Optimal control of heat and mass transfer in a laminar compressible-gas boundary layer on permeable surfaces (Q1123767)

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 \%.