Using the Bees Algorithm with the Boundary Elements Method to Solve the Inverse Problem of Transient Heat Conduction

Abstract: In this paper, a new population-based search called the Bees Algorithm (BA) is presented to estimate the time-dependent heat transfer coefficient and the corresponding heat flux at the boundaries of a two-dimensional body subjected to transient heat conduction, using the temperature measurements at discrete nodal locations on the boundaries, where heat flux is specified as the boundary condition. In the forward problem, a two dimensional transient heat conduction problem subjected to heat flux boundary conditions is solved for temperature distribution at the boundaries using the boundary elements method. In the inverse problem the heat transfer coefficient (h) at the boundaries where thermal conditions are over specified is estimated by minimizing an objective function which is defined as the sum of the squared differences between the measured and computed temperatures at the nodal locations on the boundary. The Bees algorithm which is a new global evolutionary optimization method is used to investigate the inverse problem. The average value of the heat transfer coefficient at the boundaries is assumed over each time interval from initial time until the final steady-state time. The optimum parameters of Bees algorithm are found and used to estimate the heat transfer coefficient as a function of time. The effect of temperature measurement errors on the identification process is also investigated.