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Solar concentrators with maximal concentration for cylindrical absorbers.

|February 19, 2010

Summary

This study derives a differential equation for ideal 2D radiation concentrators with convex absorbers. A closed-form solution is found for circular absorbers, and reflector absorption effects are analyzed.

Area of Science:

Optics and Photonics
Mathematical Physics

Background:

Radiation concentrators are crucial for solar energy and other applications.
Designing efficient concentrators requires precise mathematical modeling.

Purpose of the Study:

To derive a differential equation for ideal 2D radiation concentrators with arbitrary convex absorbers.
To analyze the impact of reflector absorption on radiation attenuation.

Main Methods:

Derivation of a differential equation governing the reflector's geometry.
Analytical solution of the equation for a circular absorber using specialized coordinates.
Formulation of equations to quantify radiation attenuation due to reflector absorption.

Main Results:

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A general differential equation for the reflector shape is established.

A closed-form solution is obtained for circular absorbers.

Formulas for radiation attenuation are presented, accounting for reflector absorptivity.

Conclusions:

The derived mathematical framework enables the design of ideal 2D radiation concentrators.
The analysis provides a method to quantify performance losses due to reflector absorption.