Modeling of the Thermal Output of a Flat Plate Solar Collector

Abstract

Traditionally, energy capture by non-concentrating solar collectors is calculated using the Hottel-Whillier Equation (HW): Q(u)=A(c)*F(r)*S-A(c)*F(r)*U(l)*(T(fi)-Tₐ), or its derivative: Q(u)=A(c)*F(r)*S-A(c)*F(r)*U(l)*((T(fi)-T(fo))/2-Tₐ). In these models, the rate of energy capture is based on the collector's aperture area (A(c)), collector heat removal factor (F(r)), absorbed solar radiation (S), collector overall heat loss coefficient (U(l)), inlet fluid temperature (T(fi)) and ambient air temperature (Tₐ). However real-world testing showed that these equations could potentially show significant errors during non-ideal solar and environmental conditions. It also predicts that when T(fi)-Tₐ equals zero, the energy lost convectively is zero. An improved model was tested: Q(u)=A(c)F(r)S-A(c)U(l)((T(fo)-T(fi))/(ln(T(fo)/T(fi)))-Tₐ) where T(fo) is the exit fluid temperature. Individual variables and coefficients were analyzed for all versions of the equation using linear analysis methods, statistical stepwise linear regression, F-Test, and Variance analysis, to determine their importance in the equation, as well as identify alternate methods of calculated collector coefficient modeling.