Cost of house heating with solar energy

There has long been a need for a practical method of predicting the true cost of heating a house with solar energy and designing the heating system (solar and auxiliary) to achieve the minimum total annual heating cost possible under the particular climatic, geographic, and residential characteristics involved. Rough approximations based on various types of averaged values of weather and seasonal variables have previously been developed, but the reliability of such methods and results is open to question. The authors have therefore made a rigorous analysis of projected solar heating costs in eight U.S. cities and have optimized the heating system design in each location.The analysis involved the use of a high speed computer and approximately 400,000 hourly observations in eight cities of radiation, temperature, wind, solar altitude, cloud cover, and humidity. Equations for performance of flat plate solar collectors and sensible heat storage systems were developed and programmed with the above weather variables and with eight design parameters comprising house size, collector size, storage size, collector tilt, number of transparent surfaces in collector, hot water demand, insulation on storage unit, and thermal capacity of collector. Capital and operating costs were quantitatively related to heating system design parameters, and the values of all design variables which yielded lowest annual heating cost in each city were then selected.The findings are presented in the form of two tables and ten graphs, showing heating costs as functions of various design and location factors. The relative importance of each factor is discussed, and the overall costs of solar heating are compared with the costs of conventional heat supply in each location. The method for designing the least-cost combination of solar and conventional heat supplies is also shown, and an example of the use of the method is presented.     

A numerical investigation of a photovoltaic thermal (PV/T) collector

The photovoltaic thermal collector can provide thermal and heat power at the same time.In this paper, a photovoltaic/thermal sheet and tube collector has been numerically investigated. The paper focuses on the development of a hybrid solar collector PV/T. This model will be applied to optimize the operation of the PVT collector in the semi-arid climate. A mathematical model has been developed to determine the dynamic behavior of the collector, based on the energy balance of six main components namely a transparent cover, a PV module, a plate absorber, a tube, water in the tube and insulation. It has been validated by comparing the obtained simulation results with experimental results available in literature, where good agreement has been noted. Using our developed model, the heat and electrical power of sheet and tube collector has been analyzed for four typical days of year with the meteorological parameters of Monastir, Tunisia. Furthermore, the effect of solar radiation, the inlet water temperature, the number of glazing covers and the conductive heat transfer coefficient between plate absorber and PV module have been involved to identify their influence on the thermal and electrical efficiencies. The monthly thermal and electrical energies is also evaluated.     

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.     

On the effects of solar radiation variations on solar heating system performances

The effect of solar radiation availability on the performance of different solar heating systems has been studied. The systems include a solar water heater, passive solar houses and district solar heating systems with seasonal heat storage. Also, different collector orientations and collector types have been investigated. The hourly radiation data were generated by a simple computational simulation procedure. It was found that district solar heating systems with concentrating collectors and passive solar houses showed the largest variations for the given conditions.     

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.     

Theoretical variations of the thermal performance of different solar collectors and solar combi systems as function of the varying yearly weather conditions in Denmark

The thermal performances of solar collectors and solar combi systems with different solar fractions are studied under the influence of the Danish design reference year, DRY data file, and measured weather data from a solar radiation measurement station situated at the Technical University of Denmark in Kgs. Lyngby. The data from DRY data file are used for any location in Denmark. The thermal performances of the solar heating systems are calculated by means of validated computer models. The measured yearly solar radiation varies by approximately 23% in the period from 1990 until 2002, and the investigations show that it is not possible to predict the yearly solar radiation on a tilted surface based on the yearly global radiation.The annual thermal performance of solar combi systems cannot with reasonable approximation be fitted to a linear function of the annual total radiation on the solar collector or the annual global radiation. Solar combi systems with high efficient solar collectors are more influenced by weather variations from one year to another than systems with low efficient solar collectors.The annual thermal performance of solar collectors cannot be predicted from the global radiation, but both the annual thermal performance and the annual utilized solar energy can with a reasonable approximation be fitted to a linear function of the yearly solar radiation on the collector for both flat plate and evacuated tubular solar collectors. Also evacuated tubular solar collectors utilize less sunny years with large parts of diffuse radiation relatively better than flat plate collectors.     

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.     

住宅太阳热水器的技术经济性分析

以福州地区典型气象年逐时气象数据为基础,对平板型太阳热水器的热性能进行逐时模拟。利用综合能源价格法,分析集热器面积对太阳热水器经济性的影响,并比较各类热水器的技术经济性。在当前能源价格体系下,集热器面积为8.5m~2时,系统的年平均太阳能保证率最大(为67.72%);集热器面积为4m~2时,综合能源价格现值最小(为0.283$/kWh),此时系统的年平均太阳能保证率为62.65%。     

Estimation of incident radiation on a novel spherical solar collector

Most solar collectors commonly used are of the flat-plate type. In the present work, a novel type of solar collector, namely, spherical collector, is proposed. It consists of a stationary spherical body with a cover and an absorbing surface. The receiving hemisphere, normal to the incident beam radiation, keeps on shifting with the apparent position of the sun. The main advantage of this type of collector is its ability to effectively track the sun, without any actual mechanical movement. Both daily and hourly variations of incident radiation on such a spherical solar collector are calculated on the basis of available data. The results are compared with that on an equivalent flat-plate collector for different angles of tilt and latitude. From the results, the spherical collectors are found to be more effective in receiving solar radiation over equivalent flat-plate counterparts throughout the year.     

Flux and temperature distribution in the receiver of parabolic solar furnaces

In this study, a mathematical analysis is presented on the complete interface problem between solar concentration systems and high temperature thermochemical processes. This includes the thermal process starting from the incoming solar radiation up to the heat transfer to a heat carrier fluid or reactants in a given reactor. The system considered comprises a heliostat, a parabolic concentrator and a receiver. The hourly incoming radiation, the hourly reflection and absorption losses on the heliostat and concentrator systems, the radiation flux density distribution in the receiver space, the solar and IR bands radiation exchange and the useful heat transfer are all considered in the analysis. The parameters such as temperature distribution in the receiver as well as thermal efficiency can be calculated for a given case. The model has been verified using the experimental results obtained in two different systems. In addition, a parametric study has been carried out on the global receiver efficiency with respect to temperature.     

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%.     

Development of a “volume heat-trap” type solar collector using a fine-particle semitransparent liquid suspension (FPSS) as a heat vehicle and heat storage medium Unsteady, one-dimensional heat transfer in a horizontal FPSS layer heated by thermal radiation

The objective of this work is to develop a “volume heat-trap” solar collector in which a fine-particle semitransparent liquid suspension (FPSS) is used as a heat vehicle and heat storage fluid.In the first step of our fundamental research, a multiband model, taking into consideration the effect of fine particle suspension in a continuous fluid on radiation and absorption characteristics, was formulated to analyze the unsteady one-dimensional heat transfer in a horizontal FPSS layer heated by thermal radiation.The experiments were conducted for three kinds of suspensions: diethylphthalate-graphite, -carborundum and -silicon dioxide. The time-changes of temperature distributions within the suspension layer were measured under step- and intermittent-radiative heating conditions, using an infrared lamp bundle as a simulated model of solar radiation.The experimental data obtained for the rate and efficiency of heat collection, as well as for the unsteady temperature distribution within the FPSS layer, show satisfactory agreement with calculations based on the proposed theoretical analysis.It is the feelings of the authors that the FPSS used as a heat collection fluid in this work has a good heat transfer characteristics to enable the development of high efficient solar collector.     

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.     

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.     

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.     

Thermo-ecological optimization of a solar collector

The depletion of non-renewable natural exergy resources (the thermo-ecological cost) has been accepted as the objective function for thermo-ecological optimization. Its general formulation has been cited. A detailed form of the objective function has been formulated for a solar collector producing hot water for household needs. The following design parameters have been accepted as the decision variables: the collector area per unit of the heat demand, the diameter of collector pipes, the distance of the pipe axes in the collector plate. The design parameters of the internal installation (the pipes, the hot water receiver) have not been taken into account, because they are very individual. The accumulation ability of hot water comprising one day has been assumed. The objective function contains the following components: the thermo-ecological cost of copper plate, copper pipes, glass plate, steel box, thermal insulation, heat transfer liquid, electricity for driving the pump of liquid, fuel for the peak boiler. The duration curves of the flux of solar radiation and absorbed heat have been elaborated according to meteorological data and used in the calculations. The objective function for economic optimization may have a similar form, only the cost values would be different.     

A hybrid high efficiency single-basin solar still

In this work, an attempt has been made to enhance the distillate output of a single-basin solar still by coupling it with a flat plate solar collector and by coating a thin layer of SnO₂ on one side of the transparent cover plate. The heat transfer fluid was circulated between the still and the collector through a heat exchanger and storage tank by thermosyphonically induced flow. It was observed that good insulation around the storage tank considerably increased the yield at night due to the decrease of ambient temperature. Thermosyphonically induced flow eliminated the need for pumps and control units. A layer of SnO₂ on the transparent cover lowered the thermal radiation loss, one of the major sources of heat energy loss in a solar still. Values for solar radiation, ambient air temperature, salt-water temperature in the basin, temperature of air-vapour mixture within the still, input and output temperatures of the heat exchanger heat transfer fluid, and the distillate yield were collected by a data acquisition system. After making the above modifications, the distillate yield was measured to be 6·745 litres per square metre per day for a September solar radiation of 17820 KJ at Istanbul-Gebze. To compare the distillate yield, a conventional solar still with similar dimensions to those of the improved still was constructed. The overall efficiency of the improved still was found to be 3·26 times the efficiency of the conventional still.     

Performance analysis of a hybrid photovoltaic thermal double pass air collector using ANN

This paper presents the use of artificial neural network for performance analysis of a semi transparent hybrid photovoltaic thermal double pass air collector for four weather conditions (a, b, c and d type) of New Delhi. The MATLAB 7.1 neural networks toolbox has been used for defining and training of ANN for calculations of thermal energy, electrical energy, overall thermal energy and overall exergy. The ANN model uses ambient air temperature, global solar radiation, diffuse radiation and number of clear days as input parameters for four weather conditions. The transfer function, neural network configuration and learning parameters have been selected based on highest convergence during training and testing of network. About 2000 sets of data from four weather stations (Bangalore, Mumbai, Srinagar, and Jodhpur) have been given as input for training and data of the fifth weather station (New Delhi) has been used for testing purpose. It has been observed that the best transfer function for a given configuration is logsig. The feedforward back-propagation algorithm has been used in this analysis. Further the results of ANN model have been compared with analytical values on the basis of root mean square error.     

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.     

Long-term thermodynamic performance of solar heat and power systems

This paper describes a long-term simulation study of solar thermal systems incorporating second-law considerations. Both open-loop and closed-loop heat collecting configurations are simulated using hourly meteorological data. The entropy generation in each subcomponent is calculated on an hourly basis to obtain the yearly mean second-law efficiency. The effects of load temperature, mode of operation, collector type, collector area and storage tank size are investigated. Some results are presented for a solar-Rankine power plant using R-12 and R-22 as the working fluids. The use of the plate temperature as the ‘source’ temperature gives an optimal collector size which maximizes the second-law efficiency. When the equivalent ‘sun’ temperature is used, the second-law efficiency decreases with collector area for both types of heating system.