Inverse analysis applied to retrieval of parameters and reconstruction of temperature field in a transient conduction–radiation heat transfer problem involving mixed boundary conditions

This article deals with the application of the inverse method for simultaneous retrieval of parameters and reconstruction of the temperature field in a transient conduction–radiation problem with mixed boundary conditions. The conducting–radiating medium is absorbing, emitting and isotropically scattering. The boundaries are diffuse gray. One boundary of the planar medium is at a prescribed temperature, while the other boundary is at a prescribed heat flux. A method involving lattice Boltzmann method (LBM), the finite volume method (FVM) is used to obtain the temperature field in the mixed boundary problem which in the present work is termed as the direct method. Next, random perturbations are imposed on this exact temperature field and then simultaneous reconstruction of the same and estimation of properties are accomplished by minimizing the square of the error between the exact and guessed temperature fields. This error, that in the present work is termed as the objective function, is minimized using the genetic algorithm (GA). The impact of different genetic parameters on the accuracy of the estimation is also investigated. It is observed that subject to the proper selection of the genetic parameters, simultaneous reconstruction of the temperature field along with a reasonably good estimation of the unknown parameters can be achieved using the LBM–FVM–GA.