Estimation of inlet temperature of a developing fluid flow in a parallel plate channel

A numerical model is developed for an inverse problem of estimation of inlet temperature in a parallel plate channel. A hydrodynamically and thermally developing laminar flow is considered. The upper plate of the channel is maintained at constant heat flux and the lower plate is insulated. The Lagrange multiplier method is applied for this constrained optimization problem. The minimization of the objective function is performed using the conjugate gradient method. The adjoint and sensitivity equations along with the energy equation are discretized using the finite volume method and a code is developed for the solution of the same. The momentum equations are solved using an in-house CFD source code and are coupled with the developed numerical code for the inverse method. The direct problem is first solved with known inlet and boundary conditions and the temperature field of the domain is determined. Inverse method is then applied to predict the inlet temperature with some of the additional temperature data inside the solution domain obtained from the direct problem. The prediction of inlet temperature by the present algorithm is found to be quite reasonable.

► An inverse problem for developing laminar flow in a parallel plate channel.
► Four nos. of measurements are insufficient for inverse analysis for the case considered in this study.
►  Measurements taken very close to the inlet boundary deteriorate the prediction.
► Profiles with discontinuities make a difficult case for estimation.
► The overall results show that CGM is a stable and reasonable method.