Flow area structure generation in point to area or area to point flows

Abstract

This paper deals with the constructal theory of generation of shape and structure in flow systems connecting one point to a finite size area. A cost minimization model has been used in optimization of point to area or area to point flow problems. The cost minimization model enables one to predict the shape of the optimized flow areas, but the sizes of the flow areas are not predictable. The aim of this paper is to optimize the point to area or area to point flow problems in various elemental flow area shapes and structures. The elemental flow area shapes used in this paper are either rectangular or triangular. The forms of flow area structure, made up of an assembly of optimized elemental flow areas, are rectangle-in-rectangle, rectangle-in-triangle, triangle-in-triangle and triangle-in-rectangle. We have examined more complex flow area structures in higher order assembly stages. The global minimum cost has been derived for each flow area structure, and the results have been compared with each other. The conclusion is that the rectangle-in-(triangle-in-…) flow area structure results in a smaller global minimum cost relative to the other structures.