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Consortium for Mathematics and its Applications

Product ID: 99679
Supplementary Print
Undergraduate

The Solar Concentrating Properties of a Conical Reflector (UMAP)

Author: Don Leake


This module involves applications of solar energy optics. It contains a series of thirty-three problems that guide the reader in an analysis of the effect of adding a conical reflecting surfae to a circular solar radiation collecting disk.

Table of Contents:

INTRODUCTION
The Use of a Conical Reflector in a Solar-Powered Engine Design
Statement of Objectives

FUNDAMENTAL CONCEPTS
Characterization of the Reflecting Cone
Characterization of the Energy Carried by Solar Rays
Power Passing through the Aperture of the Cone

DIRECT RAY ANALYSIS
Fundamental Law of Reflection
Cone Parameters
Radii of Reflection
Concentrating Properties of Ideal Conical Reflectors
Nonideal Reflectors

OBLIQUE RAY ANALYSIS
Incoming Ray Description
Partitioning of the Aperture
Computing the Power of the Collector
Analytic Description of the Cone
Intersection of an Incoming Ray with a Cone
Intersection with the Collecting Disk
Inward Normal to the Cone Surface
Computation of the Direction of the Reflected Ray
New Intersection Point
Power Magnification

SUMMARY

ANSWERS TO THE PROBLEMS

REFERENCES

©1987 by COMAP, Inc.
UMAP Module
27 pages

Mathematics Topics:

Calculus

Application Areas:

Engineering & Construction , Environment & Sustainability , Physical Sciences , Solar Energy, Optics

Prerequisites:

Algebra, trigonometry, basic calculus, analytic geometry, elementary vector analysis

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