Predictive Analysis of Inverse Convection Optimal Control Problem

In this work, we consider the inverse convection problem. The problem aims to recover the boundary wall flux using measurements of thermocouples placed in the fluid. We consider the case of convection by the fully developed flow. The steady-state elliptic energy equation governs the constraints of the problem. We use multiple examples of wall heat flux, and the approaches used are able to predict the original flux with high accuracy. We compare the predicted heat flux using Lagrange Multiplier and Conjugate gradient methods in case of corrupt measurements. Keywords - Inverse Convection Problem, Fully Developed Flow, Elliptic Energy Equation, Lagrange Multiplier Method, Conjugate Gradient Method.