An optimization strategy for the inverse solution of a convection heat transfer problem

In many practical situations, the desired results are given, but the conditions needed for achieving these are unknown. This circumstance leads to inverse problems, which are of particular interest in thermal processes. For instance, the temperature cycle to which a component must be subjected in order to obtain desired transformations in a manufacturing system are known or prescribed. However, the boundary and initial conditions, in terms of heat input, pressure, flow rate and temperature, are not known and must be determined by solving the inverse problem. A method based on a search and optimization approach is developed to solve the inverse natural convection problem of a two-dimensional heat source on a vertical flat plate. This problem is of interest in fires and electronic systems. The inverse problem involves determination of the strength and location of the heat source, which is taken as a fixed-length region of the wall with an isothermal or isoflux condition, by employing a few selected data points downstream. This is achieved by numerical simulations of the region at differing source strengths and locations, thus obtaining relevant temperature interpolation functions of source location and strength for selected data points. A search based optimization method, particle swarm optimization (PSO), is then applied to find the best pair of vertical locations for input of data. The system of equations based on their respective relations is solved to obtain solution to the inverse problem. The goal of this method is to reduce the uncertainty and approach essentially unique solutions. The error of the method is found to be acceptable for both source strength and location.