Solution of an inverse heat transfer problem by means of empirical reduction of modes (Q1975491)

The authors discuss the application of the Karhunen-Loève Galerkin method to the problem of estimating wall heat flux for laminar flow inside a duct. The analysis is carried out for a particular problem with the Dirichlet boundary condition on the bottom wall and an unknown heat flux across the top of the boundary. There is a parabolic laminar flow across the duct. This is done using 61 basis functions and 241 grid points along the stream. They also solve the same problem by the minimization of a functional. The results of the various approximations are illustrated by a number of diagrams.