Analytical expression for circumferential and axial distribution of absorbed flux on a bent absorber tube of solar parabolic trough concentrator

A parabolic trough has a property to concentrate the incident rays at its focal line, when tracked appropriately. The flux distribution on the absorber tube is non-uniform. Part of the absorber's periphery facing the sun receives direct incident rays where as part of the other side receives concentrated rays resulting in circumferential non-uniform flux distribution. The intensity of flux also varies along the length of the absorber tube, especially at the sun facing end, depending upon the incidence angle of the sun rays and rim angle of the parabolic cylinder. Such non-uniformity in the flux distribution on the absorber tube leads to non-uniform temperature distribution. Thus the absorber experiences thermal stresses which may lead to bending of the tube thereby creating risk of glass cover damage. In order to estimate the extent of bending, study of the flux distribution is needed. In the present work, expression for the absorbed flux on a bent absorber tube accounting circumferential and axial variations is analytically derived. Optical errors and Gaussian sun shape have also been incorporated. Results have been plotted to study the effect of bending, optical errors and rim angle of the trough on flux distribution.