Application of steady-state turbulent flow data in the solution of inverse natural heat convection problems

Abstract

Inverse heat transfer problems are a well-known part in a variety of mechanical engineering applications. The majority of research in this area has been focused on inverse heat conduction problems for its relatively simple forward problem and numerous applications. Inverse heat convection, on the other hand, presents a greater challenge with the inclusion of fluid mechanics in the problem. In this paper, a study of steady-state turbulent wall plumes is used to develop a search-based inverse heat convection methodology to determine the source heat input and location generating the plume. Using the forward problem data, interpolating functions are developed to relate source heat input and location to temperature readings on the wall, downstream of the source. Using these equations at a finite number of locations in the flow, a system of equations is formulated. Solving this system of equations allows one to estimate the unknown source heat input and location. Since the solutions of inverse problems are generally non-unique, an optimization technique, being the particle swarm optimization here, is used to obtain the system of equations which would yield the most accurate estimation possible in a fairly narrow domain of uncertainty.