Thermal performance of solar air heaters: Mathematical model and solution procedure

Abstract

A mathematical model and solution procedure for predicting the thermal performance of single-pass solar air collectors is presented. By omitting or providing a top glass cover over a plane absorber plate, or by providing a bottom plate under the absorber plate and circulating air over one or both of the air channels so formed, four common types of flat-plate solar air collector designs were considered. The surface temperatures of the walls surrounding the air streams were assumed uniform whereas the air temperatures were assumed to vary linearly along the collector. In the mathematical model, the solar collector was assumed sufficiently short for which the assumptions were valid. By considering a steady state heat transfer using the thermal network analysis procedure, a set of simultaneous equations for the mean temperature of the walls and the air streams were obtained. Instead of solving the simultaneous equations for mean temperatures explicitly, a matrix inversion method was employed using a standard sub-routine programme. Because heat transfer coefficients were temperature dependent, a set of mean temperatures was approximated which allowed the heat transfer coefficients to be evaluated as a first guess. An iterative process was then created that enabled the mean temperatures for the collector to be calculated. The newly-calculated mean temperatures were then compared with the initially-guessed temperatures. The iterative procedure was repeated until consecutive mean temperature values differed by less than 0.01°C. After this, another section of collector with a length equal to the previous one was added to the end of the first collector. The temperature conditions at the inlet of the second section were assumed equal to the outlet temperature conditions of the previous section. The iterative procedure to determine the mean temperatures was repeated for the next section. Additional sections were added until the required overall length of collector was considered. By this procedure, predictions of mean wall and air streams temperatures for a collector of any length could be obtained. Although only four, common single-pass types of flat-plate solar collectors are considered here, the solution procedure could be extended to encompass most other collector designs.