A novel stochastic energy analysis of a solar air heater: case study in solar radiation uncertainty

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 quantification 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.