A irect integrationo approach for simultaneously estimating spatially varying thermal conductivity and heat capacity

One of the difficulties in the solution of inverse heat conduction problems is that of making sufficiently accurate initial guesses of the unknowns in order to start the iterations. In this work a direct integration methodology is developed for determining good initial guesses for the unknown property coefficients. Having good initial guesses, the analyst can apply the Levenberg-Marquardt method to refine the results to within a specified convergence criteria. The problem studied here is concerned with simultaneous estimation of spatially varying thermal conductivity and heat capacity from multiple spatial and temporal measurements made during transient heat conduction. Interior temperature sensors are necessary when the properties vary spatially. A statistical analysis is performed to determine approximate confidence bounds for estimating the thermal conductivity and heat capacity per unit volume.