Abstract
A mathematical model has been derived and used to develop a three-dimensional concentrating solar collector as presented in this article. The developed solar collector gives the required flux distribution along the longitudinal direction of tubular absorber. The model requires inputs like the profile of required flux distribution, local solar flux, dimensions of the absorber, and the distance of absorber from the reflector. The model is developed under the most common assumptions and showed a high validity of 99.99%. The effects of inputs on the design geometrical parameters such as curvature, steepness, surface area, and aperture diameter, which affect the manufacturing, space limitations, and cost analysis, are presented and discussed. It is shown that decreasing the initial radius, solar flux, and slope of flux distribution required at the absorber surface results in a less steep reflecting surface (RS), which is also favored with increase in absorber's radius and initial angles. Smaller reflecting surface area can be obtained by using larger values of initial radius, solar flux, and slope of the absorber flux distribution. Smaller initial curvatures can also be obtained by increasing initial angle, absorber's radius, and slope of flux distribution. Decreasing the initial radius, initial angle, and absorber's radius can limit the aperture's diameter such that it could fit the space limitation. Locations' high solar flux would reduce the aperture's diameter.