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.

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