Effect of absorption of solar radiation in glass-cover(s) on heat transfer coefficients in upward heat flow in single and double glazed flat-plate collectors

Absorption of solar radiation in the glass cover(s) of a flat plate solar collector increases the temperature of cover(s) and hence changes the values of convective and radiative heat transfer coefficients. The governing equations for the case of single as well as double glazed collector have been solved for inner and outer surface temperatures of glass cover(s) with/without including the effect of absorption of solar radiation in the glass cover(s), with appropriate boundary conditions. The effects of absorption of solar radiation on inner and outer surface temperatures and consequently on convective and radiative heat transfer coefficients have been studied over a wide range of the independent variables. The values of glass cover temperatures obtained from numerical solutions of heat balance equations with and without including the effect of absorption of solar radiation in the glass cover(s) are compared. For a single glazed collector the increase in glass cover temperature due to absorption of solar radiation could be as high as 6°. The increase in temperatures of first and second glass covers of a double glazed collector could be as high as 14° and 11°, respectively. The effect on the convective heat transfer coefficient between the absorber plate and the first glass cover is substantial. The difference in the values of the convective heat transfer coefficients between the absorber plate and the first glass cover (h_cp1) of a double glazed collector for the two cases: (i) including the effect of absorption and (ii) neglecting the effect of absorption in glass cover, could be as high as 49%. Correlations for computing the temperatures of inner and outer surfaces of the glass cover(s) of single and double glazed flat plate collectors are developed. The relations developed enable incorporation of the effect of absorption of solar radiation in glass cover(s) in the relations for inner and outer surface temperatures in a simple manner. By making use of the relations developed for inner and outer surface temperatures of glass cover(s) the convective and radiative heat transfer coefficients can be calculated so close to those obtained by making use of surface temperatures of glass cover(s) obtained by numerical solutions of heat balance equations that numerical solutions of heat balance equations are not required.     

Effect of glass cover inclination and parametric studies of concentrator-assisted solar distillation system

In this communication, a thermal analysis of concentrator-assisted solar distillation unit has been developed to optimize the glass cover inclination. The thermal energy is based on the energy balance equation for each component of the distillation unit by incorporating the proposed modified Dunckle's relation for internal heat loss. An analytical expression for various parameters, namely the water and glass cover temperatures, hourly and daily yield and an instantaneous thermal efficiency, has been derived. Numerical computations have been carried out and it has been observed that the daily output increases with inclination.     

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.     

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.     

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.     

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.     

Comparative thermal performance evaluation of an active solar distillation system

In this paper, thermal models of all types of solar collector‐integrated active solar stills are developed based on basic energy balance equations in terms of inner and outer glass temperatures. In this paper, hourly yield, hourly exergy efficiency, and hourly overall thermal efficiency of active solar stills are evaluated for 0.05 m water depth. All numerical computations had been performed for a typical day in the month of 07 December 2005 for the climatic conditions of New Delhi (28°35′N, 77°12′E, 216 m above MSL). The thermal model of flat‐plate collector integrated with active solar still was validated using the experimental test set‐up results. Total daily yield from active solar still integrated with evacuated tube collector with heat pipe is 4.24 kg m^?2 day^?1, maximum among all other types of active solar stills. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental validation of a numerical model for heat transfer in vacuum glazing

Flat vacuum glazings consisting of a narrow evacuated space between two glass panes separated by an array of small support pillars have been fabricated. A guarded hot box calorimeter was designed and constructed to measure their heat transfer coefficients. Experimental measurements of temperatures and rates of heat transfer were found to be in very good agreement with those predicted using a developed finite element model. A method for determining the heat transfer coefficient of the evacuated gap has been established and comparisons are made between the measured and predicted glass surface temperature profiles of the exposed glass area and the heat transfer coefficients of the total glazing system in order to validated the model.     

Diurnal response of solar air heaters

A time-dependent heat transfer model has been developed to predict the diurnal performance of a conventional solar air heater which consists of a flat passage between two metallic plates through which the heating fluid (air) is made to pass. The effect of various parameters such as the heat capacities of the glass cover, the absorbing plate and the air streams, as well as the heat transfer coefficient from the absorbing plate to the air stream, have been investigated. It is found that the heat capacities of the glass cover and the absorber do not alter the performance characteristics of the solar air heater while the heat capacity of the air stream significantly influences both the rise in temperature of the fluid and the shift in phase. However, the effective heat transfer coefficient from the absorbing plate to the air stream significantly affects the diurnal response of a solar air heater.     

Experimental evaluation of the wind convection heat transfer on the glass cover of the single-slope solar still

Accurate evaluation of the wind convection heat transfer coefficient (h_w) for solar-based systems is essential, especially for solar desalination systems. Thermal behavior and productivity of solar stills are highly affected by the external heat loss through the glass cover. This paper describes a new experimental approach to estimate the h_w on the glass cover of the conventional single-slope solar distiller (CSS). Indoor experiments have been conducted under steady-state conditions for a wind speed between 0 and 3 m/s. The h_w has been evaluated through an energy balance performed on the distiller's glass cover. The results showed that increasing the wind speed increases the hw (from 5.64 to 31.57 W/m² K) and enhances the distillation rate (from 5.28 to 7.61 mL/min). A new relationship for the h_w was proposed for the CSS and compared with the experimental data available in the literature. The comparison shows that the obtained results are close to the data from solar systems, with a deviation ranging from 27.4% to 37%. However, a significant deviation was obtained with earlier models derived from flat plates (from 29.5% to 59%).     

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%.     

A mathematical model of a solar chimney

A simple mathematical model of a solar chimney is proposed. The physical model is similar to the Trombe wall. One side of the chimney is provided with a glass cover which with the other three solid walls of the chimney form a channel through which the heated air could rise and flow by natural convection. Openings provided at the bottom and top of the chimney allow room air to enter and leave the channel. Steady state heat transfer equations were set up to determine the boundary temperatures at the surface of the glass cover, the rear solar heat absorbing wall and the air flow in the channel using a thermal resistance network. The equations were solved using a matrix-inversion solution procedure. The thermal performance of the solar chimney as determined from the glass, wall and air temperatures, air mass flow rate and instantaneous heat collection efficiency of the chimney are presented. Satisfactory correlation was obtained with experimental data from other investigators. Further experimental investigation is currently under way.     

Physics of shallow solar pond water heater

This communication presents a theoretical analysis of a shallow solar pond water heater, which is in good agreement with the experiments of Kudish and Wolf (1979) and the authors. the heater consists of an insulated metallic rectangular tank with black bottom and sides and a transparent cover at the top. After the collection of solar energy during sunshine hours the heater stores a substantial amount of heat because the top glass cover is covered by an adequate insulation in the night. Analytical expressions for the transient rise of temperature of water in the tank have been derived taking into account the appropriate heat transfer processes during day and night. These experimental results as well as those of Kudish and Wolf (1979) have been found to be in good agreement with the theory presented in this paper. the effects of one more glass cover on the top, and of the thickness of the bottom and side insulation and tank depth on the water temperature have also been studied.     

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.     

Prediction and measurement of mass transport in experimental solar stills

The aim of the present investigation was the derivation of validating field measurements from an experimental passive solar still model suitable for the evaluation of the existing theory, on the internal heat and mass transfer processes in solar distillation systems. A very good agreement was found between measurements and predictions from the basic model which was originally developed by Dunkle. However, it was surprising that although this model, with its simplified assumptions relaxed, was successfully validated against measurements at least as far as lower and intermediate temperatures and mass flow rates as high as about 0.1 g/m² s is concerned, its prediction accuracy was found to degrade for higher, up to 0.2 g/m² s measured yields, corresponding to modified Ra numbers up to about 6 × 10⁶, while it was also derived that the modified Ra number is clearly a crucial dimensionless quantity which determines the heat and mass transfer processes in solar distillation systems.     

Effect of Water Flow over the Glass on the Performance of a Solar Still Coupled with a Flat Plate Solar Collector†

In this communication a transient analysis of a solar distillation system with water flow over the glass cover is presented. The system comprises of a single basin solar still coupled with a flat plate solar collector. Due to the increased difference between water and glass temperatures the yield of this system is significantly increased. The performance of this system has been compared with that of a simple single basin solar still (SBSS), SBSS with water flow over it and SBSS coupled with a flat plate collector; and it is concluded that a SBSS with water flow over it shows the best performance.     

Modeling heat and mass transport phenomena at higher temperatures in solar distillation systems - The Chilton-Colburn analogy

In the present investigation efforts have been devoted towards developing an analysis suitable for heat and mass transfer processes modeling in solar distillation systems, when they are operating at higher temperatures. For this purpose the use of Lewis relation is not new although its validity is based on the assumptions of identical boundary layer concentration and temperature distributions, as well as low mass flux conditions, which are not usually met in solar distillation systems operating at higher temperatures associated with considerable mass transfer rates. The present analysis, taking into consideration these conditions and the temperature dependence of all pertinent thermophysical properties of the saturated binary mixture of water vapor and dry air, leads to the development of an improved predictive accuracy model. This model, having undergone successful first order validation against earlier reported measurements from the literature, appears to offer more accurate predictions of the transport processes and mass flow rate yield of solar stills when operated at elevated temperatures.     

Using air flow to alleviate temperature elevation in solar cells within asymmetric compound parabolic concentrators

Air filled asymmetric compound parabolic photovoltaic concentrators (ACPPVC) have been studied using a comprehensive validated unified model for optics and heat transfer in line-axis solar energy systems. The heat transfer that occurs within the cavity of a single concentrator, multiple concentrators, the space between adjacent concentrators and in an air duct behind the photovoltaics was simulated and is presented. For a range of insolation intensities incident at the aperture cover the maximum PV cell operating temperatures are determined. From the simulations undertaken the effects on solar cell surface temperatures resulting from air flow in the air filled space at the front of the system and in the air duct to the rear of the solar cells are clearly evident.     

Heat and mass transfer in vacuum membrane distillation

In the membrane distillation (MD) literature, the heat transfer coefficients of the boundary layers are usually estimated from well known heat transfer empirical correlations developed for non-porous and rigid heat exchangers. A difference between the mechanism of heat transfer in MD systems, which is coupled with transmembrane mass transfer, and the mechanism of heat transfer in “pure” heat exchangers is expected to exist. Vacuum membrane distillation has been experimentally studied in a capillary membrane module and the heat transfer coefficients have been evaluated in both the lumen and the shell side of the membrane module. A critical review of the most frequently used heat transfer empirical correlations in MD systems is presented. Finally, the experimental results obtained in this paper are compared to those of literature, in order to test their applicability in membrane distillation systems.