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.     

Investigation of Glazing Behavior in a Fire Environment Using a Spectral Discrete Ordinates Method for Radiative Heat Transfer

Radiative heat transfer plays a major role in the analysis of glazing behavior in fires, but its rigorous modeling has received little attention. In the present study, a spectral radiative heat transfer model, based on the discrete ordinates method (DOM), is developed and employed to analyze heat transfer and the transient temperature distribution in a glazing structure subjected to fire heat flux. Comparisons are made between model predictions and literature experimental data; acceptable agreements are found. The study also investigates the influence of the glass properties and geometry on the temperature and time to breakage.     

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.     

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.     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

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.     

Computation of diffuse solar radiation

A technique for computing the spectral and angular (both the zenith and azimuthal) distribution of the solar energy reaching the surface of earth and any other plane in the atmosphere has been developed. Here the computer code LOWTRAN is used for getting the atmospheric transmittances in conjunction with two approximate procedures: one based on the Eddington method and the other on van de Hulst's adding method, for solving the equation of radiative transfer to obtain the diffuse radiation in the cloud-free situation. The aerosol scattering phase functions are approximated by the Hyeney-Greenstein functions. When the equation of radiative transfer is solved using the adding method, the azimuthal and zenith angle dependence of the scattered radiation is evaluated, whereas when the Eddington technique is utilized only the total downward flux of scattered solar radiation is obtained. Results of the diffuse and beam components of solar radiation received on surface of earth compare very well with those computed by other methods such as the more exact calculations using spherical harmonics and when atmospheric conditions corresponding to that prevailing locally in a tropical location (as in India) are used as inputs the computed values agree closely with the measured values.     

Thermal performance of an architectural window with chemically deposited SnS---CuxS solar control coating

A mathematical model enabling the prediction of the thermal performance of solar control glazings employing chemically deposited solar control coatings with or without a transparent protective polymer coating is presented. Differential energy balance for the glazing is set up assuming one-dimensional steady state case for normal incidence of air mass 2 solar radiation and by considering conductive heat transfer within the glazing and convective and radiative heat transfer into the interior and exterior of the building. Using the specific example of the optical properties of the already reported SnS---Cu_xS solar control coatings, the redistribution of the absorbed component of the solar radiation is evaluated for constant convective heat transfer coefficient and temperature in the interior and for exterior temperatures in the 0–50°C range. The results yield shading coefficient versus exterior temperature curves for two specific SnS---Cu_xS coatings without and with a protective transparent varnish and offering transmittance in the visible region of 27 and 21%.     

Numerical simulation of coupled radiation‐convection heat transfer of high‐temperature developing flow in tube

By combining the discrete ordinate method with the control volume method, the coupled radiation‐convection heat transfer of high‐temperature developing laminar flow in a tube is investigated numerically. The radiative transfer is solved by the discrete ordinate method and its contribution to thermal balance is dealt with as a source term in the energy equation, which is solved, as well as the momentum equation, by the control volume method. The effects of medium optical thickness and tube wall temperature on the temperature distribution in medium as well as the heat flux and local Nusselt number on wall are analyzed. The results show that the radiation heat transfer of high‐temperature medium influences the temperature distribution and convection heat transfer greatly, and plays an important role in the heat transfer of developing laminar flow in a tube. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 53–63, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10135     

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.     

On minimizing heat transport in architectural glazing

Significant reductions in the heating energy demand of buildings are achievable through minimization of the thermal transmittance of glazing. This paper reviews all the heat transport processes occurring in gas-filled and evacuated insulating glazing. The heat transfer mechanisms in gas-filled glazing cavities include radiative exchange between the glass sheet surfaces, convection and gaseous conduction. The application of two low-emissivity coatings (0.04) lowers the thermal conductance due to radiation between the glass pane surfaces to roughly 0.1 W m⁻² K⁻¹. At the same time, even where fill gases such as krypton and xenon are used, thermal conductance due to convection and conduction cannot be reduced to much below 1 W m⁻² K⁻¹. Heat transfer by convection and gaseous conduction only becomes negligible where the cavity is evacuated to approximately 10⁻² Pa. Heat transfer is then determined by radiation and, even more importantly, conduction in support pillars required to bear the atmospheric load on the external glass sheet surfaces. The fact that the average centre-of-glazing heat transfer rates achievable by evacuation of the cavity are some two to five times lower than those of gas-filled cavities increases the significance of heat transfer in the glazing edge regions. Consequently, in addition to the heat transfer in the cavity, the impact on glazing thermal transmittance of the edge seal and different frame constructions was also quantified. The possibilities and limitations of reducing total heat transfer in evacuated glazing are discussed on the basis of analytical and numerical methods. The results suggest that this concept offers significant advantages over current glazing technology in terms of overall thermal transmittance.     

Inverse Boundary Design Problems in Enclosures With Non-Gray Media

In this work, the inverse analysis is applied to radiative heat transfer boundary design problems with non-gray media. The objective of the inverse problem is to find the power of the heaters on the heater surface that produces the desired output, that is, temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the squared difference between estimated and desired heat flux distributions over the design surface. The non-gray optimization problem is solved using the conjugate gradient method, which is a gradient-based optimization method. The spectral line weighted-sum-of-gray-gases model (SLW) is used to account for non-gray gas radiation properties. The radiative transfer equation is solved by the discrete ordinates method combined with two models for simulation of non-gray media. Enclosures with diffuse and gray walls are considered. Radiation is assumed the dominant mode of heat transfer. Example problems including homogeneous/nonhomogeneous, isothermal/nonisothermal media are considered. The results obtained using the SLW model and the gray model are compared.     

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.     

Triple vacuum glazing: Heat transfer and basic mechanical design constraints

Given the major role played by windows with regard to energy losses from buildings in cold climates, low thermal transmittance is an indispensable property of glazing in low-energy buildings. Evacuation offers the only means of achieving negligible gaseous conduction in glazing cavities. Application of low-emittance coatings to glass sheet surfaces inside the cavity reduces the radiative heat transfer. The feasibility of double vacuum glazing using arrays of support pillars between the glass sheets has been shown by other authors. This type of glazing is commercially manufactured today. Based on these achievements, our study set out to investigate heat transfer in triple vacuum glazing by means of (i) an analytical thermal network model and (ii) a numerical finite difference model. The study focused on the impact of the following parameters on thermal transmittance: emittances of glass sheet surfaces inside the cavity, support pillar radius, support pillar separation and thermal conductivity of support pillar material. The design procedure for triple vacuum glazing taking into account not only thermal but also mechanical stresses due to atmospheric pressure, i.e., to enable identification of favourable parameter sets, is presented. Our findings suggest that use of the triple vacuum glazing concept can significantly reduce the thermal transmittances achieved by the best insulation glazing units currently on the market. E.g., a centre-of-glazing thermal transmittance of less than 0.2 W m⁻² K⁻¹ is achievable using stainless steel support pillars, 6 mm/4 mm/6 mm sheets of untempered soda-lime glass and four low-emittance coatings (ε = 0.03).     

Radiative heat transfer from potassium seeded water gas combustion plasma

Radiative heat transfer calculations from a potassium seeded water gas combustion plasma have been made to estimate the radiative heat losses through the walls of a MHD channel. Both molecular combustion products and seed contribute significantly to the total radiation loss from a plasma. The spectral emission properties of CO₂, H₂O, CO and potassium have been taken into account. It has been shown that the contribution of CO to heat flux is very small and, thus, can be neglected. CO₂ and H₂O are the primary contributors to the radiation from the combustion products. At MHD temperatures, 55–80% of the contribution to heat flux from the combustion products comes from bands lying up to 2.7 μm in the near infrared. It has been shown that accurate knowledge of absorption cross-section data is essential to predict the radiative heat transfer from potassium. It has been estimated that 25–30% of the total radiative heat flux is from the potassium seed.     

Radiative properties of a solar cavity receiver/reactor with quartz window

An energy transfer and conversion model for high-temperature solar cavity receivers has been developed using the transport behaviour of solar radiation as described by the spectral radiative exchange factors. A Monte-Carlo ray-tracing method coupled with optical properties was adopted, to predict radiation characteristics of the solar collector system by calculating radiative exchange factors. A cavity receiver with a plano-convexo quartz window was proposed, based upon the directional characteristics of the focal flux and the redistribution effect of the quartz window. Parametric studies on the windowed receiver provided a more uniform flux distribution, higher efficiency and lower loss than the windowless receivers. The predicted results serve as a design reference for the solar receivers or reactors in high-temperature applications.     

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.     

含相变材料双层玻璃窗光热分析模型

建立了含相变材料双层玻璃窗的光热传输模型,考虑相变材料和玻璃半透明特性,采用有限差分求解方程。在通过实验数据验证模型准确的基础上,分析了相变材料的融化温度对含相变材料双层玻璃窗光热性能的影响。结果显示:建立的模型可模拟相变材料双层玻璃窗的光热传输过程;随融化温度升高,含相变材料双层玻璃窗温度衰减因子则逐渐增大,相变材料融化时间延后,相变材料呈液态的时间变短,但温度滞后值、热流密度和太阳透射能则呈不规则变化。     

Heat transfer analysis of solar-driven high-temperature thermochemical reactor using NiFe-Aluminate RPCs

Converting solar energy efficiently into hydrogen is a promising way for renewable fuels technology. However, high-temperature heat transfer enhancement of solar thermochemical process is still a pertinent challenge for solar energy conversion into fuels. In this paper, high-temperature heat transfer enhancement accounting for radiation, conduction, and convection heat transfer in porous-medium reactor filled with application in hydrogen generation has been investigated. NiFe-Aluminate porous media is synthesized and used as solar radiant absorber and redox material. Experiments combined with numerical models are performed for analyzing thermal characteristics and chemical changes in solar receiver. The reacting medium is most heated by radiation heat transfer and higher temperature distribution is observed in the region exposed to high radiation heat flux. Heat distribution, O₂ and H₂ yield in the reacting medium are facilitated by convective reactive gas moving through the medium's pores. The temperature gradient caused by thermal transition at fluid-solid interface could be more decreased as much as the reaction chamber can store the transferred high-temperature heat flux. However, thermal losses due to radiation flux lost at the quartz glass are obviously inevitable.