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Computational and mathematical methods

Karstein Sorli
SINTEF Applied Mathematics, N-7465 Trondheim, Norway

Inge Morten Skaar
SINTEF Applied Mathematics, N-7465 Trondheim, Norway


Different methods of sensitivity analysis for thermal design and monitoring problems are described and applied on furnace lining problems. The methods used in this work are based on utilizing finite differences and sensitivity equations; the former being code noninvasive while the latter class of methods is code invasive. Due to this fact, finite differences were chosen for the main analysis of the present work. However, on selected modeling parameters, sensitivity equations were used for comparison purposes and showed good agreement with finite differences. The main objective of the work is to determine the location of sensors; e.g., thermocouples, in nonhomogeneous heat conducting materials such that the sensors are as sensitive as possible to thermal changes at positions some distance away from the sensors. Both simplified examples as well as realistic design and monitoring problems of refractories are studied. The results of this study are used in the development of industrial furnace monitoring systems based on the solution of inverse heat conduction problems. Due to the nature of these problems, it is of great importance to determine optimal or near-optimal sensor locations, with respect to modeling parameters like the parameters of a critical isotherm and heat transfer coefficients associated with unknown transfer of heat to the surroundings.

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