An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

Abstract

Retrieval of parameters in a non-Fourier conduction and radiation heat transfer problem is reported. The direct problem is formulated using the lattice Boltzmann method (LBM) and the finite-volume method (FVM). The divergence of radiative heat flux is computed using the FVM, and the LBM formulation is employed to obtain the temperature field. In the inverse method, this temperature field is taken as exact. Simultaneous estimation of parameters, namely, the extinction coefficient and the conduction–radiation parameter, is done by minimizing the objective function. The genetic algorithm (GA) is used for this purpose. The accuracies of the estimated parameters are studied for the effects of measurement errors and genetic parameters such as the crossover and mutation probabilities, the population size, and the number of generations. The LBM-FVM in combination with GA has been found to provide a correct estimate of parameters.

Acknowledgments

Ranjan Das is a Ph.D. student in the Department of Mechanical Engineering at the Indian Institute of Technology (IIT) Guwahati. From September 2006 to December 2008, concurrently with his Ph.D. research, he has worked in a sponsored research project of the Defense Research and Development Laboratory, Hyderabad. He did his master's thesis in the area of thermal engineering and received his M.Tech. in 2006 from the National Institute of Technology Silchar. He obtained his bachelor's degree in 2003 from Bhavnagar University, Gujarat. The area of his Ph.D. research includes parameter retrieval in heat transfer problems involving thermal radiation, optimization using genetic algorithms, and lattice Boltzmann-based heat transfer analysis.

Subhash C. Mishra holds a B.Sc. (engineering) from BIT Sindri Dhanbad (1989) and an M.Tech (1992) and Ph.D. (1997) in mechanical engineering from IIT Kanpur. He joined IIT Guwahati as a senior lecturer in December 1996 and became a full professor in October 2004. He is the recipient of a research fellowship of the Alexander von Humboldt Foundation, Germany and a fellowship by invitation of the Japan Society for Promotion of Science (JSPS).  He is a reviewer of many journals and conferences in the area of heat transfer and has about 150 research papers to his credit.

T. B. Pavan Kumar holds an M.Tech. (mechanical engineering) from IIT Guwahati (2008). During his M.Tech. work he extended the usage of the lattice Boltzmann method for non-Fourier conduction and radiation. He obtained his bachelor's degree in 2006 from Visvodaya Institute of Technology and Science, Kavali, Andhra Pradesh. He did his bachelor's project in HAL (Hindustan Aeronautics Ltd.). He completed his diploma in mechanical engineering (2003) from Govt. Polytechnic College, Proddatur, Andhra Pradesh. Currently, he is working as a CFD analyst for John Deere, Pune.

Ramgopal Uppaluri holds a B.Tech. (chemical engineering) from Andhra University, Visakhapatnam (1997), and an M.Tech. (chemical engineering) from IIT Kanpur (1999). He obtained his Ph.D. (process integration) from the University of Manchester (2002). Prior to joining IIT Guwahati, he worked as a postdoctoral fellow (2002–2004) at the Robert Gordon University, Scotland, in the field of membrane technology. Presently, he is an associate professor in the Chemical Engineering Department, IIT Guwahati. His research interests are variegated and he works exclusively in process systems engineering, heat exchanger networks, refinery process design, surfactant enhanced oil recovery, membrane technology, and electrodeless plating.