An upscaled model for heat transport in a parabolic trough collector

Parabolic trough collectors are important devices of practical use that profit from solar radiation. Currently, modeling this type of systems is mostly performed using direct numerical simulations where the governing equations at the microscale are solved in time and space, which demands considerable computational time. An alternative is to systematically reduce the number of degrees of freedom by developing upscaled models. The main finding of this work is that an upscaled model is a reliable approach to study heat transfer in the receiver tube of a parabolic trough collector. The model was derived using the volume averaging method, by capturing the essential microscale information in a cross-sectional averaging process. The model consists on a partial differential equation that accounts for the (axial) spatio-temporal changes of the average temperature and it is written in terms of four effective-medium coefficients that are predicted from the solution of two ancillary closure problems. The functionality of these coefficients with the Biot number was adjusted using a fractional function, which are the second main finding of this work. In addition, the model was validated by comparisons with direct numerical simulations (DNS). The model derived here is shown to perform adequately (i.e., with a relative error with respect to DNS smaller than 5%) under the desirable operating conditions of the system and this constitutes the third main finding of this work.