M.F. El-Refaie

Theoretical performance of cylindrical parabolic solar concentrators

Abstract This is a theoretical study of the performance of cylindrical parabolic solar concentrators under ideal conditions. Particular attention is given to the application of this type of concentrator in the intermediate temperature range, where wide targets are used. Suitable indices that describe the performance are defined and calculated, and the effects of the different parameters are studied. In particular, the energy available at the focal plane and the distribution of its intensity are determined. All ranges of rim angles are studied: less than 90°, more than 90°, and the whole range of 0–180°. The performances obtained are the best possible and can, therfore, be used as a standard of reference for the appraisal of actual concentrators of the type studied.

Performance analysis of external shading devices

Abstract The performance of the basic vertical and horizontal types of external shading devices was studied in detail. The different performance modes are presented in the form of shading masks featured by the cutoff angles. Mathematical formulae were derived to express the cutoff angles in terms of the various geometrical parameters characterizing the combination of the shading device and the fenestration. These angles define the partial and complete shading phases. The formulae are put in generalized forms, in terms of normalized geometrical ratios, so as to be independent of the absolute dimensions. A unified approach was followed for both vertical and horizontal devices so that the derived normalized expressions can be adopted for the two types. The effect of the various geometrical factors on the cutoff angles, i.e. on the form of the shading mask, was investigated for different configurations of vertical and horizontal shades. Based on the derived relations, the trends of variation, of the cutoff angles with these factors, are graphically presented for each case.

Reduced order dynamic model of the flat-plate solar collector

Abstract Pade approximation techniques are applied to obtain a reduced order dynamic model for the partial differential system representing the dynamic behaviour of the flat-plate solar collector. According to a prespecified accuracy, the collector is divided into n sections. At any position along each section the reduced order dynamic model is decoupled second order state equation, the input of which is the output of the preceding section. Numerical solutions obtained from the reduced order dynamic model are in very close agreement with the exact solution. Moreover, the computational efforts as well as the computer storage requirements are considerably reduced in comparison with other methods. The results obtained from the dynamic model are compared with those based on a simple steady-state model. The comparison reveals that the steady-state expression may only be used for collectors having a low thermal inertia and a high fluid-stream heat capacity.

Theoretical analysis of the performance of a conical solar concentrator

This paper describes a study of the conical solar energy concentrator with tubular axial absorber. The concentrated power is evaluated, in a dimensionless form, as a function of the mirror surface quality and the absorber-to-aperture diameter ratio. The irradiated length of the absorber is determined and the axial concentration distribution along its surface is expressed mathematically. An integrated, or average, concentration ratio is used to measure the concentrating power of the reflector-absorber assembly. In addition to the mirror reflectivity, the performance is shown to be influenced by three parameters--the apex angle, the diameter ratio and the truncation ratio. The effects of these parameters on the concentrated power, the concentration profile and the reflector-surface area are investigated.

Performance analysis of the stationary-reflector/tracking-absorber solar collector

This is an analytical study of the performance of the stationary-reflector/tracking-absorber (SRTA) solar collector with tubular absorber. The mathematical treatment and the derived formulae are generalized for any rim angle and any absorber-to-reflector diameter ratio. The effects of these two parameters on the average concentration ratio are investigated. Different multi-reflection zones of the mirror are identified. Their contributions to the total concentrated power and the local concentration ratio, at different absorber points, are assessed. The concentration profile along the absorber is determined under different conditions. The influence of mirror reflectance on the flux density at different points is evaluated. The circumferentially-distorted concentration profile at times of oblique incidence is displayed. The absorber surface is divided into bright, faint and dim regions. A mathematical procedure is presented to contour these regions. Their occurrence and area growth are shown to be dependent on the rim angle and diameter ratio.

Solar heat gain through vertical cylindrical glass

Abstract Spaces with nonplanar glazed envelopes are frequently encountered in contemporary buildings. Such spaces represent a problem when calculating the solar heat gain in the course of estimating the cooling or heating load; and hence, sizing of cooling or heating systems. The calculation, using the information currently available in the literature, is tedious and⧹or approximate. In the present work, the computational procedure for evaluating the solar heat gain to a space having a vertical cylindrical glass envelope is established, and, a computer program is coded to carry out the necessary computations and yield the results in a detailed usable form. The program is versatile and allows for the arbitrary variation of all pertinent parameters.

Feasibility of external shading of fenestration of different exposures

Abstract The daily chronological variation of the solar heat gain through fenestration was studied for different orientations, locations, and months. Then, a method was presented to estimate the alleviation of the solar load achievable by external shading. This method was applied to investigate the effect of external shading for different exposures. The two indices, “Effectiveness” and “Efficiency”, were introduced to describe the theoretically possible solar load reduction. The feasibility of external shading, as a means of lowering the cooling load, was assessed on different exposures and at different latitudes. The assessment was based on two counterweighing criteria. These are the actually gained saving in the cooling load and the size of the required shading device.

Effect of various factors on the shading coefficient of different types of glazing

Abstract This is a study of the effects of various factors on the shading coefficient of different types of glazing. The main objective is to investigate the sensitivity of the shading coefficient to these factors and hence the validity of adopting a fixed value for the coefficient, as given in pertinent references, under different conditions. The study covers single and double glazing, of clear or heat-absorbing glasses, with and without reflective surface coatings. Plastic glazing is also included in the work. The variations of the shading coefficient with the incidence angle, the outdoor wind velocity, and the indoor air velocity are presented for the different types of glazing. The effect of windowpane(s) treatment, by applying reflective coats, is also exposed. The study revealed that, under certain conditions and with certain types of glazing, the use of the constant shading-coefficient values available in the literature may entail untolerable error in estimating the solar heat gain through glazed fenestration. In such cases the shading coefficient may have to be treated as a variable rather than a constant. However, this incurs excessive computational effort; therefore, it can be justified only when a high degree of accuracy is required which is not the case for routine air conditioning load estimations.

Temperature distributions along the absorber of the axicon solar fluid heater

Mathematical formulae are derived to express the fluid and the absorber-wall temperatures as functions of the position along the absorber reckoned from the inlet. The expressions are put in a general form in terms of a limited number of dimensionless groups. Two types of flow arrangements are identified, namely counter flow and parallel flow. The counter-flow heater is always superior to the parallet-flow one because it yields a higher output temperature under all conditions. The effects of the various parameters on the fluid temperature at the exit from the heater are investigated. Consequently, different methods of elevating the output temperature are proposed.

Performance measures of the axicon solar fluid heater

The definition of performance indices for the axicon solar fluid heater is essential for the assessment of a particular heaters performance or the comparison of different heaters of different designs, working under different conditions and producing different outputs. Two indices, the effectiveness and the efficiency, are introduced to describe the performance from two different aspects. The first index is the achieved fluid-temperature rise across the heater, while the second is the beneficially-utilized fraction of the available energy input. The study covers the two possible arrangements of fluid flow, i.e. counter and parallel. Mathematical formulae are derived to express the two performance indices in terms of the governing lumped dimensionless groups encompassing the numerous pertinent physical variables. The understanding of the performance of this radiant heater is deepened through exposing its resemblance to an imaginarily equivalent two-stream recuperator. The effect of the various factors on the performance, as described by the two performance indices, is investigated. The effect of manipulating certain parameters is shown to have contradictory effects on the two performance indices.