IJSER. f(φ). Duffie and Beckman [1] recommended that optimum. Figure 1: beam radiation on horizontal and tilted surfaces [1]. local latitude.

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1 International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July ISSN OPTIMUM TILT FOR SOLAR COLLECTORS IN RAJSHAHI, BANGLADESH 1 Debazit Datta, M. Jamal Hossain, 3 Bimal Kumar Datta Abstract: Incient solar irraiation of photovoltaic collector is affecte by tilt an azimuth angles. This stuy measures the optimum tilt an azimuth angles for Photovoltaic Applications at Rajshahi in Banglaesh on yearly an seasonal bases. The result shows optimum tilt angles for PV applications. This stuy fins that optimum tilt angle is as the local latitue at Rajshahi for gri connecte PV system to obtain maximum yearly energy generation where energy increment rate is 8.1% than horizontal raiation. Seasonal optimum tilt is foun as 50 egree for months November-February an 10 egree for months April-September, 30 egree for March & October. Energy prouce is 4.4% more than that of annual optimum tilts. Keywors: Energy policy, tilte raiation, optimum tilt, surface orientation, annual tilt, seasonal tilt, increment rate INTRODUCTION: The techniques for estimating typical solar raiation on tilte surfaces of various irections can be use to show the special effects of slope an azimuth angle on total energy receive on a surface on a monthly, seasonal or annual basis. The surface irection leaing to highest output of a solar energy structure may be fairly ifferent from the orientation leaing to maximum incient energy. For solar energy purposes, the most favorable orientation is usually recommene to be south facing in the northern hemisphere an the optimum tilt epens simply on the local latitue, β opt = f(φ). Duffie an Beckman [1] recommene that optimum tilt is within the range (φ ± 15 eg) ± 15ewhere φ is the local latitue RATIO OF BEAM RADIATION ON INCLINED TO THAT ON HORIZONTAL SURFACE: The geometric factor,, the ratio of beam raiation on the tilte surface to that on a horizontal surface at any time, can be calculate exactly from the following equation. Figure 1 inicates the angle of incience of beam raiation on the horizontal an tilte surfaces [1]. Figure 1: beam raiation on horizontal an tilte surfaces [1]. 1Department of Mathematics, International University of Business Agriculture an Technology, Banglaesh. Department of Applie Mathematics, Noakhali University of Science an Technology, Banglaesh. 3Department of Mathematics, Pabna University of Science an Technology, Banglaesh. Christensen an Barker [4] foun that surface tilt angles an azimuth angles can be varie over a significant range without consierably ropping the amount of yearly incient irraiation. Prior to this work, a stuy was one to fin the optimum orientation of solar collectors at Dhaka, Banglaesh an has been foun 30 egree for optimum tilt at that location [11]. Then this stuy aims to check any ifference in optimum tilt at Rajshahi where solar raiation intensity is maximum than any other locations of Banglaesh [1]. The ratio is given by = G b,t = G b,n cosθ = cosθ (1) G b G b,n cosθ z cosθ z where, cosθ = sinδ sinφ cosβ sinδ cosφ sinβ cosγ + cosδ cosφ cosβ cosω + cosδ sinφ sinβ cosγ cosω + cosδ sinβ sinγ sinω an cosθ z = cosφ cosδ cosω + sinφ sinδ The best azimuth angle for solar collectors is usually 0 0 in the northern hemisphere. Thus, upon simplification equation (1) reuces to cos(φ β) cosδ cosω + sin(φ β) sinδ = () cosφ cosδ cosω + sinφ sinδ But accoring to Liu an Joran [10] R b is calculate from R b = cos(φ β)cosδsinω s + π 180 ω s sin(φ β)sinδ cosφcosδsinω s + π (3) 180 ω s sinφsinδ Where, ω s enotes the sunset hour angle an is taken to the smaller value from 014

2 International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July ISSN ω s = cos 1 ( tanφtanδ) (4) H H = K 3 T K T.137K T (6) ω s = cos 1 ( tan(φ β)tanδ) METHODOLOGY FOR THE OPTIMUM TILT: We now calculate the tilte raiation when the total horizontal raiation is known. For this we require the irections from which the beam an iffuse parts arrive at the surface. The irection from which iffuse raiation is receive, i.e., its circulation over the sky ome, is a function of conitions of clouiness an atmospheric clarity, which are mostly unpreictable. The tilte raiation is the sum of a set of raiation streams incluing beam raiation, the three parts of iffuse flux from the sky, an raiation reflecte from the ifferent surfaces seen by the tilte surface. The total raiation on this surface can be written as H T = H 1 H H R b + H 1 + cosβ + H ρ g 1 cosβ (5) Where, H is the monthly average aily iffuse raiation, R is b the monthly average aily geometric factor for beam raiation, β is the slope of the surface an ρ g is the iffuse reflectance for the total solar raiation of the location.the surface view factor to the sky is 1+cosβ an the surface view factor to the groun 1 cosβ An for ω s > an 0.3 K T 0.8 H H = K T K T 1.81K T 3 etermine. (7) For known an H H ratio, monthly average aily raiation on tilte surface was calculate. For a fixe orientation, the optimum tilt angle can be foun by solving the following equation for β β (H ) T = 0 (8) Now, since iffuse an groun reflecte parts are negligible, the above equation turns into β (R ) b = 0 (9) sin(φ β)cosδsinω s π 180 ω s cos(φ β)sinδ cosφcosδsinω s + π 180 ω s sinφsinδ (π 180 β = φ tan 1 )ω s sinδ (10) cosδ sinω s = 0 For fixe values of φ, ω s an δ for a particular month at a specific location, the optimum tilt angle is easily RESULTS AND DISCUSSION Figure : Beam, iffuse an reflecte solar raiation on tilte surface [1] The first step to calculate the average monthly tilte solar raiation is to calculate using equation (3) an the relationship H H from the measure ata or using any of the correlation moels. Equations consiere in this stuy for these correlations are as follows [9]: For ω s an 0.3 K T 0.8 TOTAL ENERGY RECEIVED ON ANNUAL BASIS: Fining the local annual optimum tilt angle is significant in etermining the optimum orientation. The maximum energy obtaine at south facing azimuth angle with latitue oriente slope as shown in figure 4. Compare with horizontally place PV collectors, the moules with optimum slope can generate 8.1% more power. Upon etermine the tilt factors by using equation (3), figure 3 presents graphically for the months for ifferent orientations. Table 1: Tilt factor an monthly average tilte raiation for latitue oriente an optimum oriente for annual optimum power output Month Tilt factor Monthly average Tilte Tilt factor (β = φ) Monthly average Tilte raiation Tilt factor (β = 30 0 ) Monthly average Tilte raiation(mj m ) 014

3 International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July ISSN (β = 0 0 ) raiation (MJ m ) (MJ m ) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual total annual total tilte raiation for ifferent tilts, where it has been foun that for tilt equal to local latitue, the annual total solar raiation is highest. Figure 5: Annual total solar raiation (MJ m ) vs tilt Figure 3: Tilt factor vs months of year for fixe slope Total energy receive on seasonal basis: If we ivie the whole year into two ifferent categories on the basis of high an low tilt factor then we get an optimum tilt angle as 50 egree for the months November-February, 10 egree for the months April-September an 30 egree for the months March & October. Energy obtaine in this case is 4.4% more than the energy obtaine for annual optimum tilt. Figure 4: solar raiation (MJ m ) vs months for fixe orientation throughout the year The yearly collecte solar raiation reuces sharply when the slopes excee 40 eg. Figure 5 shows bar charts of 014 Figure 6: Tilt factor vs months of year for variable slope (Tilt for Apr-Sep is 10 egree an Nov-Feb is 50 egree an for March & October 30 egree)

4 International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July ISSN Seasonal % 4.4% optimum Figure 7: Tilte Solar raiation (MJ m ) vs months of year for variable slope (Tilt for Apr-Sep is 10 egree an Nov- Feb is 50 egree an for March & October 30 egree) Figure 10: energy (MJ m ) output for three ifferent orientations It is seen from figure 10 that maximum power is generate for monthly optimum tilt. Seasonal tilt energy output is nearly equal to that of monthly output. Table 3: Energy increment rate at ifferent orientations Surface Annual Increment Increment orientation total rate than rate Energy (MJ m ) horizontal than annual oriente Horizontal (tilt=0) Annual optimum (tilt=4.37) % 014 Table 3 shows the increment rate of power prouce over ifferent types of surface orientations for annual fixe, seasonal fixe an monthly variations. Annual optimum (β = ) energy is increase at a rate of 8.1% than horizontal orientation. Seasonal (β = 10 0 for Apr-Sep an 50 0 for Nov-Feb an 30 0 for March & October) optimum energy is increase 4.4% than annual optimum energy obtaine. CONCLUSION: The efficiency an performance of solar collectors an Photovoltaic systems epen on the moule s orientation. The Photovoltaic collectors shoul be tilte in an appropriate manner to obtain the utmost raiation. In this stuy it is foun that optimum tilt angle in Rajshahi is equal to the local latitue of φ = 4.37 eg for both stan alone an gri connecte PV system to obtain maximum Figure 8: Optimum tilt for ifferent months of the year yearly energy generation. Seasonal optimum tilt reaches to 50 egree for months (November-February) an 30 0 for March & October an 10 egree for months (April - September). If the slopes coul be ajuste monthly, the power efficiency woul likely be much better. REERENCES [1]Duffie J. A., an Beckman. W.A., 1980, Solar Engineering of Thermal processes, John Wiley & Sons, New York. Figure 9: Tilt factors vs months for monthly optimum tilt [] Lewis. G., 1987, Optimum Tilt of Solar Collectors, Solar an Win Energy, 4, pp, [3] Asl-Soleimani, E., Farhangi, S., an Zabihi, M.S., 001, The Effect of Tilt Angle an Air Pollution on Performance of Photovoltaic Systems in Tehran, Renewable Energy, pp [4] Christensen. C.B. an Barker. G. M., 001, Effects of Tilt an Azimuth on Annual Incient Solar Raiation for Unite States Locations, Solar Engineering 001, the Power to Choose April 1-5, Washington, DC. [5] Hongxing Yang an Lin Lu, The Optimum Tilt Angles an Orientations of PV Claings for Builing Integrate Photovoltaic (BIPV) Applications, Journal of Solar Energy Engineering, May 007, Vol. 19/ 53. [6] H. R. Ghosh, N. C. Bhowmik, M. Hussain, Determining seasonal optimum tilt angles, solar raiations on variously oriente, single an ouble axis tracking surfaces at Dhaka, Renewable Energy, vol. 35, no.6, June 010, pp [7] Country Report of Solar an Win Energy Resource Assessment, Banglaesh, supporte by UNEP, GEF. [8] NASA surface Meteorology an Solar Energy. [9] Collares Pereira, M an A. Rabl, Solar Energy,, 155 (1979a), The Average Distribution of Solar raiation Correlations between Diffuse an Hemispherical an between Daily an Hourly Insolation Values.

5 International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July ISSN [10] B.Y.H. Liu an R.C. Joran, the interrelationship an characteristic istribution of irect iffuse an total solar raiation, Solar energy, 1960, 4(3), [11] Debazit Datta, Dr. Himangsho Ranjan Ghosh, Saaia Binte Alam, Utpal Kanti Das, Arijit Sen, Surface orientations an Energy Policy for Solar Moule Applications in Dhaka, Banglaesh, International Journal of Scientific an Engineering Research, Volume 5, Issue, February 014, [1] Debazit Datta, Suman Chowhury, Apurba Kumar saha, M. Moksu Islam Lalan, Mohamma Mahbubur Rahaman, Tilte an Horizontal Solar Raiation for 6 zones in Banglaesh, International Journal of Scientific an Technology Research, volume 3, issue February 014,