LBM combined with LM algorithm to estimate the unknown heat flux – A new inverse approach

Abstract

The objective of the present work is the application of the Levenberg–Marquardt method as an inverse method for the estimation of the heat flux. In this paper inverse estimation of heat flux for a two-dimensional heat conduction problem is carried out. As a direct method, in the first attempt the solution of two-dimensional inverse heat conduction problem is formulated by using Lattice Boltzmann Method as a forward model. Later the solution to the problem is also obtained by using Finite Difference Method (FDM) as the forward model for the purpose of validation. Once the forward model is established, Levenberg-Marquardt Method is used as an inverse model to estimate the input parameter i.e. heat flux which is reported. A complete error analysis of inverse model with known values is performed. As the Lattice Boltzmann Method (LBM) is acclimatizing to parallel computation, its use is recommended in Levenberg-Marquardt method for the solution of inverse heat conduction problem which is evident from the results.