Transmittance-absorptance Product Research Articles

Parametric sensitivity analysis of a one-dimensional thermal-electrical model of a photovoltaic solar module

The efficiency of a photovoltaic module decreases with the increase in the temperature of the photovoltaic cell, which makes the determination of this temperature one of the determining factors in the modeling of a photovoltaic module. The objective of this work is to make a detailed study about the input parameters of a developed thermal-electrical model of a photovoltaic module, based on a sensitivity analysis. The model includes a thermal part, in which the temperature varies along the five layers of the module, and an electrical part, which is based on a single diode five parameters model. The coupling of these models into a thermal-electrical model is described. Through differential sensitivity analysis, the parameters that have a significant impact on estimating the photovoltaic cell temperature were determined. The variations of the sensitivity coefficients throughout a simulated day are presented. Parameters with the highest absolute sensitivity coefficients, such as the transmittance-absorptance product and open circuit voltage, are crucial for accurate temperature estimation and were further researched and determined with greater precision, in order to improve the model reliability. Conversely, parameters with lower absolute sensitivity coefficients, such as albedo and parallel resistance, were considered less important and could be simplified to enhance computational efficiency.

Mathematical Modeling and Optimization of Vanadium-Titanium Black Ceramic Solar Collectors

The vanadium-titanium black ceramic (VTBC) coating on all-ceramic solar collectors has both high absorptance (0.94) and high emissivity (90%). However, the thermal conductivity of ceramic is very low (1.256 W/mK). To improve the heat collection efficiency of VTBC solar collectors, this paper establishes a mathematical model based on the energy-conservation relationships under steady-state conditions and creates a corresponding computer program. Key parameters for VTBC solar collectors include the heat-removal factor, effective transmittance-absorptance product for the absorber, total heat loss coefficient, etc. Then, via experimental testing, this study proposes a reference model for domestic VTBC solar collectors in a cold location (η = 0.89 − 2.20Tm*). Last, this work analyzes the influences of fin design and transparent cover design on VTBC solar collectors individually, using the created computer program. Results show that the most effective optimization method is to increase the transmittance of the transparent cover. By increasing the transmittance from 0.93 to 0.96, this study creates an optimized VTBC solar collector theoretical model (η = 0.92 − 2.20Tm*).

Exergy Analysis of Serpentine Thermosyphon Solar Water Heater

The performance of a solar hot water system is assessed for heat pump and domestic heating applications. Thermodynamic analysis on a serpentine-type thermosyphon flat-plate solar heater is conducted using the Second Law of thermodynamics. Exergetic optimization is first performed to determine the parameters for the maximum exergy efficiency using MATLAB optimization toolbox. Geometric parameters (collector surface area, dimensions, and pipe diameter), optical parameters (transmittance absorptance product), ambient temperature, solar irradiation and operating parameters (mass flow rate, fluid temperature, and overall heat transfer (loss) coefficient) are accounted for in the optimization scheme. The exergy efficiency at optimum condition is found to be 3.72%. The results are validated using experimental data and found to be in good agreement. The analysis is further extended to the influence of various operating parameters on the exergetic efficiency. It is observed that optical and thermal exergy losses contribute almost 20%, whereas approximately 77% exergy destruction is contributed by the thermal energy conversion. Exergy destruction due to pressure drop is found negligible. The result of this analysis can be used for designing and optimization of domestic heat pump system and hot water application.

Short-term efficiency test procedure for solar thermal collectors based on heat loss measurements without insolation and a novel conversion towards daytime conditions

In order to determine the usual thermal efficiency parameters η0,hem, a1 and a2 of solar collectors according to the current international standard ISO 9806:2013, a new and simple short-term test procedure has been developed. It bases upon the experimental determination of the fluid-temperature dependent loss coefficient F′UL without insolation using stationary heat loss measurements during night. To account for the fact neglected so far, that without insolation the mean absorber temperature is lower than the mean fluid temperature, a conversion to daytime conditions has been evolved: depending on hemispherical irradiance G, transmittance–absorptance product (ατ) and absorber efficiency factor F′, the new conversion formula calculates the (lower) mean fluid temperature during daytime operation, for which the absorber has the same temperature as during the nightly heat loss measurements. The thermal efficiency ηhem during daytime operation for arbitrary G then is obtained from the Hottel–Whillier–Bliss equation using F′UL from nightly heat loss measurements and the recalculated mean fluid temperatures. The new procedure allows the determination of ηhem with only a few hours nighttime measurements, provided the peak collector efficiency η0,hem and (ατ) is known. Otherwise, only one additional bright day is needed to perform a standard efficiency measurement at mean fluid temperature equal to ambient temperature. This effort has to be compared to typically one week of clear weather conditions necessary in today’s standard steady state tests. The test procedure was successfully validated for two completely different flat plate collectors, a modified standard collector with backside aluminium-film insulation instead of mineral wool (F′UL≈4,4Wm2K at 70K over ambient) and an ultra-flat prototype collector with only 40mm height and no insulation on the backside (F′UL≈7,0Wm2K at 70K over ambient). The results of nightly cooling measurements with subsequent conversion by the developed formula show full agreement to the results of ηhem-measurements according to ISO 9806:2013 within the common error bars. The new procedure yields an experimental error in daytime-efficiency of 3–4% and can help research institutes or R&D-departments of collector producers to shorten testing time to determine the thermal efficiencies of solar collectors. A broader application and test of the new method for further types of solar collectors by independent researchers is desirable.

Heating season performance of a full-scale heat pipe assisted solar wall

Previous computer simulations and bench-scale experiments showed that the heat pipe assisted solar wall had the potential for significantly improved performance relative to conventional passive space heating systems. To further test this potential, a full-scale prototype of the heat pipe system was designed, built and installed in a classroom on the University of Louisville campus in Louisville, KY. During the spring heating season of 2010 (January–April), maximum daily peak thermal efficiency was 83.7% and average daily peak thermal efficiency was 61.4%. The maximum hourly average room gain achieved during the season was 163W/m2. On days with good solar insolation, the thermal storage was heated to temperatures sufficient to provide significant energy to the classroom – even during the coldest days of the season. During the longest period (4 days) of low insolation during the season, average hourly heat delivery to the room from storage remained positive, and was never less than 16.6W/m2. During good insolation days following a period of consecutive low insolation days, thermal storage temperature was quickly restored to levels comparable to those obtained during consecutive good insolation days. Estimated heat removal factor * transmittance absorptance product FR(τα) and heat removal factor * overall loss coefficient FRUL values for the system were comparable to those for glazed liquid active collectors.

Thermal storage efficiencies of two solar saltless water ponds

A comparative study between two types of solar ponds is presented. The first type has its free surface covered by a thin layer of transparent paraffin oil. The second type is covered by transparent glass floating devices. Each device disposes an air-vacuum chamber. The free water surface between these devices is covered by transparent paraffin oil also. The thermal storage efficiency of each pond is estimated during two time periods: between sunrise and sunset and from midnight to midnight. The calculated efficiency between sunrise and sunset corresponds to the average transmittance–absorptance product. This is estimated using linear regression and also a maximum likelihood identification technique. The behavior of the system was studied by solving numerically the heat transfer equations of the system. Also an ARMAX (AutoRegressivie Moving Average with eXogenous signal) model allowing the assessment of its performance was presented. This efficiency is larger for the first pond during the sunrise to sunset period and smaller when calculated from midnight to midnight. Thus, the first type of pond could be preferred for a use just after the sunset of the same day, while the second for use after one or more days of heat storage.

New Approach for Analyzing Solar Collectors Subjected to Unequal Front/Rear Ambient Temperatures: The Equivalent Ambient Temperature Concept, Part 1: Modeling

Standard analyses of solar collector thermal performance are based upon an energy balance in which the environments adjoining the front and rear of the collector are assumed to be at the same temperature. This assumption is inappropriate for some collector designs, particularly building-integrated collectors. An approach for analyzing such situations is presented based upon a new conceptual temperature termed the “equivalent ambient temperature.” The concept is explained, the new temperature is defined, and the approach is applied to a typical collector geometry. The approach retains the convenience of the standard analysis while accounting for the unequal front/rear ambient temperatures and permits collector characterization in terms of the conventional parameters: plate efficiency factor, F′; heat removal factor, FR; overall heat loss coefficient, UL, and effective transmittance–absorptance product, ταe.

On optical performance and directional characteristics of plastic film liquid layer solar water heaters

An analysis is developed for the investigation of the transmittance–absorptance product ( τα), and directional characteristics of plastic-film water-bag solar water-heaters, which are important for long-term system performance investigations. The analysis allows a complete comparative investigation of the effects of a large number of parameters, like water layer thickness, bottom solar absorptance, radiation transmission conditions and extinction properties of semi-transparent films, on the transmittance–absorptance product. Finally the comparative effect of diffuse and specular reflection and transmission assumption on the derived results is investigated. It is concluded that the use of low iron content glass panes may possibly lead to ( τα) figures far in excess of 0.8 for new systems.

Transmittance-absorptance product of solar glazing with transparent insulation materials

The transmittance-absorptance product of solar glazing containing the transparent insulation material (TIM) of square celled honeycomb is investigated. A method is developed for the determination of transmittance-absorptance product of beam, sky and ground diffuse solar radiations using the individual transmittances of cellular array and encapsulating covers; the internal reflections are taken into account. Three practical cases; cellular array, cellular array with top cover, and cellular array with top and bottom covers are considered. The results are presented for beam radiation as a function of angle of incidence and sky and ground diffuse radiation as a function of tilt angle. The predicted results are tested by measuring the global radiation transmittance of commercial TIM; the predicted results deviate from the measurements by an average of 2.0%.

Modelling of flat-plate collectors based on monolithic silica aerogel

This paper presents a new method for predicting the radiative transfer in an absorbing and isotropically scattering, non-gray plane-parallel atmosphere. The technique is based upon the F̂ (“F-hat”) concept and was developed to determine the radiative transfer at short wavelengths for the transparent insulation material, monolithic silica aerogel. The angular dependence of solar transmittance of diffuse and ground reflected radiation is evaluated along with the “transmittance-absorptance product” of a collector. The F̂ technique is also used to determine the IR transmission of the cover from which the overall loss coefficient for a flat-plate collector constructed with aerogel filled covers is determined. The performance of a system using aerogel collectors is compared to systems using other types of high performing collectors. It is shown that, at least for the system investigated, the decrease in solar transmittance of monolithic silica aerogel is more than compensated by the decrease in thermal losses.

Heat Exchanger Theory Applied to the Design of Water- and Air-Heating Flat-Plate Solar Collectors

A general method for the design of flat-plate solar collectors based on solar collector theory has been developed. It can be applied to both liquid- and air-heating solar collectors. The solar collector efficiency is determined by the product of the effectiveness (ε) and the insolation use factor (IUF). The effectiveness describes the heat transfer characteristics of the collector and is shown to be a function of a solar number of transfer units (SNTU) and a parameter ψ. For an air-heating collector, the ψ parameter equals the collector efficiency factor, while for a liquid-heating collector it must account for the difference between the plate and tube heat transfer areas. The effectiveness and SNTU parameters are similar to the effectiveness and NTU parameters used in heat exchanger design methods. The IUF is a measure of the operating conditions of the collector. It represents the difference between the transmittance-absorptance product and the ratio of the minimum heat loss to the insolation on the exterior cover. The relationship between the effectiveness and the SNTU parameter is general for all nonconcentrating collectors. One advantage of this method over the traditional Hottel-Whillier method is that it separates the heat transfer characteristics of the solar collector from its optical properties and the operating conditions.

Test results and evaluation of integrated collector storage systems with transparent insulation

Two integrated collector storage (ICS) prototypes with about 1 m 2 absorber surface each have been installed and investigated at the Institut für Solare Energiesysteme (ISE). Each consists of a water tank with an integrated collector, which is covered with a highly transparent insulating material and is very well insulated on the sides and at the back. During the test period from November 1986 to October 1987 one of them was operated at water-main pressure, and 40 liters corresponding to the hot water consumption of one person, were withdrawn every day. The solar fraction was 58% (68%) with a system efficiency of 28% (36%) (the values in parentheses also take the surplus energy in summer into account, see “Results”). The second one has been installed to study the stagnation (no water flow) performance during the same period. Detailed computer simulation programs have been developed and compared with the experimental results. Based on the u value and the transmittance-absorptance product (τα), the annual performance can be predicted with an accuracy of 4%. The influence of various parameters such as specific water withdrawal, angle of inclination, profile of water withdrawal, required hot water temperature etc. on the yearly solar fraction and yearly efficiency of the ICS can be studied. Some of the results are presented here.

Prediction of Solar Air Heater Thermal Performance

ABSTRACT THE prediction of steady state thermal performance of solar air heaters requires prediction of three parameters: the effective transmittance-absorptance product, the collector heat removal factor and the collector loss coefficient. Agreement between computed values and measured values of these parameters indicated that the first two parameters could be adequately predicted for use in collector design, but the collector loss coefficient predictions did not agree with measured values. The measured values consisted of a steady-state thermal performance test using the ASHRAE Standard 93-77 as a guide, this same steady-state test but additionally using measured average plate temperature for computing the loss coefficient, a cloudless sky night test using heated air input to achieve approximately the same plate temperature and a computed value of the loss coefficient using a measured top loss coefficient from a similar absorber plate which was electically heated.

Periodic thermal analysis and simple economics of collector and collector-reflector systems

This paper presents a simple transient thermal model for predicting the water temperature at any time during sunshine as well as off-sunshine hours using collector and collector-reflector systems. The transmittance-absorptance product used in theoretical calculation of the water temperature is taken as a function of solar altitude, solar azimuth angle, hour angle and tilt angle of collector and reflector. Fourier coefficients of the recorded data of solar intensity and ambient air temperature have been determined. Water temperature for the systems was determined at different water flow rates. The theoretical analysis is found to be in close agreement with experimental observations. From the theoretical and experimental recordings, it was found that water temperature in the range of 50–56.5°C can be had during sunshine hours using plane reflectors to collectors in a typical winter month. A simple economic analysis of the solar water heating systems has also been discussed. This can be used to calculate an optimum collector area.

Calculation of the transmittance-absorptance product for flat-plate collectors with convection suppression devices

Photovoltaic (PV) systems transfer solar energy into electric form. PV-T is a hybrid system that converts solar radiation into electrical and thermal energy. For residential users with limited solar panel area, there are two options to achieve economic use of solar energy. One is to install both PV and solar water heater (SWH) systems, called PV-SWH, another one is to apply the PV-T system. In this work, a residential household energy cost model is built up that includes electric vehicle (EV), energy storage system (ESS), and the back-up electricity system in PV-SWH or hybrid PV-T. The model is used to explore operation strategies to minimize user’s energy cost. The case study results suggest that the hybrid PV-T system provides more benefits for the end user from long-term perspective. Compared with typical operation without optimization, the cost saving with the proposed strategy is evident.

Parametric study of the overall performance of a solar hot water system

The effect of varying individual parameters on the overall performance and feasibility of a solar hot water system has been investigated by a mathematic model which employs the concept of a decay constant and feasibility factor. TRNSYS results were used as inputs to apply the model. Parameters investigated include emittance of the collector plate, collector plate absorptance, transmittance absorptance product, storage tank set temperature, mass flow rate, load, and ratio of tank volume to collector area. It was found that the model is a useful tool for solar system design. Specific examples are detailed for illustration purposes.

Optimum glazing combination for solar space heating

A study is made for comparing the maximum seasonal energy yield obtainable by solar collectors for space heating application. Different glazing combinations with glass and plastic as glazing materials are considered. The study is made for four different locations. The performance of eight glazing combinations with covers ranging in number from one to three is compared to obtain the optimum combination for each location. The results show that selecting the optimum glazing combination improves the performance significantly. In general, plastic covers give higher yield. The study confirmed that the use of two covers is justified in cold, cloudy climates while a single cover is suitable for temperate climates. In most cases three covers lead to a significant reduction in the yield. Replacing plastic by glass as a top cover for longer life results in a small yield reduction. Some of the other conclusions are that the ratio of average to normal transmittance-absorptance product changes significantly with location and month of the year. However, the seasonal average value of this ratio is almost constant for any number of covers but changes with location.

Derivation of efficiency and loss factors for solar air heaters

The collector efficiency factor which measures the effectiveness of a collector absorber plate in transferring heat to the transport fluid, and the loss factor for air-type collectors, are mathematically derived. These equations provide a method for computing these two factors, which with the effective transmittance-absorptance product, enables one to write the generalized performance equation. The prediction of performance provided by this procedure is particularly useful in comparing performance of different collectors and for studying a specific collector's performance with changes in environment and design parameters which can be controlled to some extent by the designer.

Calculation of the monthly-average transmittance-absorptance product

A method is presented for estimating the ratio of the monthly average transmittance-absorptance product for a solar collector surface to the value of this product for normal incidence. Theoretical and experimental determinations of the (direct) beam component contribution to the transmittance-absorptance product are discussed. A calculation of the monthly average daily solar radiation per unit area absorbed on a collector plate is given for the Madison, Wisconsin climate. (SPH)

Design application of the Hottel-Whillier-Bliss equation

A method is presented for experimentally determining the three factors that determine collector efficiency in the Hottel-Whillier-Bliss equation, Q u = F R A c [( τα) c I - U L ( T f, i - T a )]. These factors are: the collector heat removal factor, F R ; the effective transmittance-absorptance product, ( τα) e ; and the overall heat loss coefficient, U L . The method of testing requires: computation of ( τα) e from measurements of cover transmittance and collector reflectance; computation of F R from a test in which the heat loss term equals zero; and computation of U L from a test in which insolation equals zero. This method was applied to collectors used on Solar House I at Colorado State University, with experimental and theoretical results being in close agreement. The method can be used to experimentally evaluate collector performance and for optimization of collector design.