Inverse estimation of boundary conditions with forced convection heat transfer in two dimensional channels

Abstract

In this paper, the inverse estimation of boundary conditions in a parallel plates channel with forced convection heat transfer is studied. The direct problem involves solving energy equation which is solved by use of finite difference method. A hydrodynamically fully developed and thermally developing laminar flow is considered. To minimize the objective function, heuristic optimization algorithms includes the particle swarm optimization and the gravitational search algorithms are used. The objective function is expressed by the sum of square residuals between measured and estimated temperatures. At the end, the results of solving the direct problem are validated by previous research. Then, the ability of optimization algorithms mentioned in inverse estimation of boundary conditions is discussed. The results indicate that the particle swarm optimization algorithm has a high accuracy in estimating boundary conditions, but in the gravitational search algorithm, the convergence rate becomes constant after the first few iterations. Furthermore, the effect of sensors number in the boundary conditions estimation indicates that the increase in the number of sensors improves the accuracy of estimations.