Premium
Optimization of the protrusion shape for a couette‐type flow
Author(s) -
Kacimov A. R.
Publication year - 1994
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660150304
Subject(s) - conformal map , mathematics , maxima and minima , constant (computer programming) , mathematical analysis , cauchy distribution , type (biology) , domain (mathematical analysis) , flow (mathematics) , boundary value problem , flux (metallurgy) , geometry , geology , computer science , materials science , paleontology , metallurgy , programming language
A study is made of the longitudinal 2D viscous steady flow and heat flux between two plates. Optimal shape design problems are solved in explicit form and shown to have unique global extrema. Conformal mappings are used to bring the problems into a fixed domain and solve them as Dirichlet boundary value problems in the form of Cauchy integrals and series expansions. For the simplest problem statement the optimum is shown to coincide with the well‐known concrete dam outline of constant hydraulic gradient.