Mathematical Modeling of Heat Losses from Cylindrical Cavity Receiver in Solar Parabolic Dish

Abstract

The recent experimental investigations on model receiver with constant heat flux boundary condition have shown that the temperature profile along the cavity walls is non-uniform and seen to vary with cavity inclination. This paper presents a mathematical analysis of heat losses from cylindrical cavity receiver applied to constant heat flux boundary conditions. In addition, the empirical correlations for the radiation Nusselt number and total heat loss Nusselt numbers, with its influencing parameters like Grashof number (\({\text{Gr}}\)), cavity inclination angle \((\theta )\), temperature ratio \(\left( {T_{\text{a}} /T_{\text{w}} } \right)\), and conductance parameter (\(\gamma ),\) are proposed. The mathematical analysis and empirical correlations are based on experimental results in previous published data. In mathematical analysis, the heat loss by natural convection is observed to be more sensitive to the cavity inclination angle in comparison with heat loss by radiation and conduction. The heat loss by radiation and conduction are not constant as initially estimated; they increase with increase in cavity inclination. It led us to conclude that it may not be accurate to predict convection heat loss using previously developed correlations based on the isothermal wall condition. Secondly, even though the variation in heat loss by radiation and conduction with cavity inclination is small, it needs to be considered for accurate design of solar parabolic dish receiver system.