Mathematical methods for the optimization of solar collector area in a solar heating system

Abstract

Economic optimization procedure in particular solar heating design is based on the estimation of the size of a solar system in terms of collector area that will yield the highest total saving produced on behalf of the solar system in comparison with the total expenditures of a conventional alternative during the life-cycle. The most influential design parameter in a total saving is considered to be the collector area. A case study is then realized so as to find the optimum collector area for maximum saving. Saving function for a particular system is defined. Optimum collector area is considered to be the one which makes zero the first derivative of saying function with respect to the collector area. To this end three different methods, namely, Newton's, Secant and Regular falsi are applied for a variety of changes in values for design, climatic and economic parameters. Finally, the ability to use these methods are discussed from the computational point of view.