Multiparameter Estimation in a Transient Conduction-Radiation Problem Using the Lattice Boltzmann Method and the Finite-Volume Method Coupled with the Genetic Algorithms

Abstract

This article deals with the exploration of the lattice Boltzmann method (LBM) and the finite-volume method (FVM) in conjunction with the genetic algorithms (GA) for estimation of unknown parameters in an inverse transient conduction-radiation problem. The conducting-radiating planar participating medium is absorbing, emitting, and scattering. Its boundaries are diffuse gray. In both the direct and inverse methods, the energy equations are solved using the LBM, and the FVM is employed to compute the radiative information. In the inverse method, the optimization is achieved using the GA. For a given set of parameters, first a direct problem is solved using the LBM-FVM, and temperature fields are estimated at various time levels, which, in the inverse problem, are taken as exact. Effects of measurement errors are also considered. With temperature fields known from the direct method, in the inverse method, too, the LBM-FVM combination is used to solve the energy equation involving volumetric radiation, and the GA is used to optimize the objective function. The LBM-FVM-GA combination in the inverse method has been found to provide correct estimates of the unknown parameters in a transient conduction-radiation heat transfer problem.

A research grant for this work received from Defence Research and Development Laboratory, Kanchanbagh, Hyderabad, is duly acknowledged.

Notes

^a Values in parenthesis are those two parameters which were simultaneously estimated in the inverse method (LBM-FVM-GA).