Estimation of Multiple Contact Conductances in a Silicon-Indium-Silicon Stack

Author:

Woodbury Keith A.1,Cutler Grant23,Najafi Hamidreza4,Kota Maya53

Affiliation:

1. Department of Mechanical Engineering, The University of Alabama , Box 870276, Tuscaloosa, AL 35487

2. Lawrence Berkeley National Laboratory, Mechanical Engineering , One Cyclotron Road, Berkeley, CA 94720

3. Lawrence Berkeley National Laboratory

4. Department of Mechanical and Civil Engineering, Florida Institute of Technology , 150 W University Blvd, Melbourne, FL 32901

5. Lawrence Berkeley National Laboratory , Manufacturing EG and CAD, One Cyclotron Road, Berkeley, CA 94720

Abstract

Abstract This report documents evaluation of simultaneous estimation of multiple interfacial heat transfer coefficients (HTCs) using transient measurements from an experiment designed for steady-state operation. The design of a mirror system for directing X-rays under cryogenic conditions requires knowledge of the interfacial HTC (contact conductance) between silicon and indium. An experimental apparatus was constructed to measure temperatures in a stack of five 7.62-mm thick pucks of silicon separated by 0.1-mm thick sheets of indium, which is operated under cryogenic temperatures in vacuum. Multiple pucks and interfaces are incorporated into the apparatus to allow evaluation of HTCs for surfaces of different roughness from a single experiment. Analysis of the sensitivity of each of the measured temperatures to each of the unknown HTCs reveals lack of linear independence of these sensitivities and suggests the recovery of the HTCs will be challenging. Artificially noised “data” were created from two different computational models by solving for temperatures and adding random Gaussian noise with a specified standard deviation. These data are subsequently analyzed using two different iterative parameter estimation methods: a Levenberg scheme and a Tikhonov iterative scheme. The required sensitivity matrix is computed using forward finite difference approximations. The results for the heat transfer coefficients for this model problem suggest that coefficients cannot be estimated independently, but the ratios relative to one of the unknowns can be recovered.

Funder

Lawrence Berkeley National Laboratory

Publisher

ASME International

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