Analytical methods for evaluating two-dimensional effects in flat-plate solar collectors

Presently, there exist significant discrepancies between experimental and theoretical predictions of flat-plate solar collector performance. There is a need to identify both those areas of analysis which need improvement as well as those which are already adequate.

Two new methods of absorber-plate thermal analysis which can be used within the framework of existing theory were developed. The first method used the separation of variables technique in a unique manner to solve exactly for the coupled axial and transverse temperature distributions in an absorber plate-tube assembly. The conventional assumption of an overall uniform loss coefficient U_L was used in the analysis. The first method is practical only for parallel-flow collectors. The second method used two sectionally uniform loss coefficients -- U_LI for internal collector sections and U_LE for edge sections -- to evaluate collector performance. The second method is applicable for both parallel-flow and serpentine configurations.

The validity of two assumptions commonly made in flat-plate collector analysis was investigated using the new methods. The first assumption that was investigated involved the approximate treatment of the effect of axial conduction on the absorber-plate temperature distributions. Results from the first new method were graphically compared to the predictions of approximate analytical treatments given by Whillier and Phillips. The comparisons showed that, for conventional flat-plate designs, the method given by Phillips yields values of the heat removal factor F_R accurate to within 1 per cent. The more commonly used method given by Whillier is accurate to within 10 per cent for conventional designs. The second assumption that was investigated dealt with the manner in heat losses from the collector peripheral area are taken into account. Results from the second new method indicated that, for typical collector designs, the conventional edge loss treatment yields values of instantaneous collector efficiency n_c accurate to within 3 per cent absolute and 15 per cent relative. Analysis of the net effect of the two improvements indicated that approximate axial and edge-loss treatments are not the primary source of error between experimental and theoretical results for typical collectors.

The solution technique developed in the first new method has potential applications to a number of conduction-convection problems. The second new method has the inherent capability to better evaluate performance and design questions related to edge effects.

Convenient relations between the mean plate and fluid temperatures and the heat removal factor F_R were obtained. The relations apply for parallel-flow analysis under the assumption of a uniform loss coefficient U_L.