DIRECT INTEGRATION APPROACH FOR SIMULTANEOUSLY ESTIMATING TEMPERATURE-DEPENDENT 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 for the unknowns in order to start the iterations. In this work a direct integration method is developed for determining good initial guesses for the unknown property coefficients within about 10% error. The Levenberg-Marquardt method is then applied to refine the results to within a specified convergence criterion. The problem studied here is concerned with simultaneous estimation of temperature dependent thermal conductivity and heat capacity from the multiple spatial and temporal measurements taken during transient heat conduction. Interior temperature sensors are found to be necessary when the properties vary with respect to temperature. A statistical analysis is performed to determine approximate confidence bounds for estimating the thermal conductivity and heat capacity per unit volume.