Volume 7, Issue 3, March 2018


A Normalized Mathematical Model for Optimum Tilt Angles Based on the Desired Solar Fraction

Authors: Ala Elwani, Elhadi Dekam, Khairy Agha

Abstract- This paper presents a normalized mathematical model that determines the basic factors influencing domestic solar water heating systems, and in specific, discusses the optimum design time as well as the optimum tilt angle of the solar collector, bearing in mind the contribution of the energy obtained to meet the targeted load. The paper considers the required thermal capacity that should be provided by the solar collector. The study is thoroughly based on normalized mathematical parameters. In the case of 100% solar contribution, for heated water temperature of 45oC and consumption of 100 liters/Person per day for a given house sited at Tripoli city, 32.68°N latitude, the optimum design time is the month of December, the optimum tilt angle is 75°, and the solar collector area, fulfilling the following specifications: glazed type, Fr. (τα) = 0.58, a (d Fr UL=4.0(W/m2 . oC), is 2.83 m2 . The results designate an optimum tilt angle of 50°, which is the same angle obtained by the traditional famous technique, and solar collector area of 1.6 m 2 if up to 80% of demand is to be covered by solar energy. Results obtained by RETScreen commercial computer package are compared and validated.

Keywords- Domestic Water Heating Systems, Optimum Tilt Angle, Solar Fraction, Solar Collector Area, Capacity Of Storage Unit.


[1] Agha, k. R. and Sbita, M. N., “On the sizing Parameters of Alone Solar Energy Systems”, Journal of Applied Energy, Vol. 65, 2000, PP. 73-84.

[2] Khasawneh, Q. A., Damrab, Q. A., and Salmanb, O. H. B., Determining the Optimum Tilt Angle for Solar Applications in Northern Jordan, Jordan Journal of Mechanical and Industrial Engineering Volume 9 Number 3, June-2015, Pages 187 – 193.

[3] Zang, H., Wei, M. G. Z., and Sun, G., Determination of the Optimal Tilt Angle of Solar Collectors for Different Climates of China, Journal Of Sustainability, 11 July 2016.

[4] Wessley, J. J. G., Narciss Starbell, R., and Sandhya, S., Modelling of Optimal Tilt Angle for Solar Collectors Across Eight Indian Cities, International Journal Of Renewable Energy Research, Vol. 7, No. 1, 2017.

[5] Baccoli, R., Mastino, C.C., Innamorati, R., Serra, L., Curreli, S., Ghiani, E., Ricciu, R., and Marini, M., A mathematical model of a solar collector augmented by a flat plate above reflector: Optimum inclination of collector and reflector, Elsevier Ltd., 2015.

[6] Wang, S., and Hong, B., Optimum Design of Tilt Angle and Horizontal Direction of Solar Collectors under Obstacle’s Shadow for Building Applications, Journal of Building Construction and Planning Research, 2015, 3, 60-67.

[7] Beckman W. A., Klein S. A., and Duffie J. A., A design procedure for solar heating systems, Solar Energy, 1976; 18:113.

[8] Klein S. A. and Beckman W. A., A general design method for closed-loop solar energy systems, Solar Energy, 1979; 22:269.

[9] Mean monthly solar radiation measurements during the period of 1981-1984, information department, Center for Solar Energy Studies, Tripoli, Libya.

[10] Mean monthly temperature data during the period of 1945-1984, meteorological department, international Report, Tripoli, Libya.

[11] Hsieh, J. S., Solar Energy Engineering, Prentice-Hall, Inc. (1986).

[12] Elwani, A. B., “On Sizing The Main Components Of Solar Domestic Water Heating Systems Under Different Meteorological And Load Conditions”, M. Sc. Thesis, Mechanical and Industrial Engineering Department, University Of Tripoli, Tripoli, Libya, 2013.

[13] RETScreen energy model, Solar Water Heating Project, www.retscreen .com

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