icramid_114

Keywords: LFRSC, concentration ratio, instantaneous collection efficiency, ray tracing technique.

Abstract

Linear Fresnel reflector solar concentrator technology is similar to solar trough technology in which the sunlight is reflected by a series of mirrors onto an absorber tube, thus linear Fresnel reflector solar concentrator, is a linear line concentrator. The performance of the system depends on the design parameters, mass flow rate, etc. In the present work, by using MATLAB simulation program, a detailed design parameters analysis including the effect of variation in the height of the absorber, width of the absorber plane and the width of the reflector mirror elements on the concentration on the surface of the absorber plane has been made. The width of the absorber plane was investigated by using analytical and ray tracing techniques. Then, the optimized width of the absorber plane was used to design the absorber tubes. Also, detailed thermal performance analysis for the above design has been made. Results have been plotted graphically and discussed.

I. Introduction. A typical linear Fresnel reflector solar concentrator (LFRSC) basically consists of long narrow plane mirror elements arranged in a planar configuration and oriented so as to form a linear image of the sun on the absorber [1]. The absorber is generally a tube or a series of tubes which contains a heat transfer fluid. Considerable attention has been paid of late to develop linear Fresnel reflecting concentrators for photo thermal as well as photovoltaic conversion of solar energy [2, 3]. A variety of designs of linear solar concentrators were developed and tested for their suitability to deliver solar thermal energy in the medium temperature range [2-4]. The thermal efficiency of such a LFRSC system depends on the design parameters, mass flow rate,

desired temperature difference, tracking accuracy, etc., [5]. Optical designs and performance characteristics of a linear Fresnel reflector solar concentrator with a flat vertical absorber have been presented the distribution of local concentration ratio on the surface of the absorber has been investigated using the ray tracing technique [6, 7]. The amount of power delivered by the reflector to absorber (tubular) plays a key role in solar thermal energy systems [8]. Also, the recent work on the design of LFRSC with trapezoidal cavity absorbers have shown that the efficiency with the round pipe (multi-tube) absorber was 2-8% higher as compared to rectangular pipe absorber [9]. LFRSC has several advantages, (i) it is useful for medium-temperature (70 - 200oC)

[email protected] Thiagarajar College of Engineering,

Department of Mechanical Engineering, Associate Professor, BOYSCAST Fellow,

[email protected], Tamil Nadu, India

Virudhunagar – 626001, Kamaraj College of Engineering and Technology,

Department of Mechanical Engineering, Assistant Professor,

R.Manikumar * A.Valan Arasu Concentrator With Multi Tube Absorber

Performance Analysis Of Linear Fresnel Reflector Solar Design Parameters Optimization And Theoretical

International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments [ICRAMID - 2014]

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range applications (ii) it is fabricated with narrow flat reflectors and constituent materials for its fabrication as well as replacement which are readily available in the market; (iii) the planar configuration and the air gap between the adjacent reflectors result in very small wind loading on the concentrator. Because of this, it can be mounted on rather simple cost-effective supporting structure.

It is immense importance to study the effect of the various design parameters of the concentrator and absorber on thermal performance of the LFRSC. The designing of the LFRSC for multi tube absorber configuration by employing mirror elements of equal width has been examined here. The study was conducted to investigate the effect of concentration power, concentration ratio and mass flow rate of working fluid on the thermal performance of the Fresnel reflecting device. Findings of the study have been discussed in this paper. II. Analysis of design parameters

II.I Optical design. Following assumptions were made to facilitate the designing of LFRSC (i) The concentrator is perfectly tracked, so as to follow the apparent movement of the sun [10], (ii) the reflector elements are specularly reflective (iii) the solar radiation incident axially (in the present study, beam radiation of 0.8 kW/m2 was assumed). A schematic representation of a LFRSC is shown in fig. 1. The concentrator consists of 2N reflector elements, with N reflectors present on either side from the centre of the concentrator plane in which solar radiation incident axially. In the event of perfect tracking, a LFRSC is assumed to imply, that, it is made up of a large number of flat, front reflecting reflector elements, each with a finite width (w) and a length equal to the length of the linear absorber (L). The reflectors are oriented so as to form an overlapping image of the sun on the absorber

tubes.

fig. 1: Schematic of linear Fresnel reflecting solar concentrator with absorber plane

The designing of a LFRSC employing mirror elements of equal width can be carried out using conventional geometrical optics. The tilt of each mirror elements is chosen such that a ray incident normally on the aperture plane and striking the midpoint of the mirror element, after reflection, reaches the focal point. If absorber tubes are arranged horizontally along the absorber plane such that the centre of the absorber plane coincides with the point f, then the lower sides of the absorber tubes will be illuminated by the radiation reflected from the constituent mirror elements. It is clear from the geometry of the concentrator that the widths of the images produced on the absorber surface will increase as one move towards the rim of the concentrator from the centre of the aperture of the concentrator. This effectively means that the radiation reflected from the mirror elements placed at the edge of aperture plane will produce large images on the absorber surfaces. As a result, the contribution of these mirror elements to the concentration on the absorber tubes surfaces may be small.

Using simple geometrics optics, the tilt of the first mirror element with the


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concentrator plane XX can be calculated as [6],

1

1111

sin2

cos2tan21

wf

wR

(1) Where, R1 is the location of the first mirror element on the either half of the concentrator, w is the width of the constituent mirror elements ad f is the distance between the centre of the absorber and the concentrator plane. The above implicit equation may be solved iteratively for θ1. The location of the second mirror element and its tilt with the concentrator plane are chosen such that: (i) the ray emanating from the centre of the solar disc and striking the midpoint of the mirror element, after reflection, reaches the point f and (ii) the extreme ray of the cone incident on the lower edge of the second mirror element strikes the absorber, thus the radiation reflected from the second mirror element is not blocked by the first mirror element. This necessitates introducing a certain space between two consecutive mirror elements. The necessary shift for the second mirror element is given by:

212 2tansinws (2) On the basis of similar geometrics optical considerations, the following generalized expressions for the shift (sn), location (Rn) and the tilt (θn) parameters associated with the nth mirror element can be derived as:

nnn ws 2tansin 1 (3) nnnn swRR 11 cos (4)

and

n

nnn wf

wR

sin2

cos2tan21 1

(5) with θ0=0, s1=0 and R0= -w/2, R1=w/2 as initial values for iteration and n= 1,2,….,N, where, N is the total number of mirror

elements placed on each half of the concentrator. The width of the absorber plane is calculated from the largest intercept produced on the absorber plane by a constituent mirror element. As explained earlier, the last mirror element produces the largest intercept on the absorber, and thus, that width of the intercept may be taken to be the width of the absorber plane. Hence all the solar radiation reflected from the constituent mirror elements will be intercepted by the absorber.

II.II Basic absorber design. The analytical technique used for determining the distribution of local concentration ratio (LCR) on the surface of the absorber and width of the images produced on the absorber plane for single absorber tube has been presented by the authors [8]. The same technique has been used for multi-tube absorber in the present work. Further, the optimum width of the absorber plane which is found out by analytical technique is validated by using ray tracing technique. A brief description of the techniques is given below.

II.II.I Analytical technique. For a LFRSC employing mirror elements of equal width, concentration ratio (CR) is obtained by summing up the concentration contribution of the each reflector element. Contribution of concentration of nth reflector element (CIn) to the local concentration ratio distribution on the absorber plane, is given by [11], CIn = (w. cos(θn)) / Gn (6)

where Gn represents the width of the image produced on the absorber plane. Since each constituent mirror element on the concentrator plane illuminates the complete radiation on the surface of the flat horizontal absorber plane, total concentration at any point on the surface of the absorber may be calculated from,

N

nCR

1n CI2

(7) In the Linear Fresnel reflector solar


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concentrator system, different reflector elements, reflect energy to different portions of the tubular absorber and the concentrated flux from all the reflectors distributes large on the tubular absorber. So, it is necessary to determine the total concentrated power reaching the absorber plane. Thus, the total concentrated power on the absorber due to the contributions from all the reflector elements is given by [8],

c

N

1nn P)P(2CP

(8) where, Pc = ρ. Ib.(w –W) . L (9)

If width of the reflector is equal to total width(W) of the absorber plane, solar power (Pc) on the tubular absorber contributed from the central reflector is equal to zero and if both the values are not equal then the Pc value is added to the total concentrated power.

II.II.II Ray tracing technique. The ray trace technique developed for the purpose of the present work, the aperture diameter of the concentrator is divided into a large number of divisions (say, K) of equal width. On each division a cone subtending an angle equal to the angular subtense of the sun (= 32') at any point on the earth, and containing 33 rays with an angular interval of 1' is considered. Depending on the distance of the incident cones from the centre of concentrator aperture, the cones would either strike one of the constituent mirror elements and would be reflected back towards the absorber or would fall on the shift introduced between two consecutive mirror elements. In the first case the points of intersection of the incident cones with the constituent mirror elements they strike are found out, whereas in the later case the rays are assumed to be lost. Once the points of intersection of the incident cones with the constituent mirror elements are known, the equations of the reflected rays can be derived using simple geometrical optics.

The next step is to calculate the point of intersection of the reflected rays with the surface of the absorber. The absorber surface is also divided into a large number of equal size divisions such that the width of each division is equal to the width of the divisions on the aperture of the concentrator.

The distance of an incident point of a typical cone on any division on either half of the concentrator from the centre of the concentrator plane is specified by [6],

KxDX I

12

(10) where K, in the present work, is taken to be equal to 100, i.e., 100 divisions of equal width have been made in the aperture diameter (D) of the concentrator and x varies from 1 to ((4 K) + 1).

The incident cone would strike a typical mirror element (say, nth) if XI lies between Rn and Rn + wncos θn (edges of the nth mirror element). The equation of the typical ray of the incident cone under consideration may be expressed as [6],

90tan)( II XXYY (11) where (XI, YI) are the (X, Y) coordinates of the point of intersection of the incident cone with the nth mirror element and is the angular deviation of a ray of the incident cone from the ray emanating from the centre of the sun and it varies from 0 to 16'. The positive sign with is taken for those rays of the cone which make an angle greater than 90° and a negative sign is taken for those rays which make an angle less than 900 with the concentrator plane (fig. 1). If the values of XI and YI are substituted in the Eq. 11, then the equation of any typical ray of incident cone can be obtained. YI is defined as,

nnII RXY tan (12) where Rn and θn are the location and the tilt of the nth mirror element, respectively. Having located the mirror element on which the incident cone under consideration falls, the equation of the reflected ray can be


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derived. The slope of the reflected ray associated with the incident ray represented by Eq. 11 is given by

nn 290tan (13) In the above equation, positive sign before (2θn ± ) is taken for the rays falling on the mirror elements placed on the right half of the concentrator and negative sign for the rays falling on the mirror elements placed on the left half of the concentrator. The equation for the reflected ray may be derived as,

IPnIP XXYY (14) Using Eq. 14 and the equation representing the horizontal absorber plane, the point of intersection of the reflected ray with the absorber can be calculated. The horizontal absorber plane can be represented by,

ay (15) where a is the optimum height of the absorber plane from the concentrator plane corresponding to the maximum concentrated power, i.e., a=f.

From Eq. 14, Eq. 15, the coordinates of the intersection point (Xp,Yp) of the reflected ray with the horizontal absorber plane may be calculated. The above procedure is repeated for all the 33 rays of the cones incident on the different divisions made on the aperture diameter of the concentrator. Sample intersection point of the incident ray in the mirror and reflected ray on the absorber plane is shown in fig. 2.

fig. 2: Representation of ray’s intersection point in the mirror and absorber plane The aperture diameter, D, of the concentrator achieved in many practical case may be expressed as [8],

nnn wQD cos2 (16)

II.II.III Absorber tube design. The absorber tubes are assumed to be made of a set of six mild steel round tubes (outer diameter: 0.016m and length:1m) brazed together in a single layer. Cross-sectional view of the absorber tubes placed in the absorber plane is shown in fig. 3. The internal pressure restriction of the absorber tubes is estimated from Indian Boiler Regulations. For the assumed design temperature of 130oC [12], saturation pressure (Ps), is taken from the steam table. The maximum allowable material stress, (AS) is 68MPa for 320 Grades steel. Given then an outside diameter (d0), the minimum wall thickness (t) of one absorber tube is given by,

fig. 3 : Cross sectional view of absorber tubes in the absorber plane (dimensions are in mm)

CtdCtASPs

o

)(**2 (17)

Where C is equal to 0.75 * 10-3 m (from IBR standards). By using the above formula the thickness of the tube has been found out and hence the internal diameter (di) of the tube which is used for further calculation. III. Thermal and optical efficiency analysis of LFRSC. The LFRSC can be imagined as a broken-up parabolic trough reflector [2,13] and thermal analysis is carried out as similar to the parabolic trough reflector [14]. The solar thermal performance of a multi tubular absorber is assumed as employing ordinary matt black paint coated absorber tube whose absorbance (α) is assumed as 0.96 [9] has an outer diameter do and inner diameter di. The fluid which is to be heated in the absorber

(XI, YI)

(Xp, Yp) Absorber Plane

Concentrator Plane


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tubes has a mass flow rate m, specific heat c, an inlet temperature Ti, an outlet temperature To and ambient temperature is Ta. Heat gain (Q) can be expressed by energy balance in the absorber tube considering heat loss by convection and reradiation [15] which gives,

\Q =

)(

U** l

aiaR TTC

SAF (18)

= m*c*(To-Ti) (19) where, S = Ib* ρ*γ*(τα), (20) where, Ib is the beam radiation, ρ (0.98) is the reflectivity of glass, γ (0.94) is the intercept factor and τ is the transmittance assumed as 1.

cmLAF

UAcmF r

lrR *

*'*exp1* (21)

l

o

UUF ' (22)

The instantaneous collection efficiency (or) thermal efficiency is given by,

ab AIQ*

(23)

The pressure drop in the absorber tube (6 nos.) may be calculated from the following relation,

∆p = 6**2

****4 2'

idVLf (24)

For fully developed laminar flow,

Re64' f (25)

And for fully developed turbulent flow (3000 Re 5*106)

'f = (0.790 * ln(Re) – 1.64)-2 (26) In order to obtain a break-up of the

losses occurring in the concentrator, optical losses and thermal losses has been distinguished. Optical losses are those which occur in the path of the incident solar radiation before it is absorbed at the surface of the absorber tubes, while thermal losses are due to convection and reradiation from the absorber tubes and conduction through the

ends. On this basis, optical efficiency (ηo) is defined as the fraction of the solar radiation incident on the aperture of the concentrator which is absorbed at the surface of the absorber tubes. Thus it is expressed as [14],

DIWDS

bo *

)(* (27)

IV. Results and discussion IV.I Concentrated power of the

system. In the present work, the various design parameters considered are shift (s), width of reflector (w), location of each reflector (R), height of the absorber plane (f).The range of the height of the absorber plane is taken as 0.8 to 1.4m with the interval of 0.1m.The range of the width of the reflector mirror is taken as 0.02 to 0.04m with the interval of 0.01m. Hence the design parameter like tilt, shift and location of each reflector depends on the height of the absorber plane and width of the reflector, the program is developed to calculate the concentrated power for the considered range of height of the absorber plane and width of the reflector. The total concentrated power of the system was found out by using Eq. 8, Eq. 9. The maximum concentrated power is obtained as 2.47 kW (app. 2.5kW) for the value of w=0.04m, f=1.1m for a set of 40 numbers of reflectors.

fig. 4: Number of reflectors vs Concentrated power

fig. 5: Solar Intensity Vs Concentrated power for optimum values


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By using the above optimum value of the design parameters (f and w), a MATLAB program has been developed to calculate the total concentrated power for different sets of reflectors (N =10, 20, 30, 40, 50, etc..,). The variation of concentrated power with respect to number of reflectors is shown in fig. 4. The concentrated power is observed to increase rapidly with number of reflectors upto about 40. The extra-axial reflectors beyond N= 40 contributed little to the concentrated power due to larger cosine losses associated with them. Therefore the initial assumption of 40 numbers of reflectors is justified by fig. 4. Also the variation of concentrated power with respect to solar intensity at optimum values of design parameter is shown in fig. 5. The concentrated power is increasing linearly with increase in solar intensity of beam radiation (Ib). The results obtained is similar to the trend shown in the literatures [9,17].

IV.II Concentration ratio of the system. The concentrator aperture area and corresponding concentration ratio of the LFRSC by using analytical technique are given in Table 1. Table 1: Concentration ratio of the LFRSC at different

concentrator aperture area (Analytical Technique)

Concentrator aperture area [m2] Concentration ratio Total number of

reflectors [2N] 0.68 7.7 20 1.48 14.2 40 2.28 19 60 3.08 22.4 80

fig. 6: Total number of reflectors Vs Concentration ratio

Fig. 6 shows the graph between total number of mirror reflector and concentration ratio. The growth of the concentration ratio declines slowly with increase in the number of reflectors. This may be attributed to the

cosine effect of the reflector angle. Contribution made to the concentration ratio by the nth mirror reflector depends upon the factor Cos θn as given in the Eq. 6. Gain in concentration ratio reduced significantly with increasing number of reflector mirrors after concentration ratio of 19. The aperture area of the LFRSC (Aa) is obtained by deducting the shaded area (0.12 m2) due to the optimum absorber plane width from the respective concentrator aperture area of the collector at different values of N. The values of the solar energy reached to the absorber are shown in Table 2. Table 2: Analysis of concentrated power reached to the

absorbers at different concentration ratio for glass.

The solar energy availability is estimated as 78% and 66.4% at concentration ratio of 7.7 and 22.44 respectively for the assumption of ordinary matt black paint coated absorber. The comparative energy availability to the absorbers is decreased with increase in concentration ratio because of increase in non-contributing concentrator area (Eq. 3). The observation is found in line with the literature results [9,17]

IV.III Absorber plane width and absorber tubes. For illustrating the design and performance evaluation procedure some typical numerical calculations have been made for the design of LFRSC, and the results obtained are presented in this section. The aperture diameter (D) of the concentrator, for the design is calculated as 4.1m by using the Eq. 16. In this typical case the analytical technique gives uniform concentration over a width of 0.12m on the absorber plane by the last mirror element. The last mirror element gives the maximum width on the absorber plane as shown in fig. 7.

Concentrator aperture area

[m2]

Concentration ratio

Solar power reached to the absorber [kW]

(% of input solar energy) 0.68 7.7 0.48 (78%)

1.48 14.2 1.05 (74%) 2.28 19 1.61 (70.9%)

3.08 22.44 2.18 (66.4%)


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fig. 7: Interception of reflected rays on the absorber plane

In ray tracing technique, the coordinates of the intersection point of the reflected ray with the absorber plane is calculated by using Eq. 10 to Eq. 15. Total number of intersected rays in the absorber plane is 4653 and the last intersection point is 0.13m from the absorber plane centre on both sides. Out of 4653 rays, 332 rays (7% of the total) are intersected between 0.06m to 0.13m and the 93% remaining rays intersected between 0.0 to 0.06m from the centre of the absorber plane on one side of the concentrator plane. So, the value of the aperture plane width (0.12m) which was found out from analytical technique is validated by using ray tracing technique.

IV.IV Effect of mass flow rate on various parameters. The concentrator is considered to be oriented in N-S horizontal and E-W tracking configuration. The ambient and inlet water temperatures are considered as 32oC and 38oC. The overall heat loss coefficient (Ul) and heat loss coefficient from inside of the tube to surroundings (Uo) were assumed as 6 and 5 W/m2 K [7]. A MATLAB program has been written to find out the outlet temperature of the water by varying the mass flow rate of the fluid by using Eq. 18 to Eq. 22. The graph is drawn between them and shown in fig. 8. From the graph, it is inferred that increase in mass flow rate results in decrease in outlet temperature of the fluid. The linearity of the slope of the curve is more at the initial mass flow rate and slowly slope of the curve is reduced when the mass flow rate reaches final value. The final value of the outlet temperature is 80oC for 0.01 kg/s of mass flow rate. Therefore the thickness and internal diameter of the absorber tubes has been calculated for the design temperature of 130oC which is 50oC more than the operating

fluid temperature [12].

80

66.859.7

55.4 53

0

10

20

30

40

50

60

70

80

90

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Mass flow rate (kg/s)

Flui

d ou

tlet t

empe

ratu

re (

o C)

fig. 8: Mass flow rate Vs Fluid outlet temperature

The various heat transfer properties of

the water [16] are determined for the mean water temperature (average of inlet and outlet temperature) and a simulation program is developed to find the pressure drop in the six absorber tubes by using Eq. 24 to Eq. 26. Graph is drawn between the mass flow rate of the water and instantaneous collection efficiency and pressure drop. An increase in the mass flow rate of the water increases the value of the heat transfer coefficient Uo. Due to this, concentrator efficiency factor and the heat-removal factor increase and the efficiency also increases. This effect is illustrated in fig. 9, in which the mass flow rate is varied from 0.01 kg/s to 0.03 kg/s. It is seen that the slope of the efficiency curve goes on decreasing with increasing values of mass flow rate and that the value of η tends to attain asymptotic value. This trend is similar to the one shown in the literature [14]. At the same time, the pressure drop increases, thereby increasing the demand for pumping power. Fortunately, this increase is not so rapid because of high prandtl number of the fluid. Thus, an optimum value of mass flow rate would be one for which the asymptotic value of instantaneous collection efficiency (η) was almost attained without any high pressure drop. From graph, this optimum value was found as 0.025 kg/s, in the present study. The instantaneous collection efficiency and fluid outlet temperature for the optimum mass flow rate and an assumed fluid inlet temperature of 38oC are evaluated as 72.6% and 55oC. The obtained results are in line with the literatures [8].


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fig. 9: Mass flow rate Vs Efficiency and pressure drop

fig. 10: Fluid inlet temperature Vs Efficiencies

IV.V Effect of Inlet fluid temperature. For the optimum mass flow rate of the fluid, the effect of fluid inlet temperature on instantaneous collection efficiency is found out. As the fluid inlet temperature increases, the temperature of the absorber tube surface also increases. As a result, losses due to re-radiation and convection to the surroundings increase, resulting in a decrease in efficiency. This is apparent from the useful heat gain rate for the concentrator. In order to illustrate this effect, calculations are done for the glass reflector operating under the same conditions with inlet temperature varying between 34oC and 42oC. The results are plotted in the fig. 9. It is seen that the value of η decreases significantly with Ti and the decrease is slightly non-linear. The non-linearity is due to the fact that value of the overall loss coefficient increases slightly as Ti increases. The optical efficiency is calculated by using the Eq. 27 for the reflector and it was included in the graph between instantaneous collection efficiency and fluid inlet temperature. From the fig. 10, it is identified that the optical efficiency does not depend on fluid inlet temperature. The difference between the values of η and ηo is a measure of the losses due to reradiation and convection. Also, a computer program has been developed to find out the optical efficiency at different concentration ratios.

The results are presented in Table 3. The raise of optical efficiency is decreasing with increase in concentration ratio. Table 3: Variation of optical efficiency at

different concentration ratio Concentrator

aperture area [m2] Concentration

ratio Optical

efficiency [%] 0.68 7.7 76.0 1.48 14.2 82.3 2.28 19 84.7 3.08 22.44 85.8

V. Conclusion. The paper has described preliminary design work for a linear concentrating system. The optimum value of the design parameters were obtained by using MATLAB simulation program for an optimum value of 40 numbers of reflectors (N) and corresponding concentrated power and concentration ratio were calculated. The concentration ratio was found as 22.44 by the way of analytical technique. The width of the absorber plane has been found out by using analytical technique and it is validated by ray tracing technique. The optimum width of the absorber plane was used to locate the absorber tubes for better heat transfer to the working fluid. The outlet temperature of the fluid, instantaneous collection efficiency and pressure drop were found out by varying the mass flow rate of the fluid and an optimum mass flow rate found out from the graph. The instantaneous collection efficiency was calculated as 72.6% for the glass reflector, at the optimum mass flow rate. Further, it is seen that the value of instantaneous collection efficiency decreases significantly with fluid inlet temperature and the optical efficiency does not change with fluid inlet temperature. The design procedure presented in the paper shall be used for modeling and evaluating theoretically the performance of LFRSC for an application. VI: References (1) R.M. Cosby, Concentration

Characteristics of Fresnel Solar Strip Refelction Concentrator, NASA Report NASA- CR_120336. U.S.A., 1974.

(2) J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, John Wiley, New York, 1980.


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(3) Jr. Harry K. Charles, Solar Photovoltaic Energy Systems, hand book of energy technology and economics, Chap.16 (Edited by Robert A. Meyers), John Wiley, New York, 1983.

(4) S.S. Mathur, T.C. Kandpal, Solar Concentrators, Reviews of Renewable Energy Resources, Chap.5 (Edited by M.S.Sodha, S.S. Mathur and M.A.S.Malik), Wiley Eastern Ltd., New Delhi, 1984.

(5) M.S. Sharma, S.S. Mathur, R.N. Singh, Performance Analysis of a Linear Solar Concentrator Under Different Flow Regimes, Technical note, Applied Energy, 13 (1983) 77-81.

(6) B.S. Negi, T.C. Kandpal, S.S. Mathur, Designs and Performance Characteristics of A Linear Fresnel Reflector Solar Concentrator With A Flat Vertical Absorber, Solar and Wind Technology, 7 (4) (1990) 379-392.

(7) B.S. Negi, S.S. Mathur, T.C. Kandpal, Optical and Thermal Performance Evaluation of a Linear Fresnel Reflector Solar Concentrator, Solar and Wind Technology, 6 (5) (1989) 589-593.

(8) R. Manikumar, A. Valan Arasu, Design and theoretical performance analysis of linear Fresnel reflector solar concentrator with a tubular absorber, International journal of renewable energy and technology, Inderscience Publications, 3 (3) (2012) 221-236.

(9) P.L. Singh, R.M. Sarviya, J.L. Bhagoria, Thermal performance of linear Fresnel reflecting solar concentrator with

trapezoidal cavity absorbers, Applied Energy, 87 (2010) 541-550.

(10) B.S. Negi, S.S. Mathur, T.C. Kandpal, Annual useful energy collection by linear solar concentrators, Technical note, Solar and Wind Technology, 2 (¾ ) (1985) 205-207.

(11) M.S. Sharma, A.K. Sehgal, T.C. Kandpal, S.S. Mathur, Geometrical-optical design and performance studies of a linear Fresnel reflector. In: Proc. of Naitonal solar energy conversion, New Delhi, Tata McGraw Hill publishing Co. Ltd., (1990) 3.032 – 3.035

(12) C.J. Dey, Heat transfer aspects of an elevated linear absorber, Solar energy, 76 (2004) 243-249.

(13) S. Kalogirou, Solar thermal collectors and applications, Progress in energy and combustion science, 30 (2004) 231-295.

(14) S.P. Sukhatme, J.K. Nayak, Solar energy Principles of thermal collection and storage, third edition, Tata McGraw-Hill Publication, New Delhi, 2009.

(15) G.D. Rai, Solar energy utilization, Khanna Publishers, New Delhi, 1999. (16) C.P. Kothandaraman, S. Subramanyan,

Heat and Mass Transfer Data Book, New Age International Publishers, New Delhi, 2008.

(17) R.Manikumar, A.Valan Arasu, An analytical and experimental study of the linear Fresnel reflector concentrator system, Distributed Generation and Alternative Energy, Accepted, Article in press.


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