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.     

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.     

Computational study of heat transfer in solar collectors with different radiative flux models

Two‐dimensional steady incompressible laminar Newtonian viscous convection‐radiative heat transfer in a rectangular solar collector geometry is considered. The ANSYS FLUENT finite volume code (version 17.2) is used to simulate the thermo‐fluid characteristics. Extensive details of computational methodology are given to provide engineers with a framework for simulating radiative‐convection in enclosures. Mesh‐independence tests and validation are conducted. The influence of aspect ratio, Prandtl number ( Pr), Rayleigh number ( Ra) and radiative flux model on temperature, isotherms, velocity, and pressure is evaluated and visualized in colour plots. In addition, local convective heat flux is computed, and solutions are compared with the MAC solver for various buoyancy effects achieving excellent agreement. The P1 model is shown to better predict the actual influence of solar radiative flux on thermal fluid behaviour compared with the limited Rosseland model. With increasing Ra, the hot zone emanating from the base of the collector is found to penetrate deeper into the collector and rises symmetrically dividing into two vortex regions with very high buoyancy effect. With increasing Pr there is a progressive incursion of the hot zone at the solar collector base higher into the solar collector space and simultaneously a greater asymmetric behaviour of the dual isothermal zones.     

Transient thermal analysis of semitransparent composite layer with an opaque boundary

Transient coupled radiative and conductive heat transfer in a two-layer, absorbing, emitting, and isotropically scattering non-gray slab is investigated by the ray tracing method in combination with Hottel's zonal method. One outer boundary is opaque, and another is semitransparent. The radiative energy transfer process in a semitransparent composite is divided into two sub-processes, one of which considers scattering, the other does not. The radiative transfer coefficients of the composite are deduced under specular and diffuse reflection and combined specular and diffuse reflection, respectively. The radiative heat source term is calculated by the radiative transfer coefficients. Temperature and heat flux are obtained by using the full implicit control-volume method in combination with the spectral band model. The method presented here needs only to disperse the space position, instead of the solid angle. A comparison with previous results shows that the results are more accurate.     

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     

Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine

A numerical analysis was carried out in order to investigate the combustion and heat transfer characteristics in a liquid rocket engine in terms of non-gray thermal radiation and soot formation. Governing gas and droplet phase equations with PSIC model, turbulent combustion model with liquid kerosene fuel, soot formation, and non-gray thermal radiative equations are introduced. A radiation model was implemented in a compressible flow solver in order to investigate the effects of thermal radiation. The finite-volume method (FVM) was employed to solve the radiative transfer equation, and the weighted-sum-of-gray-gases model (WSGGM) was applied to model the radiation effect by a mixture of non-gray gases and gray soot particulates. After confirming the two-phase combustion behavior with soot distribution, the effects of the O/F ratio, wall temperature, and wall emissivity on the wall heat flux were investigated. It was found that the effects of soot formation and radiation are significant; as the O/F ratio increases, the wall temperature decreases. In addition, as the wall emissivity increases, the radiative heat flux on the wall increases.     

Non-gray radiative convective conductive modeling of a double glass window with a cavity filled with a mixture of absorbing gases

Coupled radiation and natural convection heat transfer occurs in vertical enclosures with walls at different temperatures filled with gas media. In glass window thermal insulation applications in hot climates, infrared absorbing gases appear as an alternative to improve their thermal performance. The thermal modeling of glass windows filled with non-gray absorbing gases is somewhat difficult due to the spectral variation of the absorption coefficients of the gases and the phenomena of natural convection. In this work, the cumulative wavenumber (CW) model is used to treat the spectral properties of mixtures of absorbing gases and the radiative transport equation is solved using CW model and the discrete ordinates method. Due to the range of temperature variation, the mixture of gases is considered as homogeneous. The absorption coefficients were obtained from the database HITRAN. First, the natural convection in a cavity with high aspect ratio is modeled using a CFD code and the local and global Nusselt numbers are computed and compared with available empirical correlations. Also, the flow pattern for different Rayleigh numbers is analyzed. Then, the heat transfer in the gas domain is approximated by a radiative conductive model with specified heat flux at boundaries which is equivalent to convective transport at the walls surroundings. The energy equation in its two-dimensional form is solved by the finite volume technique. Three types of gas mixtures, highly absorbing, medium and transparent are investigated, to determinate their effectiveness in reducing heat gain by the gas ambient. Reflective glasses are also considered. The numerical method to solve radiative heat transport equation in gray and non-gray participant media was validated previously. The temperatures distributions in the gas and the glass domain are computed and the thermal performance of the gas mixtures is evaluated and discussed. Also, comparison with pure radiative conductive model is shown.     

Three-dimensional CFD analysis for simulating the greenhouse effect in solar chimney power plants using a two-band radiation model

The greenhouse effect in the solar collector has a fundamental role to produce the upward buoyancy force in solar chimney power plant systems. This study underlines the importance of the greenhouse effect on the buoyancy-driven flow and heat transfer characteristics through the system. For this purpose, a three-dimensional unsteady model with the RNG k–ε turbulence closure was developed, using computational fluid dynamics techniques. In this model, to solve the radiative transfer equation the discrete ordinates (DO) radiation model was implemented, using a two-band radiation model. To simulate radiation effects from the sun's rays, the solar ray tracing algorithm was coupled to the calculation via a source term in the energy equation. Simulations were carried out for a system with the geometry parameters of the Manzanares power plant. The effects of the solar insolation and pressure drop across the turbine on the flow and heat transfer of the system were considered. Based on the numerical results, temperature profile of the ground surface, thermal collector efficiency and power output were calculated and the results were validated by comparing with experimental data of this prototype power plant. Furthermore, enthalpy rise through the collector and energy loss from the chimney outlet between 1-band and two-band radiation model were compared. The analysis showed that simulating the greenhouse effect has an important role to accurately predict the characteristics of the flow and heat transfer in solar chimney power plant systems.     

Optimum outlet temperature of solar collector for maximum work output for an Otto air-standard cycle with ideal regeneration

The optimum solar collector outlet temperature for maximizing the work output for an Otto air-standard cycle with ideal regeneration is investigated. A mathematical model for the energy balance on the solar collector along with the useful work output and the thermal efficiency of the Otto air-standard cycle with ideal regeneration is developed. The optimum solar collector outlet temperature for maximum work output is determined. The effect of radiative and convective heat losses from the solar collector, on the optimum outlet temperature is presented. The results reveal that the highest solar collector outlet temperature and, therefore, greatest Otto cycle efficiency and work output can be attained with the lowest values of radiative and convective heat losses. Moreover, high cycle work output (as a fraction of absorbed solar energy) and high efficiency of an Otto heat engine with ideal regeneration, driven by a solar collector system, can be attained with low compression ratio.     

A theoretical study of the transient coupled conduction and radiation heat transfer in glass: phonic diffusivity measurements by the flash technique

Evaluating the phonic conductivity of glasses is difficult because of the combined mode of heat transfer. In this work, a model is developed for the flash experiment, and numerical results are reported. Simulations in the non-gray case have shown that heat transfer in the sample is completely free from any radiative contribution for conditions of small optical thicknesses and reflecting walls. Thus diffusivity identified: from the rear-face thermogram is a quantity of phonic origin. Experimental values for phonic conductivity are presented. The results for float glass are in agreement with literature data. For silica, a new result has been obtained: the temperature dependence of the phonic conductivity is found to be similar to that of its specific heat, confirming microscopic models of thermal conductivity in disordered systems.     

Some new developments on coupled radiative-conductive heat transfer in glasses—experiments and modelling

The difficulty in obtaining reliable phonic thermal conductivity of glasses at high temperature leads the authors to propose a methodology based on an experimental and numerical investigation, in order to separate the conductive and radiative part in a combined heat transfer in semi-transparent materials. The thermal conductimeter is composed of a guard plane plate and a Mach-Zehnder interferometer, supplying the total heat flux and the temperature distribution. With such a device no contacts are needed between sample and hot plate or heat sink. These measurements are treated numerically by a nodal analysis modelling of simultaneous conductive-radiative heat transfer. A monodimensional (non-diffusing) non-gray analysis including multireflections was considered. Determinations of the temperature derivative of the refractive index and the infrared spectra of materials at high temperature have been carried out. Values of the phonic conductivity of silica glass up to 900 K and borosilica glass up to 750 K for samples with different thicknesses and frontier's emissivities have been obtained by an identification process. Results are in agreement with literature data.     

Transient coupled heat transfer in multilayer composite with one specular boundary coated

By the ray tracing?node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.     

Experimental and numerical investigation on solar parabolic trough collector integrated with thermal energy storage unit

Solar parabolic trough collector (PTC) is the best recognized and commercial‐industrial‐scale, high temperature generation technology available today, and studies to assess its performance will add further impetus in improving these systems. The present work deals with numerical and experimental investigations to study the performance of a small‐scale solar PTC integrated with thermal energy storage system. Aperture area of PTC is 7.5 m², and capacity of thermal energy storage is 60 L. Paraffin has been used as phase change material and water as heat transfer fluid, which also acts as sensible heat storage medium. Experiments have been carried out to investigate the effect of mass flow rate on useful heat gain, thermal efficiency and energy collected/stored. A numerical model has been developed for the receiver/heat collecting element (HCE) based on one dimensional heat transfer equations to study temperature distribution, heat fluxes and thermal losses. Partial differential equations (PDE) obtained from mass and energy balance across HCE are discretized for transient conditions and solved for real time solar flux density values and other physical conditions of the present system. Convective and radiative heat transfers occurring in the HCE are also accounted in this study. Performance parameters obtained from this model are compared with experimental results, and it is found that agreement is good within 10% deviations. These deviations could be due to variations in incident solar radiation fed as input to the numerical model. System thermal efficiency is mainly influenced by heat gain and solar flux density whereas thermal loss is significantly influenced by concentrated solar radiation, receiver tube temperature and heat gained by heat transfer fluid. Copyright © 2016 John Wiley & Sons, Ltd.     

Performance evaluation of a solar thermal energy storage system using nanoparticle-enhanced phase change material

This paper presents a numerical investigation on the thermal performance of a solar latent heat storage unit composed of rectangular slabs combined with a flat-plate solar collector. The rectangular slabs of the storage unit are vertically arranged and filled with phase change material (PCM: RT50) dispersed with high conductive nanoparticles (Al₂O₃). A heat transfer fluid (HTF: water) goes flow in the solar collector and receives solar thermal energy form the absorber area, then circulates between the slabs to transfer heat by forced convection to nanoparticle-enhanced phase change material (NEPCM). A numerical model based on the finite volume method and the conservation equations was developed to model the heat transfer and flow processes in the storage unit. The developed model was validated by comparing the obtained results with the experimental, numerical and theoretical results published in the literature. The thermal performance of the investigated latent heat storage unit combined with the solar collector was evaluated under the meteorological data of a representative day of the month of July in Marrakesh city, Morocco. The effect of the dispersion of high conductive nanoparticles on the thermal behavior and storage performance was also evaluated and compared with the case of base PCM without additives.     

A detailed nonuniform thermal model of a parabolic trough solar receiver with two halves and two inactive ends

In this paper a detailed one dimensional nonuniform thermal model of a parabolic trough solar collector/receiver is presented. The entire receiver is divided into two linear halves and two inactive ends for the nonuniform solar radiation, heat transfers and fluid dynamics. Different solar radiation and heat transfer modes can be taken into consideration for these four different regions respectively. This enables the study of different design parameters, material properties, operating conditions, fluid flow and heat transfer performance for the corresponding regions or the whole receiver. Then the nonuniform model and the corresponding uniform thermal model are validated with known performance of an existing parabolic trough solar collector/receiver. For applications, the uniform thermal model can be used to quickly compute the integral heat transfer performance of the whole PTC system while the nonuniform thermal model can be used to analyze the local nonuniform solar radiation and heat transfer performance characteristics and nonuniform heat transfer enhancements or optimizations. Later, it could also be effectively used with an intelligent optimization, such as the genetic algorithm or the particle swarm optimization, to quickly evaluate and optimize the characteristics and performance of PTCs under series of nonuniform conditions in detail.     

Heat losses from parabolic trough solar collectors

Parabolic trough solar collector usually consists of a parabolic solar energy concentrator, which reflects solar energy into an absorber. The absorber is a tube, painted with solar radiation absorbing material, located at the focal length of the concentrator, usually covered with a totally or partially vacuumed glass tube to minimize the heat losses. Typically, the concentration ratio ranges from 30 to 80, depending on the radius of the parabolic solar energy concentrator. The working fluid can reach a temperature up to 400°C, depending on the concentration ratio, solar intensity, working fluid flow rate and other parameters. Hence, such collectors are an ideal device for power generation and/or water desalination applications. However, as the length of the collector increases and/or the fluid flow rate decreases, the rate of heat losses increases. The length of the collector may reach a point that heat gain becomes equal to the heat losses; therefore, additional length will be passive. The current work introduces an analysis for the mentioned collector for single and double glass tubes. The main objectives of this work are to understand the thermal performance of the collector and identify the heat losses from the collector. The working fluid, tube and glass temperature's variation along the collector is calculated, and variations of the heat losses along the heated tube are estimated. It should be mentioned that the working fluid may experience a phase change as it flows through the tube. Hence, the heat transfer correlation for each phase is different and depends on the void fraction and flow characteristics. However, as a first approximation, the effect of phase change is neglected. Copyright © 2013 John Wiley & Sons, Ltd.     

Radiation collection by an optimized fixed collector

Criteria are presented for optimizing solar thermal energy collection. These criteria are then used in setting the design of a fixed solar thermal energy collector. This design is obtained by proceeding carefully through a series of optimization steps. While seeking near optimum performance, features have been retained which should lead to low cost. Initial optimization steps lead to an all glass vacuum collector tube whose side and lower walls are internally silvered to provide optimal Winston concentration on an interior glass tube coated with a selective absorber. Heat transfer calculations, performed for an array module of these collector tubes, produce values for the radiation, heat conduction and pumping losses and indicate operating conditions which minimize these losses. Near this minimum, heat conduction and pumping losses are small and can usually be neglected. Liquids provide much better heat transfer than gases. For liquid heat transfer fluids, the minimum loss collector tube window width (setting the transverse scale) is 3 cm and tube length 4 m, depending somewhat upon array area and the weighting used for the various losses. A window width of5 cm and tube length2 m should provide lower cost fabrication, while still allowing operation near minimum loss. Skills now used in the glass and lighting industry are expected to lead to low cost production of these tubes.     

Optimization of a fixed solar thermal collector

Criteria are presented for optimizing solar thermal energy collection. These criteria are then used in setting the design of a fixed solar thermal energy collector. This design is obtained by proceeding carefully through a series of optimization steps. While seeking near optimum performance, features have been retained which should lead to low cost. Initial optimization steps lead to an all glass vacuum collector tube whose side and lower walls are internally silvered to provide optimal Winston concentration on an interior glass tube coated with a selective absorber. Heat transfer calculations, performed for an array module of these collector tubes, produce values for the radiation, heat conduction and pumping losses and indicate operating conditions which minimize these losses. Near this minimum, heat conduction and pumping losses are small and can usually be neglected. Liquids provide much better heat transfer than gases. For liquid heat transfer fluids, the minimum loss collector tube window width (setting the transverse scale) is ～3 cm and tube length ～4 m, depending somewhat upon array area and the weighting used for the various losses. A window width of～5 cm and tube length～2 m should provide lower cost fabrication, while still allowing operation near minimum loss. Skills now used in the glass and lighting industry are expected to lead to low cost production of these tubes.     

An optimum performance of flat-type solar air heater with porous absorber

This investigation is concerned with the design and performance of a flat-type solar air heater in which air flows perpendicularly from the transparent cover to a porous absorber plate. The design phase involved a stability analysis to determine the critical distance (maximum allowable distance) between the absober and transparent cover, for suppressing convection currents, at various environmental and operating conditions. These results are useful to designers of solar collectors of the proposed type. In addition, the thermal performance of this solar heater at its optimum design conditions was computed for a wide range of system parameters illustrating the contribution of conduction and radiative modes of heat transfer. The results indicate that the best operating efficiency can be obtained when running the collector with a mass flow rate of m > 40 kg/m².h. Furthermore, the collector thermal performance is superior than channel type solar air heaters operating under similar conditions and much simpler than honeycomb porous bed solar air heaters.