Calculation of the concentrated flux density distribution in parabolic trough collectors by a semifinite formulation

Abstract

A first integral of the concentrated radiant flux density for trough concentrators is derived by exploiting the symmetry of these cylindrical systems. The resulting semifinite formulation yields both conceptual advantages and computational efficiency. The formulation is illustrated by application to the parabolic trough concentrator. The elementary example of determining the concentrated flux density at the nominal focal plane is first considered. The more realistic case of a round absorber tube, which can shade the reflector, centered on the focal line is also studied. This more practical geometry, which corresponds to most commercial designs, has previously received little attention in the open literature. These applications illustrate that the semifinite formulation presented herein can be a simple and useful tool for the analysis and design of trough concentrators.