GATE 2025 AG – Question 44
A south-facing flat-plate solar collector at Bhopal (23°15′N,77°42′E) is tilted 30° from horizontal. On June 30,2023 at 3 PM local apparent time, the hour angle is 45°. Find the beam incidence angle with the plate normal, in degrees, to two decimals.
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Correct answer: 53.00 to 53.50
Explanation
June 30 is day n=181. The usual declination approximation gives $\delta=23.45\sin[360(284+n)/365]=23.18449^\circ$. For a south-facing tilted surface,$\cos\theta=\sin\delta\sin(\phi-\beta)+\cos\delta\cos(\phi-\beta)\cos\omega$. With $\phi=23.25^\circ,\beta=30^\circ,\omega=45^\circ$,the incidence angle is **53.19°**. Longitude does not require a further time correction because local apparent time/hour angle are already supplied.