,- -. Determination f of Thermal Proceedings of NHTC ’00 34th National Heat Transfer Conference PMsburgh, Pennsylvania, August 20-22,2000 Conductivity of 304 Stainless Steel Using Parameter Estimation Techniques’ Bennie F. Blackwei12, Walter Gi113,Kevin J. Dowding4, and Thomas E. Voth4 Sandia National Laboratories Engineering Sciences Center MS 0828 Albuquerque, NM 87185 ABSTRACT Sensitivity coefficients were analyzed in order to guide the design of an experiment to estimate the thermal conductivity of 304 stainless steel. The uncertainty on the temperature measurements was estimated by several means and its impact on the estimated conductivity is discussed. The estimated thermal conductivity of 304 stainless steel is consistent with results from other sources. NOMENCLATURE c k Np iv. Nf s T Tk Tm T min t x i fij specific heat, J/Kg-K thermal conductivity, W/m-K no. of parameters no. of sensors no. of measurement times sum of squares function, see Eq. (6) temperature, “C scaled sensitivity coefficient, “C, see Eq. (1) maximum temperature, ‘C minimum temperature, ‘C time, s sensitivity matrix position vector temperature measurement for sensor i at timej, “C 1. 2. 3. 4. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000. Dktinguished Member of Technical Staff, Fellow ASME. Principaf Member of Technical Staff, Member ASME. Senior Member of Technicat Staff, Member ASME. Greek A D-optimality condition, see Eq. (4) A+ dimensionless D-optimality condition, see Eq. (5) AT = Tma - Tmin At data sample rate U thermal diffusivity, m2/s P density, Kg/m3 . ‘P estimated standard deviation in parameter p, units of p INTRODUCTION Thermal systems often incorporate a number of mechanical joints between individual components. These joints allow assembly/disassembly, fitrnish mechanical support, and provide pathways for redistribution of thermal energy. To predict the behavior of a thermal system, it is necessary to incorporate thermal contact phenomena into computational tools. An accepted modeling approach is to use correlations that provide contact conductance based on joint characteristics, such as material pair, surface finishes, surface harnesses, and contact pressure. These parameters are important because the surface irregularities deform upon contact and control the actual interface area. An experimental apparatus has been designed to develop contact conductance correlations for metal-to-metal interfaces. As part of the data reduction procedure, it is necessary to know the thermal conductivity of the metals on each side of the contact interface. This thermal conductivity information is often obtained from either handbooks or separate experiments designed to measure those values. An unpublished uncertainty analysis for the steady-state contact conductance experiment