Selection And Evaluation Of Different Tracking Modes Performance For Parabolic Trough Solar Collector

Selection And Evaluation Of Different Tracking Modes Performance For Parabolic Trough Solar Collector

Mr. Arvind Kumar	Prof. (Dr). Satish Chand	Mr. O.P.Umrao
MIT, Bulandshahr	VGI, Greater Noida	VGI, Greater Noida

Abstract

The tracking and orientation of parabolic trough is very important for efficient performance of collector. In this paper, we have evaluated the performance parameters of PTC such instantaneous efficiency of collector, heat removal factor, solar incident normal to surface, and correction of glass in respect of Local apparent time for the location New Delhi, June 10 . We have also reckoned which tracking is mode suitable in respect economic, operational control tracking system for large solar power generation. We have made program in EES software for entire evaluation and performance graphs.

[1.]Introduction

Parabolic trough solar water heating is one of several well proven solar energy technologies. It is being used on a commercial scale to produce high pressure steam for power generation, as well as on a small scale for commercial and residential applications .The

performance of this type of solar collector can be

to the dynamic curvature adjustment proposed in our previous work for a solar furnace, a fixed asymmetric curvature is used here with the spinning-elevation tracking method. Chia-Yen Lee et al. [1] providing a high level overview of the sun tracking system field and then describes some of the more significant proposals for closed-loop and open-loop types of sun tracking systems. We have studied the two-axis solar tracking system consumes more energy than the single solar tracking techniques due to the extra control power requirement. Therefore, using the two-axis mode cannot be justified unless the amount of energy produced compensates for the additional elements and maintenance cost.

[2.] Parabolic trough collector orientation and tracking modes methodology

PTC is oriented with its focal axis pointed either in the E-W or N-S direction. In the E-W orientation, the focal axis is horizontal, while N-S situation

improved greatly by using one of the solar tracking techniques to concentrate a direct solar beam onto the focal point. The tracking technique basically depends on the tracking axis of a solar beam reflector. A comparison of different tracking modes has been thoroughly investigated in the literature. These studies showed that adopting the two-axis solar tracking technique causes the highest increase in system energy output and improves solar energy contribution. Soteris

A. Kalogirou [5] provided analysis different collector such optical, thermal and tracking analysis. Duffie et al. [2] delivered depth knowledge solar engineering thermal application. It also provide f-chart design the thermal system Saad D. Odeh et al. [4]presents the

Sun

Normal to tilted plane

N

Normal to horizontal plane S

Tilted plane horizontal plane

design, development, testing and evaluation of an educational single-axis solar tracking parabolic trough collector that represents a standalone system to produce process heat at a moderate temperature for instructional and demonstrative purposes. Hossein Mousazadeh et al. [3] provided the types of sun- tracking systems are reviewed and their cons and pros are discussed. The most efficient and popular sun- tracking device was found to be in the form of polar- axis and azimuth/elevation types. Y. T. Chen et al. [7] investigates the performance of a heliostat field composed of the newly proposed heliostats. In contrast

Figure1 this diagram illustrated different angles

, the focal axis may be horizontal or inclined. The following tracking can be adapted, are as follows SP Sukhatme et al [6]

Mode I The focal axis is E-W and horizontal. The collector is rotated about a horizontal E-W axis and adjusted once every day so that the solar beam is normal to the surface of the collector aperture plane at solar noon. The aperture plane is imaginary surface with either =00 or 1800. The case of =00 happens

when (-) <0.then to find the slope of the aperture plane putting in eq. (1) the condition at the solar noon, viz. = 00, = 00. We get

Plane perpendicular

magnitude of the solar azimuth angle s is less than 900, in respect =1800, s >900

The expression for the minimum angle of incidence is obtained by substituting eqs (3.18) & (3.19), for both

cases

Sun

Normal to aperture

S

Tracking angle

Mode III The focal axis is N-S and horizontal. The collector is rotated about a horizontal N-S axis and adjusted continuously so that the solar beam makes the minimum angle of incidence with aperture at all the times. In this mode, surface azimuth angle = +90

E W

Tracking axis

N

before noon and = -90 after noon. The before noon equation becomes

Figure 2 Single axis tracking system rotating about

1. axis

   [

   ]

   = (-) for =00 (2)

   = (-) for =1800 (3)

   The angle of indigence of the beam radiation on the aperture plane whole day is obtained by eqs (2) & (3) in eqs (1). For the both cases, =00 or 1800, we obtain the same relation

   This is used to find the slope of the aperture plane at any hours before noon. The equation for the corresponding minimum angle of the incidence is obtained by putting, giving

   After noon = -900, we have

   Mode II The focal axis is same as mode I. the collector is turned about the horizontal E-W axis and

   [

   The expression for cos remains same.

   ]

   adjusted continuously so that the solar beam makes the minimum angle of incidence with aperture at all the hours. In order to find the condition to be satisfied for to be a minimum, we differentiate the right hand side of the resulting equation with respect to and equate it to zero.

   Mode IV the line of receiver is N-S and inclined at a

   fixed angle equal to the latitude Thus, it is parallel to the earths axis. This orientation is sometimes referred to as a polar mount. The collector is rotated about an axis parallel to the earths axis at an angular velocity equal and opposite to the earths rate of the rotation (150 per hour). It is adjusted such that at solar noon the

   aperture plane is inclined surface facing due south. Thus, putting = and =0 in eqs (1), we get

   = (11)

   Above equations can be used for the finding the slope of the aperture plane. Corresponding =00, the

   Mode V The focal axis is N-S and inclined. The collector is rotated continuously( but not at a constant angular velocity) about an axis parallel to the focal axis, as well as about a horizontal axis perpendicular to

   this axis and adjusted so that the solar beam is normally inclined on the aperture plane at all the times. In this situation cos =1, it is easy to show that at solar noon

   600

   500

   Aperture

   plane =

   Sun rays

   =

   Earth axis

   Equator

   400

   S (W/m2)

   S (W/m2)

   300

   200

   100

   0

   400 600 800 1000 1200 1400 1600 1800

   Time in hr

   Figure 4 Incident radiation versus LAT

   Figure 3 for Cylindrical parabolic collector where

   =

   | |

   It is of interest to compare the amount of the beam radiation which would be incident on the collector aperture plane over a day if one adopted the various trackin modes.

   [3.] Performance of different modes of tracking with graphs

   The Location is New Delhi (28.580 N, 77.200 E); the

   radiation falls on one square meter of the aperture plane of the collector from 0600 to 1800 h (LAT) on June 10. The following value of S is given in table then we have compared performance of tracking mode which is applicable for requirement. I have made program by EES software for this condition. By this program code prepared graphs between important parameters. In this paper, we have shown all equation in program section 4 avoid the paper space and time.

   Table 1 Solar radiation incident data on 10 June, New Delhi from 6.30 am to 5.30 pm

   Time (h)	S (W/m2)	Time (h)	S (W/m2)
   0630	110	1230	523
   0730	240	1330	495
   0830	333	1430	445
   0930	424	1530	322
   1030	495	1630	220
   1130	550	1730	118

   [4.]EES software codes for evaluation tracking modes

   "This program code is prepared for EES software. There are five tracking mode and orientation. This program is evaluated which tracking mode is best for New Delhi location for June 10, by comparing data such incident flux, heat removal factor, collector efficiency factor ,instantaneous efficiency of collector from time 0600 to 1500 hrs. . I have plotted number of graphs to check the performance particular time of day"

   "Orientation and tracking mode" d=a*60;

   LAT=(a+b)*100 [Hrs.]

   Min=d+b*100; IST=720

   omega=(IST-Min)/4 delta=23.45*sin((360/365)*(284+n))"declination in degree"

   "For horizontal surface beta = 0 degree" theta_z=arccos(sin(phi)*sin(delta)+cos(phi)*cos(delta)

   *cos(omega))

   "According tracking mode I" theta_mode1=arccos((sin(delta)^2+cos(delta)^2*cos(o mega)))

   "According tracking mode II" theta_mode2=arccos((1- sin(omega)^2*cos(delta)^2)^(1/2)) "According tracking mode III"

   beta=arctan((cos(delta)*sin(omega))/(sin(phi)*sin(delt a)+cos(phi)*cos(delta)*cos(omega))) theta_mode3=arccos((sin(phi)*sin(delta)+cos(phi)*cos (delta)*cos(omega))*cos(beta)+cos(delta)*sin(omega)

   *sin(beta))

   "According tracking mode IV"

   theta_mode4=delta "According tracking mode V" theta_mode5=0

   "Tilt factor r_b for the aperture plane" r_b1=cos(theta_mode1)/cos(theta_z) r_b2=cos(theta_mode2)/cos(theta_z) r_b3=cos(theta_mode3)/cos(theta_z) r_b4=cos(theta_mode4)/cos(theta_z) r_b5=cos(theta_mode5)/cos(theta_z)

   "Beam flux incident normally on aperture plane" S_mode1=I_b*r_b1

   S_mode2=I_b*r_b2 S_mode3=I_b*r_b3 S_mode4=I_b*r_b4 S_mode5=I_b*r_b5 "Absorbed flux S"

   tau=0.89; alfa=0.94; rho=0.94; gamma=0.94; D_o=0.07 [meter]; W_a=5.76 [meter] S_1=S_mode1*tau*alfa*(rho*gamma+(D_o)/(W_a- D_o)) S_2=S_mode2*tau*alfa*(rho*gamma+(D_o)/(W_a- D_o)) S_3=S_mode3*tau*alfa*(rho*gamma+(D_o)/(W_a- D_o)) S_4=S_mode4*tau*alfa*(rho*gamma+(D_o)/(W_a- D_o)) S_5=S_mode5*tau*alfa*(rho*gamma+(D_o)/(W_a- D_o))

   "Inside convective the heat transfer coefficient for receiver tube"

   D_i=.055 [meter]; L=98.5 [meter]; A_r=3.14*D_i*L "Receiver area" m_steam=1.11 [Kg/sec]

   mu_water=.000128 [Kg/ms] c_p=4800 [J/kgK]

   k_f=.622 [KW/mK]; K=20.2 [W/mK] U_L=20.46 [W/(m^2*K)];

   D_g=0.1[meter] R_e=4*m_steam/(3.14*D_i*mu_water) "Renold number"

   P_r=(c_p*mu_water)/(k_f) "Prandtl number" N_u=0.23*(R_e)^(0.8)*(P_r)^(0.4) "Nusselt number" h_fi=(N_u*k_f)/D_i "Inside heat transfer coefficient" F=(1/U_L)/((1/U_L)+((D_o)/(h_fi*D_i))+D_i/(2*K)*l n(D_o/D_i)) "Collector efficiency factor" F_R=(m_steam*c_p)/(A_r*U_L)*(1-exp(- (U_L*F*A_r)/(m_steam*c_p)))"Heat removal factor" "Useful heat gain rate"

   T_i=100 [0C]; T_a=35 [0C]

   C=(W_a-D_o)/(3.14*D_o)

   Q_U1=F_R*(W_a-D_o)*L*(S_1-U_L*(T_i-T_a)/C) "Mode I"

   Q_U2=F_R*(W_a-D_o)*L*(S_2-U_L*(T_i-T_a)/C) "Mode II"

   Q_U3=F_R*(W_a-D_o)*L*(S_3-U_L*(T_i-T_a)/C) "Mode III"

   Q_U4=F_R*(W_a-D_o)*L*(S_4-U_L*(T_i-T_a)/C) "Mode IV"

   Q_U5=F_R*(W_a-D_o)*L*(S_5-U_L*(T_i-T_a)/C) "Mode V"

   "The rate of heat loss" Q_1=(W_a-D_o)*L*S_1-Q_U1

   P_1=3.14*D_o*L*U_L*(T_m1-T_a) Q_1=P_1

   Q_2=(W_a-D_o)*L*S_2-Q_U2 P_2=3.14*D_o*L*U_L*(T_m2-T_a) Q_2=P_2

   Q_3=(W_a-D_o)*L*S_3-Q_U3 P_3=3.14*D_o*L*U_L*(T_m3-T_a) Q_3=P_3

   Q_4=(W_a-D_o)*L*S_4-Q_U4 P_4=3.14*D_o*L*U_L*(T_m4-T_a) Q_4=P_4

   Q_5=(W_a-D_o)*L*S_5-Q_U5 P_5=3.14*D_o*L*U_L*(T_m5-T_a)

   Q_5=P_5

   "Overall heat transfer coefficient for wind" rho_air=1.105 [Kg/m^3]

   v_air=3.01 [m^2/s] mu_air=.0000205 [Kg/ms] k_air=0.028 [W/mK] Re_air=rho_air*v_air*D_g/mu_air N_u_air=0.3*(Re_air)^(0.6) h_w=N_u_air*k_air/D_g b_a=(D_g-D_o)/2

   "Heat transfer coefficient between the absorber tube and cover evaluated by Raithby and Holland"

   "The properties are based on the mean temperature between tube and glass cover"

   k_a= 0.0323 [W/mK];

   nu_a=23.52*10^ (-6) pr_a=0.688 T_guess=30 [0C]

   T_ra1=(T_m1+T_guess+273+273)/2

   "Mean Temperature of air between tube and cover" T_ra2=(T_m2+T_guess+273+273)/2 T_ra3=(T_m3+T_guess+273+273)/2 T_ra4=(T_m4+T_guess+273+273)/2 T_ra5=(T_m5+T_guess+273+273)/2 Ra_1=9.81*(T_ra1)^(-1)*(T_m1- T_guess)*b_a^3*pr_a/(nu_a)^2 Ra_star1=ln(D_g/D_o)*(Ra_1)^(1/4)*(b_a)^(- 3/4)/(D_o^(-3/5)+(D_g)^(-3/5))^(5/4) K_eff1/k_a=0.317*(Ra_star1)^(1/4)

   h_c_1= (2*k_eff1)/ (D_o*ln(D_g/D_o))

   Ra_2=9.81*(T_ra2)^(-1)*(T_m2- T_guess)*b_a^3*pr_a/(nu_a)^2 " Rayleigh number " Ra_star2=ln(D_g/D_o)*(Ra_2)^(1/4)*(b_a)^(- 3/4)/(D_o^(-3/5)+(D_g)^(-3/5))^(5/4) "Modified Rayleigh number related to the usual Rayleigh number "

   K_eff2/k_a=0.317*(Ra_star2)^(1/4) "Effective thermal conductivity"

   h_c_2= (2*k_eff2)/(D_o*ln(D_g/D_o)) Ra_3=9.81*(T_ra3)^(-1)*(T_m3- T_guess)*b_a^3*pr_a/(nu_a)^2 Ra_star3=ln(D_g/D_o)*(Ra_3)^(1/4)*(b_a)^(- 3/4)/(D_o^(-3/5)+(D_g)^(-3/5))^(5/4) K_eff3/k_a=0.317*(Ra_star3) ^(1/4)

   h_c_3= (2*k_eff3)/(D_o*ln(D_g/D_o)) Ra_4=9.81*(T_ra4)^(-1)*(T_m4- T_guess)*b_a^3*pr_a/(nu_a)^2 Ra_star4=ln(D_g/D_o)*(Ra_4)^(1/4)*(b_a)^(- 3/4)/(D_o^(-3/5)+(D_g)^(-3/5))^(5/4) K_eff4/k_a=0.317*(Ra_star4) ^ (1/4)

   h_c_4= (2*k_eff4)/(D_o*ln(D_g/D_o)) Ra_5=9.81*(T_ra5)^(-1)*(T_m5- T_guess)*b_a^3*pr_a/(nu_a)^2 Ra_star5=ln(D_g/D_o)*(Ra_5)^(1/4)*(b_a)^(- 3/4)/(D_o^(-3/5)+(D_g)^(-3/5))^(5/4) K_eff5/k_a=0.317*(Ra_star5)^(1/4)

   h_c_5= (2*k_eff5)/(D_o*ln(D_g/D_o)) "General Correlation of energy" sigma=5.70*10^(-8); epsilon_r=0.93 epsilon_g=0.88; T_sky=30 [0C] x_1=h_c_1*(T_m1-

   T_g1)*3.14*D_o+sigma*3.14*D_o/(1/epsilon_r+D_o* (D_g)^(-1)*(1/epsilon_g-1))*((T_m1+273)^4- (T_g1+273)^4)

   y_1=h_w*(T_g1- T_a)*3.14*D_g+sigma*3.14*D_g*epsilon_g*((T_g1+ 273)^4-(T_sky+273)^4)

   x_1=y_1 x_2=h_c_2*(T_m2-

   T_g2)*3.14*D_o+sigma*3.14*D_o/(1/epsilon_r+D_o* (D_g)^(-1)*(1/epsilon_g-1))*((T_m2+273)^4- (T_g2+273)^4)

   y_2=h_w*(T_g2- T_a)*3.14*D_g+sigma*3.14*D_g*epsilon_g*((T_g2+ 273)^4-(T_sky+273)^4)

   x_2=y_2 x_3=h_c_3*(T_m3-

   T_g3)*3.14*D_o+sigma*3.14*D_o/(1/epsilon_r+D_o* (D_g)^(-1)*(1/epsilon_g-1))*((T_m3+273)^4- (T_g3+273)^4)

   y_3=h_w*(T_g3- T_a)*3.14*D_g+sigma*3.14*D_g*epsilon_g*((T_g3+ 273)^4-(T_sky+273)^4)

   x_3=y_3

   x_4=h_c_4*(T_m4- T_g4)*3.14*D_o+sigma*3.14*D_o/(1/epsilon_r+D_o* (D_g)^(-1)*(1/epsilon_g-1))*((T_m4+273)^4- (T_g4+273)^4)

   y_4=h_w*(T_g4- T_a)*3.14*D_g+sigma*3.14*D_g*epsilon_g*((T_g4+ 273)^4-(T_sky+273)^4)

   x_4=y_4 x_5=h_c_5*(T_m5-

   T_g4)*3.14*D_o+sigma*3.14*D_o/(1/epsilon_r+D_o* (D_g)^(-1)*(1/epsilon_g-1))*((T_m5+273)^4- (T_g5+273)^4)

   y_5=h_w*(T_g5- T_a)*3.14*D_g+sigma*3.14*D_g*epsilon_g*((T_g5+ 273)^4-(T_sky+273)^4)

   x_5=y_5

   Correction of overall heat transfer coefficient" U_correct1=x_1/ (3.14*D_o*(T_m1-315.1)) U_correct2=x_2/ (3.14*D_o*(T_m2-315.1)) U_correct3=x_3/ (3.14*D_o*(T_m3-315.1)) U_correct4=x_4/ (3.14*D_o*(T_m4-315.1)) U_correct5=x_5/ (3.14*D_o*(T_m5-315.1))

   "Exit temperature of steam going to steam turbine c_po=4800[J/kgK]

   m_steam*c_po*(T_fo1-100) =Q_U1/1000 m_steam*c_po*(T_fo2-100) =Q_U2/1000 m_steam*c_po*(T_fo3-100) =Q_U3/1000 m_steam*c_po*(T_fo4-100) =Q_U4/1000 m_steam*c_po*(T_fo5-100) =Q_U5/1000

   "Instantaneous efficiency" eta_i1=Q_U1/ (S_mode1*W_a*L) eta_i2=Q_U2/ (S_mode2*W_a*L) eta_i3=Q_U3/ (S_mode3*W_a*L) eta_i4=Q_U4/ (S_mode4*W_a*L) eta_i5=Q_U5/ (S_mode5*W_a*L)

   LAT		Smode1	Smode2	Smode3	Smode4	Smode5
   630	82.5	99	154	360	346	376
   730	67.5	231	254	476	445	484
   830	52.5	328	335	489	451	490
   930	37.5	422	424	512	471	512
   1030	22.5	496	496	529	488	530
   1130	7.5	552	552	554	512	557
   1230	-7.5	525	525	527	487	529
   1330	-22.5	496	496	529	488	530
   1430	-37.5	443	445	537	495	537
   1530	-52.5	317	324	473	437	474

   LAT		Smode1	Smode2	Smode3	Smode4	Smode5
   630	82.5	99	154	360	346	376
   730	67.5	231	254	476	445	484
   830	52.5	328	335	489	451	490
   930	37.5	422	424	512	471	512
   1030	22.5	496	496	529	488	530
   1130	7.5	552	552	554	512	557
   1230	-7.5	525	525	527	487	529
   1330	-22.5	496	496	529	488	530
   1430	-37.5	443	445	537	495	537
   1530	-52.5	317	324	473	437	474

   Table 2. Calculated results of solar radiation flux for different tracking modes during LAT by EES software

   Mode I

   Mode II

   Mode IV

   Mode III

   Mode V

   Mode I

   Mode II

   Mode IV

   Mode III

   Mode V

   70

   Table 3.Calculated results of collector efficiency for

   different tracking modes during LAT by EES software 60

   LAT	z	i1	i2	i3	i4	i5
   630	73	0.22	0.39	0.576	0.57	0.582
   730	60.2	0.5	0.52	0.609	0.6	0.611
   830	47.2	0.56	0.57	0.612	0.6	0.612
   930	34.1	0.6	0.6	0.616	0.61	0.616
   1030	21	0.61	0.61	0.62	0.61	0.62
   1130	8.75	0.62	0.62	0.624	0.62	0.624
   1230	8.75	0.62	0.62	0.619	0.61	0.62
   1330	21	0.61	0.61	0.62	0.61	0.62
   1430	34.1	0.6	0.6	0.621	0.61	0.621
   1530	47.2	0.56	0.56	0.6	0.6	0.609

   LAT	z	i1	i2	i3	i4	i5
   630	73	0.22	0.39	0.576	0.57	0.582
   730	60.2	0.5	0.52	0.609	0.6	0.611
   830	47.2	0.56	0.57	0.612	0.6	0.612
   930	34.1	0.6	0.6	0.616	0.61	0.616
   1030	21	0.61	0.61	0.62	0.61	0.62
   1130	8.75	0.62	0.62	0.624	0.62	0.624
   1230	8.75	0.62	0.62	0.619	0.61	0.62
   1330	21	0.61	0.61	0.62	0.61	0.62
   1430	34.1	0.6	0.6	0.621	0.61	0.621
   1530	47.2	0.56	0.56	0.6	0.6	0.609

   50

   Incident Angle ( )

   Incident Angle ( )

   40

   30

   20

   10

   0

   1.02

   Mode V

   Mode V

   Mode II

   Mode II

   1

   Mode III

   Mode III

   0.98

   Mode IV

   Mode IV/p>

   Tilt factor (rb)

   Tilt factor (rb)

   0.96

   0.94

   Mode I

   Mode I

   0.92

   -10

   600 800 1000 1200 1400 1600

   LAT hr

   Figure 7 Incident angle versus LAT hr. June 10

   Mode III

   Mode V

   Mode IV

   Mode II

   Mode I

   Mode III

   Mode V

   Mode IV

   Mode II

   Mode I

   0.76

   0.75

   0.74

   Collector Efficiency

   Collector Efficiency

   0.73

   0.72

   0.71

   0.9

   600.0 800.0 1000.0 1200.0 1400.0 1600.0

   LAT hrs.

   Figure 5 Tilt factor versus local apparent time

   Mode IV

   Mode V

   Mode III

   Mode II

   Mode I

   Mode IV

   Mode V

   Mode III

   Mode II

   Mode I

   600

   550

   500

   Beam flux Incident (W/m2)

   Beam flux Incident (W/m2)

   450

   400

   350

   300

   250

   200

   150

   100

   600 700 800 900 1000 1100 1200 1300 1400 1500 1600

   LAT hr

   Figure 6 Beam flux incident versus LAT hr. for June 10

   0.7

   0.69

   600 800 1000 1200 1400 1600

   LAT h

   Figure 8 Collector efficiency versus Local Apparent time in hr. June 10

   [5.]Conclusion

   We observed from the graph and tabular data that shows Collector efficiency, Mode V>Mode III>Mode IV>Mode II >Mode I.

   • Mode V is highest efficiency but it is complicated operational control three axis and costly but we can be used for small scale power generation.

   • Mode IV is not economic for power generation because lesser efficiency as compared Mode III

   • Mode III and Mode II is the best tracking mode for large scale power generation.

   • Mode I is lowest efficiency thus it can be used for heating water and cooling purpose not for power generation.

Nomenclature

Aa Aperture area of the collector, [m2] Ar area of the receiver, [m2]

cpw Specific heat of water, [J/kg.K] cpa Specific heat of air at Ta , [J/kg.K]

Do outer diameter of receiver tube [m] Di Inner diameter of receiver tube [m] Tr Receiver temperature [K]

FR Collector heat-removal factor

S Direct normal (beam) irradiance, [W/m2]

Heat transfer coefficient inside the

Solar altitude angle

c Absorptance of the absorber surface coating Intercept factor

water Dynamic viscosity of water, [N.s/m2] air Dynamic viscosity of air, [N.s/m2]

References

[1.] Chia-Yen Lee, Po-Cheng Chou, Che-Ming Chiang and Chiu-Feng Lin, Sun Tracking Systems: A Review sensors ISSN 1424-8220

[2.] Duffie; J. A.; Beckman, W. A.: Solar

hfi

pipe,[W/m2.K]

Engineering of Thermal Processes; John Wiley & Sons, New York, Brisbane, USA, 1991, 2nd

Kss Stainless steel Thermal conductivity of pipe, [W/m.K]

Kf Thermal conductivity of water, [W/m.K] Kair Thermal conductivity of air , [W/m.K]

edition

[3.] Hossein Mousazadeh, Alireza Keyhani, Arzhang Javadi, Hossein Mobli, Karen Abrinia, Ahmad

Msteam

Mass flow rate of the steam [kg/s]

Sharifi, Renewable and Sustainable Energy

Reviews 13 (2009) 18001818

Collector efficiency factor

hw loss coefficient for wind

Tg Glass cover temperature,[K] Dg Diameter of glass cover ,[m] Dr Diameter of receiver ,[m]

n Day number

QU Solar collector useful output, [W/m2]

To Heat transfer fluid outlet (from the collector) temperature, [K]

Ti inlet temperature of fluid in the collector, [K] Ta Ambient temperature, [K]

Mean temperature of the heat transfer fluid

[4.] Saad D. Odeh & Hosni I. Abu-Mulaweh, Design and development of an educational solar tracking parabolic trough collector system, Global Journal of Engineering Education,

Volume 15, Number 1, 2013

[5.] Soteris A. Kalogirou, Solar Energy Engineering Processes and Systems, Academic Press is an imprint of Elsevier

[6.] SP Sukhatme, JK Nayak, Solar energy: Principles of thermal collection and storage Page no.206, Mc raw Hill

Tm across the collector or the solar field, [K]

V Wind speed, [m/s]

U Overall heat loss coefficient from absorber

L surface, [W/m2.K]

Wa Collector width, [m] Dimensionless groups

Nu Nusselt number

Pr Prandtl number

Ra Rayleigh number

Re Reynolds number Greek symbols

i Instantaneous efficiency

Emissivity coefficient

w Density of water, [kg/m3]

Reflectivity constant

Transmittance of the receiver glass envelope

[7.] Y. T. Chen, A. Kribus, B. H. Lim, C. S. Lim, K.

K. Chong, J. Karni, R. Buck, A. Pfahl and T. P. Bligh Comparison of Two Sun Tracking Methods in the Application of a Heliostat Field

,Journal of Solar Energy Engineering ,Volume 126 ASME,124:98