Elsayed in [18] also presented an analytical model based on long-term averaging of solar data. He outlined values of optimum tilt angles given in different literature and conducted that value of tilt angle that can be recommended. Some authors noted the existence of a correlation between the optimum tilt angle and the latitude. Authors of [19] determined monthly optimum tilt angles for Izmir, Turkey; they found the optimum tilt angle to be equal to U throughout the year, while for summer and for winter was suggested, these values were suggested also by [20].
They advised to mount the solar collector at the monthly average tilt angle. During the last decade there have also been investigations by using simulation software. This software which was developed in order to simulate an entire solar power plant, takes the most influential parameters into account. The soft ware usually possesses a database of monthly mean global radiation data and different empirical models: for example authors of [21] applied the simulation software TRNSYS to calculate the optimum tilt angle for Cairo, Egypt.
What they did was calculating the monthly mean of solar radiation data and compared it with the output power of solar cells. They stated the yearly optimum tilt angle to be 2. Some of the scattered sunlight is scattered back into space and some of it also reaches the surface of the earth.
This is also part of the diffuse radiation which the observer can see. This amount can be significant in areas in which the ground is covered with snow or reflectors. The total solar radiation on a horizontal surface is called global irradiance and it is the sum of incident diffuse radiation plus the direct normal irradiance projected onto the horizontal surface. If the surface under study is tilted with respect to the horizontal, the total irradiance is the incident diffuse radiation plus the direct normal irradiance projected onto the tilted surface plus ground reflected irradiance that is incident on the tilted surface.
As recommended by ASHRAE and presented in all text books of solar energy [22, 23], hourly global radiation hourly beam radiation hourly diffuse radiation and hourly reflect radiation on the inclined surface on a clear day are calculated using the following expression: 1 2 3 4 Where: is the beam normal radiation A is the apparent solar-radiation constant in B is the atmospheric extinction coefficient, and C is the diffuse sky factor and there values are tabulated in table 1 for a widely range of latitudes Table 1.
Meanwhile, is the view factor between the sky and the tilt surface and is the view factor between the ground and the surface that tilted at angle from the horizontal. These coefficients evaluated from: 5 for isotropic diffuse: 6 7 where: is the solar incident angle and it is given by: 8 where: is latitude, the angular location north or south of the equator, north positive; slope of the surface; is the surface azimuth angle, with zero due south, east negative, west positive, is the hour angle, morning negative, zero at noon and afternoon positive; and is solar declination angle, it can be found from: 9 where: is the Julian day.
Meanwhile, is the solar zenith angle, which equal to: 10 3. Results and Discussions A comprehensive computer program in FORTRAN has been created in order to calculate the hourly solar radiation incident on a surface when the tilt angle is changed by interval of The surface azimuth is either for south facing or for north facing.
In regard to the daily optimization, the basis is the daily total hourly radiation, for the monthly optimization the basis is the monthly total daily and for annual optimization the basis is the annual total monthly. It is well known that a unique surface tilt angle which exists for each time, and which corresponds to each latitude angle for a particular day through which the solar radiation is at peak value. Accordingly, this study enhances these two parameters as independent variables for the daily, monthly, seasonal and annual optimum angle prediction.
The seasonal average tilt angle was calculated by finding the average value of the tilt angle for each season, but the implementation of this condition requires the collector tilt to be changed four times a year. The process of adjusting the tilt angle to its monthly optimum values throughout the year does not seem to be practical, and at the same time rises the consideration of changing the tilt angle once seasonal.
The general form of the polynomial that prescribed the optimum tilt angle is expressed in fifth order three dimension as: 11 The coefficients and the variables and are defined below in table 2. Table 2. The definition of the coefficients P P 05 and the independent variables x, y for the offered polynomial The obtained results were plotted and tabulated for comparison with other measurements and data recommended by NASA.
Figure 1 presents the Daily optimum angles for various latitudes for a complete calendar year. The abscissa presents the Julian day The markets present the calculated results and the dash lines present the daily polynomial. Obviously, depending on figure 1, it can be stated that the polynomial is well fitted to the calculated data. The positive value depicted means that the surface was inclined towards the equator, where as the negative value means that the surface was inclined towards the North Pole.
The slopes were within the range of for any location on the northern hemisphere. Fig ure 1. Daily optimum angle as a function of the Julian day n and the latitude angle L. Figures 2 presents the optimum angles for monthly tracking from January to December.
From figure 2, the step-like lines present the calculated results, and the dash curves illustrate the polynomial equation that fitted the calculated data. Results were tabulated in table 4, for many cities from other references beside NASA data available on the internet to ease the comparison.
Table 3 shows a considerably agreement in results obtained by the offered polynomial with the local measurements specially for mid and high latitudes even in some times better than NASA's data. Unfortunately, for low latitudes the model needs to more arrangements. Fig ure 2. Monthly optimum angle as a function of the Julian day n and the latitude angle L.
Values of monthly optimum angles from many sources Table 4. That means December in the northern hemisphere will be June in the southern hemisphere. The months must be shifted every 6 months after the ordinary calendar.
Empirical models for the correlation of global solar radiation with meteorological data for Iseyin. Nigeria Int. B and Teliat, R. Correlations to estimate monthly mean of daily diffuse solar radiation in some selected cities in Nigeria. Advances in Applied Science Research, 2 4 Pelagia Research Library. Folayan CO Nigeria J. Solar Energy, 3: Gueymard, C. Evaluation of conventional and high-performance routine solar radiation measurements for improved solar resource, climatological trends, and radiative modeling.
Solar Energy 83, — Calculation of monthly average global solar radiation on horizontal for station five using daily hour of bright sunshine, Solar Energy,pp Hamdy K. Experimental and theoretical investigation of diffuse solar radiation: Data and models quality tested for Egyptian sites. An Introduction to solar radiation Academic press. New York pp. D and Kaltsounides, N. Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation.
Renewable Energy 31, — Klein S. Calculation of monthly average insulation on tilted surfaces. Sol Energy ; 43 3 — Krishnaiah, T. H and Jordan R. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation.
Sol Energy ; — Lopez, G. Martinez, M. Rubio, J. Torvar, J. Barbero and F. Batlles, Estimation of hourly diffuse fraction using a neural network based model. Mohandes, M. Balghonaim, M.
Kassas, S. Rehman and T. Halawani, Use of radial basis functions for estimating monthly mean daily solar radiation. Solar Energy, 68 2 : Munner, T. Second edition , Grear Britain, Okogbue E. C, Adedokun J. On the estimation of solar radiation at Ondo, Nigeria. Oliveira A. P, Escobedo J. F, Machado A. J, Soares J. Correlation models of diffuse solar radiation applied to the city of Sao Paulo, Brazil.
Appl Energy, 59— Orgill J. F and Holland K. Correlation equation for hourly diffuse radiation on a horizontal surface. Sol Energy,—9. Page, J. Prescott JA Evaporation from a water surface in relation to solar radiation. Sambo AS Solar radiation in Kano. A correlation with meteorological data. Solar Energy, 4: Sayigh AA Improved Statistical procedure for the Evaluation of solar radiation Estimating models. Solar Energy, Serm J and Korntip T A model for the Estimation of global solar radiation from sunshine duration in Thailand.
The joint international conference on Suitable energy and environment SEE , pp. Skeiker K Correlation of global solar radiation with common geographical and meteorological parameters for Damascus province, Syria. Energy conversion and management, Sodha M. S, Bansal N. K, Kumar K. P and Mali A. Solar Passive building: Science and design persanon Press, pp. Trabea A. Multiple linear correlations for diffuse radiation from global solar radiation and sunshine data over Egypt.
Renewable Energy — Contribution to the relationship between solar radiation of sunshine duration to the tropics, A case study of experimental data at Ilorin Nigeria, Turkish J. Physics Ulgen, K. Hepbasli, Estimation of solar radiation parameters for Izmir, Turkey.
Energy Res. Estimation of daily diffuse solar radiation in China. Renewable energy, Elisha B. Babatunde ISBN Hard cover, pages Publisher InTech Published online 21, March, Published in print edition March, The book contains fundamentals of solar radiation, its ecological impacts, applications, especially in agriculture, architecture, thermal and electric energy. Chapters are written by numerous experienced scientists in the field from various parts of the world. Apart from chapter one which is the introductory chapter of the book, that gives a general topic insight of the book, there are 24 more chapters that cover various fields of solar radiation.
This book aims to provide a clear scientific insight on Solar Radiation to scientist and students. How to reference In order to correctly reference this scholarly work, feel free to copy and paste the following: E. Falayi and A. Rabiu Duffie J. A, Beekman W.
A Solar Engineering of Thermal Processes, 2nd Edition. John Wiley, New York. EL-Sebaii A. A and Trabea AA Estimation of global solar radiation on horizontal surfaces over Egypt, Egypt J.
Solids, Erbs DG, Klein S. A and Duffie J. Estimation of the diffuse radiation fraction for hourly, daily and monthly average global radiation.
Sol Energ y,— Fagbenle R. O Estimation of total solar radiation in Nigeria using meteorological data Nig. Falayi E. O, Rabiu AB Modeling global solar radiation using sunshine duration data. Physics, 17S: Falayi, E. Adepitan and A. Rabiu, Empirical models for the correlation of global solar radiation with meteorological data for Iseyin. Nigeria Int. B and Teliat, R. Correlations to estimate monthly mean of daily diffuse solar radiation in some selected cities in Nigeria.
Advances in Applied Science Research, 2 4 Pelagia Research Library. Folayan CO Nigeria J. Solar Energy, 3: Gueymard, C. Evaluation of conventional and high-performance routine solar radiation measurements for improved solar resource, climatological trends, and radiative modeling.
Solar Energy 83, — Calculation of monthly average global solar radiation on horizontal for station five using daily hour of bright sunshine, Solar Energy,pp Hamdy K. Experimental and theoretical investigation of diffuse solar radiation: Data and models quality tested for Egyptian sites. An Introduction to solar radiation Academic press. New York pp. D and Kaltsounides, N. Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation.
Renewable Energy 31, — Klein S. Calculation of monthly average insulation on tilted surfaces. Sol Energy ; 43 3 — Krishnaiah, T. H and Jordan R. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Sol Energy ; — Lopez, G. Martinez, M. Rubio, J. Torvar, J. Barbero and F. Batlles, Estimation of hourly diffuse fraction using a neural network based model. Mohandes, M. Balghonaim, M. Kassas, S. Rehman and T. Halawani, Use of radial basis functions for estimating monthly mean daily solar radiation.
Solar Energy, 68 2 : Munner, T. Second edition , Grear Britain, Okogbue E. C, Adedokun J. On the estimation of solar radiation at Ondo, Nigeria. Oliveira A. P, Escobedo J. F, Machado A. J, Soares J. Correlation models of diffuse solar radiation applied to the city of Sao Paulo, Brazil. Appl Energy, 59— Orgill J. F and Holland K. Correlation equation for hourly diffuse radiation on a horizontal surface.
Sol Energy,—9. Page, J. Prescott JA Evaporation from a water surface in relation to solar radiation. Sambo AS Solar radiation in Kano. A correlation with meteorological data. Solar Energy, 4: Sayigh AA Improved Statistical procedure for the Evaluation of solar radiation Estimating models. Solar Energy, Serm J and Korntip T A model for the Estimation of global solar radiation from sunshine duration in Thailand.
The joint international conference on Suitable energy and environment SEE , pp. Skeiker K Correlation of global solar radiation with common geographical and meteorological parameters for Damascus province, Syria. Energy conversion and management, Sodha M.
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