Energy Syst
https://doi.org/10.1007/s12667-017-0263-7
ORIGINAL PAPER
A novel stochastic energy analysis of a solar air heater:
case study in solar radiation uncertainty
Hamed Johnny Sarnavi
1
· Ali M. Nikbakht
1
·
Ali Hasanpour
1
· Feyzollah Shahbazi
2
·
Niccolo Aste
3
· Fabrizio Leonforte
3
Received: 10 April 2017 / Accepted: 13 November 2017
© Springer-Verlag GmbH Germany, part of Springer Nature 2017
Abstract There is a growing recognition of the fact that solar energy utilization plans
cannot be carried out without explicitly accounting for the uncertainty presented in
the received solar irradiation. This may be expressed as an uncertainty quantifica-
tion problem. A novel stochastic energy analysis is introduced to study the transient
heat transfer problem of a typical flat plate solar air heater, based on the polynomial
chaos expansion approach. The constructed model was equipped with the numerical
finite difference method and the Galerkin projection scheme in the random space.
The numerical model was verified against the available exact analytical solutions. The
results of polynomial chaos method was compared to corresponding basic Monte Carlo
sampling results. Finally, a case study with realistic solar irradiance data of Urmia, a
cold climate city in Iran, was conducted for a typical solar air heater. Afterward, the
outlet temperature of the air heater was tracked in a probabilistic framework, to find the
reliable hours for extracting solar energy stably during a typical summery day. These
hours were found between 11 am to 5 pm.The proposed approach could be highly
worthwhile in the designing and contriving control plans taking into consideration the
non-negligible uncertainty of solar radiation.
Keywords Solar energy · Air heater · Stochastic modeling · Radiation uncertainty
B Ali M. Nikbakht
a.nikbakht@urmia.ac.ir
1
Department of Mechanical Engineering of Biosystems, Urmia University, PO.Box: 165, Urmia,
Iran
2
Department of Mechanical Engineering of Biosystems, Lorestan University, Khorramabad, Iran
3
Department of Architecture, Built Environment and Construction Engineering, Politecnico di
Milano University, Milan, Italy
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