Optimal control of heat and mass transfer in a laminar compressible-gas boundary layer on permeable surfaces
type: Item
instance of: scholarly article
title: Optimal control of heat and mass transfer in a laminar compressible-gas boundary layer on permeable surfaces
zbMATH Open document ID: 0677.76096
DOI: 10.1007/BF01054748
author: K. G. Garaev
published in: Fluid Dynamics
publication date: 1988-01-01T00:00:00Z
review text: The problem of minimization of the convective heat flux transmitted from a compressible-gas boundary layer to a porous curved wall is considered for a given limitation on the power of the cooling system; the local rate of flow of gas through the porous surface serves as the control variable. The variational problem is solved by means of a group-theory approach to the construction of the differential conservation laws for two- dimensional variational problems of the Mayer type based on the Lie- Ovsyannikov theory and Noether's first theorem. The variational problem is completely algorithmized: the construction of the optimal control is reduced to the recurrent integration of two systems of ordinary differential equations with resolvable singularities at the flow stagnation point. A representative calculation of the equations of the optimal controlled boundary layer on a permeable circular cylinder demonstrated the rapid convergence of the iteration process: with an accuracy sufficient for practical purposes it is possible to confine oneself to the optimal control in the first approximation, which was obtained in analytic form. In carrying out the calculations we varied the temperature of the surface, the length of the porous zone, and the power of the cooling system; the heat flux advantage obtainable with optimal as opposed to nonoptimal control can amount to 57 \%.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 4110385
zbMATH Keywords: minimization of the convective heat flux
zbMATH Keywords: compressible-gas boundary layer
zbMATH Keywords: porous curved wall
zbMATH Keywords: two-dimensional variational problems of the Mayer type
zbMATH Keywords: Lie-Ovsyannikov theory
zbMATH Keywords: Noether's first theorem
zbMATH Keywords: optimal control
zbMATH Keywords: optimal controlled boundary layer
MaRDI profile type: Publication
cites work: Optimal control of processes with distributed parameters given incomplete information
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cites work: Calculation of the laminar boundary layer in a compressible gas in the presence of suction or blowing
description: scientific article; zbMATH DE number 4110385