Circumferential Variations of Bore Heat Flux and Outside Surface Temperature for a Solar Collector Tube

An analysis is made of the heat transfer processes in a solar collector tube subjected to large circumferential heat flux variations on its outer surface. The analysis is carried out for a collector plate configuration in which the tubes are situated in embossments in the otherwise flat surface of the plate. The solar energy absorbed by the collector plate is conducted to the tubes and gives rise to large heat flux spikes at discrete circumferential locations on the outer surface of a tube. The two-region heat conduction problem encompassing the embossed portion of the collector plate and the tube is solved by a novel procedure which provides closed form solutions of high numerical accuracy. The influence of system dimensions, thermal properties, and tube bore convection is examined by means of five dimensionless parameters, of which the Biot number was found to be the most important. The results showed that for realistic dimensions and thermal properties of the plate and tube, circumferential variations of the outside surface temperature and bore heat flux can be neglected, provided that the tube flow is laminar. For turbulent flow conditions, the variations in bore heat flux are substantially greater than for laminar flow.