Combined non-gray radiative and conductive heat transfer in solar collector glass cover

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.     

Heat loss coefficients and effective πα products for flat-plate collectors with diathermanous covers

This paper presents an efficient algorithm for solving the set of nonlinear equations governing the total heat transfer across an arbitrary number of parallel flat plate solar collector covers, each of which can be partly transparent to longwave thermal radiation. The governing equations are sufficiently general to permit each cover to have assymetric radiative properties and to account for absorption of solar energy on the individual covers. This theory is shown to be in good agreement with the approximate equations of Whillier (provided certain interpretations are placed on his quantities) and with experiments using a plastic inner cover and bounding plates of various emissivities. Using this theory, it is demonstrated that if the absorber plate has a selective surface, an inner cover transparent to long wave radiation is to be preferred over one which is opaque.     

Theoretical approach of a flat plate solar collector with clear and low-iron glass covers taking into account the spectral absorption and emission within glass covers layer

Accurate modeling of solar collector system using a rigorous radiative model is applied for the glass cover which represents the most important component of the system and greatly affects the thermal performance. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one dimensional case using the radiation element method by ray emission model (REM²). The optical constants of a clear and low-iron glass materials proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of such materials, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational times for predicting the thermal behavior of solar collector were found to be prohibitively long for the non-gray calculation using 160 values of n and k for both glasses. Therefore, suitable semi-gray models have been proposed for rapid calculation. The temperature distribution within the glass cover shows a good agreement with that obtained with iterative method in case of clear glass. It has been shown that the effect of the non-linearity of the radiative heat exchange between the black plate absorber and the surroundings on the shape of the efficiency curve is important. Indeed, the thermal loss coefficient is not constant but is a function of temperature, due primarily to the radiative transfer effects. Therefore, when the heat exchange by radiation is dominant compared with the convective mode, the profile of the efficiency curve is not linear. It has been also shown that the instantaneous efficiency of the solar collector is higher in case of low-iron glass cover.     

Influence of thermal emittance on the performance of laminated solar control glazing

Influence of thermal emittance on the performance of laminated solar control glazing is presented. A transient one-dimensional mathematical model allowing the prediction of conductive heat transfer within the glazing and convective and radiative heat transfer from the glazing towards the interior and exterior are considered separately. A constant normal incidence of air mass 2 solar radiation of 750 W/m² was assumed. The redistribution of the component of the solar radiation absorbed by the laminated glass and the shading coefficient (SC) were calculated for solar transmittance, 0.05 to 0.35; thermal emittance of the inner surface of the glazing, 0.15 to 0.85; convective heat transfer coefficient for the exterior surface, 10–100 W/m² K and exterior ambient temperatures of 15°C, 32°C and 45°C. The results indicate that as the emittance decreases, the SC decreases by 10–20% for all cases of ambient temperatures considered. The contribution from the convective mechanisms to the heat transfer to the interior is always higher than that from radiative process in the range of ambient temperatures considered. The results presented in this paper would help to decide whether for a given location of interest, the incorporation of a heat mirror glazing would make a meaningful reduction in the cooling load in enclosures with single glazed windows.     

Thermal modeling of solar stills: an experimental validation

Expressions for water and glass temperatures, yield and efficiency of both single and double slope multiwick solar distillation systems in quasi-steady state conditions have been derived. The analysis is based on the basic energy balance for both the systems. A computer model has been developed to predict the performance of the solar stills. Experimental validation of the thermal model has been carried out by using modified heat transfer coefficients. Internal heat transfer coefficients have been evaluated based on both inner and outer glass cover temperatures for typical days namely January 22, and June 19, 2001 in Delhi. A fair agreement has been observed between theoretical and experimental results by using the modified internal heat transfer coefficients based on inner glass cover temperature.     

Natural convective heat transfer in trapezoidal enclosure of box-type solar cooker

This paper presents simple thermal analysis to evaluate the natural convective heat transfer coefficient, h_c12 for a trapezoidal absorber plate-inner glass cover enclosure of a double-glazed box-type solar cooker. Several indoor simulation experiments in steady state conditions have been performed to measure the temperatures of absorber plate, inner and outer glass covers, ambient air, electrical input supply and wind speed. The experimental data has been correlated by an equation of the form, Nu = CRaⁿ. The values of the constants C and n, obtained by linear regression analysis are used to calculate the convective heat transfer coefficient. The heat transfer analysis predicts that h_c12 varies from 4.84 to 6.23 W m^{−2 o}C⁻¹ for the absorber plate temperature from 54 to 141 ^oC. The results of h_c12 are compared with those of rectangular enclosure for the same absorber-inner glass cover temperatures and gap spacing. The study reveals that the values of convective heat transfer coefficient and top heat loss coefficient for rectangular enclosure are lower by 31–35% and 7% respectively.     

Three-dimensional numerical study of heat transfer characteristics in the receiver tube of parabolic trough solar collector

The solar energy flux distribution on the outer wall of the inner absorber tube of a parabolic solar collector receiver is calculated successfully by adopting the Monte Carlo Ray-Trace Method (MCRT Method). It is revealed that the non-uniformity of the solar energy flux distribution is very large. Three-dimensional numerical simulation of coupled heat transfer characteristics in the receiver tube is calculated and analyzed by combining the MCRT Method and the FLUENT software, in which the heat transfer fluid and physical model are Syltherm 800 liquid oil and LS2 parabolic solar collector from the testing experiment of Dudley et al., respectively. Temperature-dependent properties of the oil and thermal radiation between the inner absorber tube and the outer glass cover tube are also taken into account. Comparing with test results from three typical testing conditions, the average difference is within 2%. And then the mechanism of the coupled heat transfer in the receiver tube is further studied.     

Computation of glass-cover temperatures and top heat loss coefficient of flat-plate solar collectors with double glazing

A set of correlations for computing the glass-cover temperatures of flat-plate solar collectors with double glazing is developed. A semi-analytical correlation for the factor f₂—the ratio of outer to inner thermal resistance of a double-glazed collector—as a function of collector parameters and atmospheric variables is obtained by regression analysis. This relation readily provides the temperature of the second (outer) glass cover (T₂). For estimating the temperature of first (inner) glass cover (T₁), another relation for the factor f₁—the ratio of thermal resistance between the two glass covers to the thermal resistance between the absorber plate and first glass cover—is developed. A wide range of variables is covered in the present analysis. The results are compared with those obtained by numerical solutions of heat-balance equations. Using the proposed relations of glass-cover temperatures, the values of top heat loss coefficient (U_t) can be computed and are found to be very close to those obtained by numerical solutions of heat-balance equations. The maximum absolute error in the calculation of U_t by the proposed method is only 1.0%, so numerical solutions of heat-balance equations for the computation of U_t are not required.     

Theoretical approach of a flat-plate solar collector taking into account the absorption and emission within glass cover layer

A rigorous theoretical approach of a flat-plate solar collector with a black absorber considering the glass cover as an absorbing–emitting media is presented. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one-dimensional case using the Radiation Element Method by Ray Emission Model (REM²). The optical constants of a clear glass window proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of a clear glass, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational time for predicting the thermal behavior of solar collector was found to be prohibitively long for the non-gray calculation using 160 values of n and k. Therefore a suitable semi-gray model is proposed for rapid calculation. The profile of the efficiency curve obtained in the present study was found to be not linear in shape. Indeed, the heat loss from the collector is a combination of convection and radiation and highly non linear. The effect of the outside convective heat transfer on the efficiency curve is also studied. In fact, when the convection is the dominant heat transfer mode compared with the radiation one, the profile of the efficiency curve is more or less straight line. Consequently, the heat loss coefficient could be calculated using Klein model. It has been also shown that the effect of the wind speed on the glass cover mean temperature is very important. This effect increases with the increase of the mean absorber temperature.     

Particle–gas reacting flow under concentrated solar irradiation

A transient heat transfer model is developed for a reacting flow of CH₄ laden with carbon particles directly exposed to concentrated solar radiation and undergoing thermal decomposition into carbon and hydrogen. The unsteady mass and energy conservation equations, coupling convective heat and mass transfer, radiative heat transfer, and chemical kinetics for a two-phase solid–gas flow, are formulated and solved numerically for both phases by Monte Carlo and finite volume methods using the explicit Euler time integration scheme. Parametric study is performed with respect to the initial particle diameter, volume fraction, gas composition, and velocity. Validation is accomplished by comparing temperatures and reaction extent with those measured experimentally using a particle-flow solar reactor prototype subjected to concentrated solar radiation. Smaller particles and/or high volume fractions increase the optical thickness of the medium, its radiative absorption and extinction coefficients, and lead to higher steady-state temperatures, reaction rates, and consequently, higher extent of chemical conversion.     

The equivalence of outdoor and mixed indoor/outdoor solar collector testing

An extension of the heat transfer analysis for a flat plate collector is presented in order to provide a single equation incorporating the effects of solar heating in the collector cover, variations in longwave atmospheric radiation and variations in the individual heat transfer coefficients in the collector.

By considering this equation it is shown that variations in longwave atmospheric radiation can influence the collection efficiency by up to 3 per cent, and that solar absorption in typical collector cover glasses also has an influence of 2–3 per cent.

The magnitude of the plate efficiency factor (F′) is shown to decrease as the collector temperature increases because it is a function of collector heat transfer coefficients. In poor collectors this effect can alter the collection efficiency by as much as 10–15 per cent.

The sum of these variations in collector efficiency is small for “good” collectors and it follows that the mixed indoor/outdoor test will produce quite representative results for these. However, when the variations are large, such as is the case for poor collector designs, then the mixed indoor/outdoor test will over-estimate the collection efficiency.     

An experimental and analytical evaluation of the insulative properties of double glazing and thick curtains

Theoretical and experimental evaluations are made of thermal curtains applied to double-glazed greenhouse structures. The reflectance and emittance of the curtain is permitted to be different on the two surfaces: It may be partially transparent or opaque to thermal radiation, and it may have thick blanket insulative properties. The effect of cloud cover upon the night-sky radiation temperature is included in the model. Convection coefficients are prescribed for the curtain and glazed surfaces, and the effect of air leakage into the space between the curtain and inner layer of glazing is included as an empirically defined parameter. The thermal balance for the system is obtained in terms of the radiative, convective and air-leakage parameters relevant to each component. The resulting set of thermal balance equations are solved iteratively using existing matrix-solution programs at the University of Waterloo. An experimental rig was constructed to determine nighttime heat loss from a conventional double-walled polycarbonate glazing material which is partially transparent to thermal radiation. The rig was operated with and without an insulating curtain. An opaque multilayer curtain and a semitransparent bubble film curtain were tested. The agreement between the thermal model and the test rig was within ±5% for all cases. Cloud cover was found to be a significant parameter that alters heat loss upwards by 11% from fully cloudy to clear-sky conditions. Intermediate cloud cover conditions were investigated as well and were found to be well predicted by an existing correlation for sky temperature vs cloud cover. The analysis is extended to provide a simple resistance coefficient for heat loss from the glazed structure based upon inside and outside temperatures for a specified cloud cover. It is found that the semiopaque curtain and double-glazed combination has 3.74 times the thermal resistance of a single glass structure as compared to a value of 3.81 for the opaque curtain and double-glazed arrangement. In addition the semiopaque curtain can be used for solar shading during the summer time, thereby serving a dual purpose that significantly increases its economic advantage.     

Thermal performance of solar air heaters: Mathematical model and solution procedure

A mathematical model and solution procedure for predicting the thermal performance of single-pass solar air collectors is presented. By omitting or providing a top glass cover over a plane absorber plate, or by providing a bottom plate under the absorber plate and circulating air over one or both of the air channels so formed, four common types of flat-plate solar air collector designs were considered. The surface temperatures of the walls surrounding the air streams were assumed uniform whereas the air temperatures were assumed to vary linearly along the collector. In the mathematical model, the solar collector was assumed sufficiently short for which the assumptions were valid. By considering a steady state heat transfer using the thermal network analysis procedure, a set of simultaneous equations for the mean temperature of the walls and the air streams were obtained. Instead of solving the simultaneous equations for mean temperatures explicitly, a matrix inversion method was employed using a standard sub-routine programme. Because heat transfer coefficients were temperature dependent, a set of mean temperatures was approximated which allowed the heat transfer coefficients to be evaluated as a first guess. An iterative process was then created that enabled the mean temperatures for the collector to be calculated. The newly-calculated mean temperatures were then compared with the initially-guessed temperatures. The iterative procedure was repeated until consecutive mean temperature values differed by less than 0.01°C. After this, another section of collector with a length equal to the previous one was added to the end of the first collector. The temperature conditions at the inlet of the second section were assumed equal to the outlet temperature conditions of the previous section. The iterative procedure to determine the mean temperatures was repeated for the next section. Additional sections were added until the required overall length of collector was considered. By this procedure, predictions of mean wall and air streams temperatures for a collector of any length could be obtained. Although only four, common single-pass types of flat-plate solar collectors are considered here, the solution procedure could be extended to encompass most other collector designs.     

Validation of CFD simulation for flat plate solar energy collector

The problem of flat plate solar energy collector with water flow is simulated and analyzed using computational fluid dynamics (CFD) software. The considered case includes the CFD modeling of solar irradiation and the modes of mixed convection and radiation heat transfer between tube surface, glass cover, side walls, and insulating base of the collector as well as the mixed convective heat transfer in the circulating water inside the tube and conduction between the base and tube material. The collector performance, after obtaining 3-D temperature distribution over the volume of the body of the collector, was studied with and without circulating water flow. An experimental model was built and experiments were performed to validate the CFD model. The outlet temperature of water is compared with experimental results and there is a good agreement.     

New development in the theory of heat and mass transfer in solar stills

A single basin solar still with basin area of 0.98 × 0.98 m was constructed from galvanized iron sheets and an inclined glass cover. The still was provided with 525 W electrical heating tapes, fixed under the still basin for indoor steady state operation. The variation of basin temperature, glass temperature and evaporation rate were measured during both indoor and outdoor operation. The hourly variation of solar radiation, ambient temperature, and wind velocity were also taken during the outdoor measurements. Transient analysis of the still requires the evaluation of evaporative, convective and radiative heat transfer coefficients. The Dunkle model, which has been widely used for the prediction of the evaporative coefficient, was found to overpredict evaporation rates. The models developed in this work were found to provide better prediction for the evaporation rate measured in this work and in some previous works.     

Combined nongray radiative and conductive heat transfer in multiple glazing taking into account specular reflection and absorption

The problem of combined nongray radiative and conductive heat transfer in multiple glazing subjected to solar irradiation is analyzed. A spectral solar model proposed by Bird and Riordan is used to calculate direct and diffuse solar irradiance. The radiation element method by ray emission model, REM², is used to analyze the spectral dependence of radiative heat transfer. Specular reflection at boundary surfaces is taken into account. The spectral dependence of radiation properties of glass such as specular reflectivity, refraction angle, and absorption coefficient is taken into account. The steady‐state temperature and heat flux distributions in the glass layer are obtained and the insulating efficiency of multiple glazing is examined. The overall heat transfer coefficients predicted by the present method are compared with those based on the JIS method. The values obtained by the present method are slightly lower than those obtained by the JIS method. To investigate the spectral variation of radiative heat flux attenuated in the glass layer, the spectral heat flux at the room‐side surface and incident radiation are compared. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(8): 712–726, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10125     

CFD analysis of the thermal losses on the upper part of a flat solar collector

To investigate the reduction of heat losses on the upper part of a flat solar collector, a two‐dimensional study was carried out by CFD analysis using Fluent. For this purpose, the heat transfer behavior in the air gap over a wide range of thicknesses of the latter (1‐20 mm) and the addition of a second glass cover fixed at midheight of the air gap spacing have been investigated. For small thicknesses of the air gap (1‐8 mm), the heat transfer is essentially conductive. An increase in the thickness leads to the intensification of the natural convection which induces high thermal losses. The simulation results have shown that the addition of a second cover glazing leads to the weakening of the natural convection and thus to an average enhancement of the solar collector temperature over the range of thicknesses studied of approximately 17%. The overall thermal losses coefficient is then reduced by an average of 26% compared with the single‐glazed solar collector. They have also shown that the thickness of the air gaps resulting in the minimum overall heat losses is 8 mm and that the thickness of the second glass cover has no significant effect on these results. In addition, this study has highlighted the importance of taking into account the radiation heat transfer in establishing the thermal balance of a flat solar collector. Indeed, this consideration leads to an average decrease of the absorber temperature of about 30%.     

An air-cooled solar collector using all-cylindrical elements in a low-loss body

A novel IX air-cooled solar collector has a phenolic polymer structural foam body, a black painted fiberglass mat absorber and a coplanar, parallel, close-packed array of evacuated cylindrical glass tubes for a cover. Modeling suggests, and measurements confirm, high efficiency performance as well as a substantial dispersion of performance characteristic arranged so that the specific temperature difference increases as the radiant intensity decreases. This dispersion suggests greatly improved cloudy weather performance. In a steady state simulation at full sun under northern midwinter conditions this collector can deliver a minimum of 1.9 times more heat per day to Glauber's Salt storage than can a IX double glazed water-cooled collector with a non-selective black flat absorber plate. Under cloudy conditions this advantage ratio rises to 12.1 at sun. Effective heat collection continues at intensities as low as sun. Under summertime conditions the collector can operate an absorption air conditioner at sun.     

Heat transfer characteristics in double tube helical heat exchangers using nanofluids

In the present work a three-dimensional analysis is used to study the heat transfer characteristics of a double-tube helical heat exchangers using nanofluids under laminar flow conditions. CuO and TiO₂ nanoparticles with diameters of 24 nm dispersed in water with volume concentrations of 0.5–3 vol.% are used as the working fluid. The mass flow rate of the nanofluid from the inner tube was kept and the mass flow rate of the water from the annulus was set at either half, full, or double the value. The variations of the nanofluids and water temperatures, heat transfer rates and heat transfer coefficients along inner and outer tubes are shown in the paper. Effects of nanoparticles concentration level and of the Dean number on the heat transfer rates and heat transfer coefficients are presented. The results show that for 2% CuO nanoparticles in water and same mass flow rate in inner tube and annulus, the heat transfer rate of the nanofluid was approximately 14% greater than of pure water and the heat transfer rate of water from annulus than through the inner tube flowing nanofluids was approximately 19% greater than for the case which through the inner and outer tubes flow water. The results also show that the convective heat transfer coefficients of the nanofluids and water increased with increasing of the mass flow rate and with the Dean number. The results have been validated by comparison of simulations with the data computed by empirical equations.     

Analysis of the top heat loss factor of flat plate solar collectors with single and double glazing

The dependence of the top heat loss factor of flat plate solar collectors with single and double glazing on the basic parameters was studied. An improved technique for calculation of the top heat loss factor of flat plate collectors with single glazing has recently been proposed by the authors. The present work, covering the flat plate collectors with single as well as double glazing, carefully examines the impact of the glass cover temperature(s) estimated by simple empirical relation(s) on the individual heat transfer coefficients and hence on the top heat loss factor. An analysis of the capability of the new method to accurately compute the top heat loss factor over an extensive number of combinations of the basic parameters has been carried out.