The Use of an Artificial Diffusion Term to Improve a Distributed-Parameter Model of a Flat-Plate Solar Collector

Two models for the temperature distribution within a flat-plate solar collector are investigated. The simpler of the two (the one-temperature model) is a distributed-parameter model that determines the temperature of the collector fluid without reference to the temperature of the collector plate. The more accurate model of the two (the two-temperature model) takes into consideration the temperatures of both the collector plate and the fluid. In previous work the authors showed how the solutions of the two-temperature model tend to the solutions of the one-temperature model as the thermal coupling between the fluid and the collector plate increases. In the present work we include an artificial diffusion term in the one-temperature model. We show that this diffusion term causes the solutions of the one-temperature model to better approximate those of the more accurate two-temperature model. In essence, the artificial diffusion term produces effects similar to those caused by the thermal coupling between the fluid and the collector plate, which is not accurately modeled in the original one-temperature model. In realistic collectors the value of the diffusivity associated with this artificial diffusion term is much smaller than the diffusivity of the collector fluid, which we neglect in all models under consideration. Graphical results further demonstrate the good agreement between the revised one-temperature model and the two-temperature model.