Retieval of parameters in heat transfer problems involving thermal radiation

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In the design and analysis of engineering devices, it is essential to have the knowledge of medium properties, initial and/or boundary conditions that yield the desired information which could either be stress/strain fields in a machine element or any of one or more among the velocity, the pressure, the temperature and the heat flux fields in fluid mechanics and heat transfer problems. Depending upon the situation, with known information about the stress/strain/velocity/pressure/temperature field, unknown medium properties and/or initial and boundary conditions need to be retrieved. Problems of such kind fall under the purview of inverse problems. Unlike direct problems whose solutions proceed with known medium properties and initial and/or boundary conditions and thus their solution methods are well established, the analysis of inverse problems are relatively difficult. Inverse problems are ill-posed, and apart from the methods employed in the direct methods, they invariably require a tool for regularization and optimization. Analyses of inverse problems become essential in the estimation of the medium properties or boundary conditions. In many heat transfer problems, temperature and/or heat flux distributions are known from experiments. However, one or more of the medium properties and/or one or more of the boundary conditions that yield, for example, the desired temperature distribution, remain unknown. The number of unknown parameters to be retrieved depends upon the complexity of the problem. In case of heat transfer problems involving thermal radiation, because of the volumetric nature of radiation, many combinations of parameters need to be retrieved, and thus owing to an increased complexity, they require an efficient solution algorithm..
Supervisor: S. C. Mishra and R. Uppaluri