads to a maximum system efficiency of 54.2%. The research indicates that the pre-heating section should be as short as possible for effective use of solar energy.     

Theoretical analysis of the thermal performance of all-glass evacuated tube solar collectors with absorber coating on the outside or inside of the inner tube

Theoretical efficiencies (η) and thermal behaviour of all-glass Evacuated Tube solar Collectors with an Internal Absorber Film (ETCIAF), i.e. the absorber film deposited in the inner surface of the inner tube, are compared and contrasted with the traditional design of all-glass Evacuated Tube solar Collectors with an External Absorber Film (ETCEAF), using the absorber film on the external surface of the inner tube. The values of η of the ETCIAF are unacceptably lower than that of ETCEAF for any particular value of the heat transfer coefficient (h_b) for the annular space, except in the case of a highly leaky ETCEAF, with h_b > 2.6 W/m² K. However, it is shown that the use of a transparent conductive coating with moderately low emittance 0.1−0.25 on the outside of the absorber tube of ETCIAF can offer efficiences 0.75−0.63, respectively, for f = 0.1 °C m²/K, competing well (η = 0.76) with the ETCEAF design operating under best conditions (α = 0.91, = 0.05, and h_b = 0.026 W/m² K).     

Discrete two-positional tracking of solar collectors

Northern European regions, such as Estonia at 60° latitude, receive about 980 kWh m⁻² y⁻¹ of solar radiation. These low insolation levels motivate solar collectors to be equipped with a tracking mechanism for an increased yield. Classical active tracking is complicated and energy intensive, negating tracking benefits for PV modules and thermal flat-plate collectors. This paper describes mainly the performance of PV modules with daily two-positional tracking. The symmetrical and asymmetrical positions about the north–south axis are analyzed, corresponding to the positions of sun in the morning and in the afternoon. The tracking drive is simple and requires a minimum energy input during the brief daily triggering of movement. Results indicate that the seasonal energy yield is increased by 10–20% over the yield from a fixed south-facing collector tilted at an optimal angle. The results are based on long-term solar data measured at the Tartu-Tõravere Meteorological Station in Estonia, confirmed by experimental testing during summer 2004 and 2005 in Tallinn University of Technology.     

A potential interconnect material for solid oxide fuel cells: Nd0.75Ca0.25Cr0.98O3−δ

Chromium-deficient Nd_0.75Ca_0.25Cr_1−xO_3−δ (0.02 ≤ x ≤ 0.06) oxides are synthesized and assessed as a novel ceramic interconnect for solid oxide fuel cells (SOFCs). At room temperature, all the samples present single perovskite phase after sintering at 1600 °C for 10 h in air. Cr-deficiency significantly improves the electrical conductivity of Nd_0.75Ca_0.25Cr_1−xO_3−δ oxides. No structural transformation occurs in the Nd_0.75Ca_0.25Cr_1−xO_3−δ oxides in the temperature range studied. Among all the samples, the Nd_0.75Ca_0.25Cr_0.98O_3−δ sample with a relative density of 96.3% exhibits the best electrical conductivity of 39.0 and 1.6 S cm⁻¹ at 850 °C in air and hydrogen, respectively. The thermal expansion coefficient of Nd_0.75Ca_0.25Cr_0.98O_3−δ sample is 9.29 × 10⁻⁶ K⁻¹ in the temperature range from 30 to 1000 °C in air, which is close to that of 8 mol% yttria stabilized zirconia electrolyte (10.3 × 10⁻⁶ K⁻¹) and other cell components. The results indicate that Nd_0.75Ca_0.25Cr_0.98O_3−δ is a potential interconnect material for SOFCs.     

Determination of glazing area in direct gain systems for three different climatic zones

This study determines the glazing area in direct gain passive systems needed to ensure thermal comfort inside a building (room air temperature 20 ± 2°C). A 4 m × 4 m × 3 m single zone isolated house is analyzed in three different types of climates namely composite (8°C to 20°C, New Delhi), cold-cloudy (−2°C to 5°C, Srinagar), and cold-sunny (−14°C to −3°C, Leh). The analysis is based on the periodic solution of the heat conduction equations describing heat transmission in the building components, floor, walls, and roof, and the Fourier representation of the ambient temperature vnd the total solar radiation intercepted by the building envelope. Two types of construction are analyzed: the first type is a traditional construction with 22-cm-thick brick wall, plastered 15 mm on both the sides (U = 2.0 W m⁻² K⁻¹); and the second one is of the same type but with 10 cm of expanded polystyrene insulation on all the four walls and the roof (U = 0.31 W m⁻² K⁻¹). It is found that for traditional construction with U = 2.0 W m⁻² K⁻¹, the glazing U value has almost no effect on the room temperature even for large variation of the glazing area (10% to 40%, expressed in terms of percentage of floor area). For a well-insulated house (U = 0.31 W m⁻² K⁻¹), the glazing U value has no effect upon the room air temperature if the glazing area is small (less than 10%). The position of the insulation on the external surfaces is more effective in reducing large inroom air temperature. Finally, for an insulated house, we recommended glazing is 30%, 20%, and 10% for cold-sunny, cold-cloudy, and composite climates, respectively.     

Simulation and model validation of a horizontal shallow basin solar concentrator

Salt removal from drainage water is becoming increasingly important for sustainable irrigated arid land agriculture, where inadequate drainage infrastructure exists. Solar evaporation and concentration systems are currently in development in California for this purpose. The thermal behavior and evaporation rates of a horizontal shallow basin solar concentrator were modeled for design purposes and investigated experimentally in order to validate the model. Three different evaporation rate models were evaluated and compared. Measured and predicted peak brine temperatures differed by as much as 5 °C when using prescribed literature coefficients without calibration. Model prediction was improved by calibration so that peak brine temperature deviated less than 3 °C when tested against independent data sets.Minimum root mean square error was used to calibrate the mass transfer coefficient and absorptance of the collector surface for solar radiation, which are the main factors affecting the heat transfer associated with the solar concentrator. Calibrated collector surface absorptance for solar radiation declined while mass transfer coefficients were increased from reported literature values. Under calibration, the absorptance of the collector surface was adjusted from 0.8 to 0.61, and mass transfer coefficients estimated by Newell et al. [Newell, T.A., Smith, M.K., Cowie, R.G., Upper, J.M., Cler, C.L., 1994. Characteristics of a solar pond brine reconcentration system. Journal of Solar Energy Engineering 116 (2), 69–73] from 1.36 × 10⁻⁶(1.9 + 1.065V) to 1.70 × 10⁻⁶(1.84 + 1.0V) kg m⁻² s⁻¹ mm Hg⁻¹, by Manganaro and Schwartz [Manganaro, J.L., Schwartz, J.C., 1985. Simulation of an evaporative solar salt pond. Industrial & Engineering Chemistry Process Design and Development 24, 1245–1251] from 0.0208(1 + 0.224V) to 0.0233(1 + 0.214V) kg m⁻² h⁻¹ mm Hg⁻¹, and by Alagao et al. [Alagao, F.B., Akbarzadeh, A., Johnson, P.W., 1994. The design, construction, and initial operation of a closed-cycle, salt-gradient solar pond. Solar Energy 53 (4), 343–351] from 2.8 + 3.0V to 3.0 + 3.33V W m⁻² °C⁻¹. The calibrated models were tested using an independent data set. Maximum deviation between measured and predicted brine temperatures differed by less than 3 °C. The measured and predicted peak evaporation rates were between 1.2 and 1.4 kg m⁻² h⁻¹.The calibrated Newell model was used to predict the monthly productivity and daily maximum evaporation rates at Five Points, California for the year 2004. The productivity from April to September and from March to October was 80.7% and 94.3% of the total annual productivity, respectively.