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This paper presents a noncontact optical technique for measuring the thermal contact conductance between wafer-like thin solid samples. The technique is based on heating one solid surface by a modulated laser beam and monitoring the corresponding temperature modulation of the other solid surface across the interface using the reflectance of a probe laser beam. The phase lag between the two laser signals is independent of the optical properties of the samples as well as the laser intensities, and can be related to the thermal contact conductance. A detailed theoretical analysis is presented to estimate the thermal contact conductance as well as the thermophysical properties of the solids from the phase lag measured as a function of the modulation frequency. Closed-form solutions in the high-frequency limit are derived in order to provide a simple estimation procedure. The effect of misalignment of the two lasers is studied and the conditions for robust measurements are suggested. As a benchmark for this technique, the thermal conductivity of a single crystal silicon sample was measured to within two percent of reported values. The thermal contact conductance was measured for Al-Si samples, each about 0.22 mm thick, in the pressure range of 0.8–10 MPa. In contrast to traditional contact conductance measurement techniques that require steady-state operation and insertion of thermocouples in thick solid samples, the noncontact dynamic optical technique requires much less time and is particularly well suited for electronic packaging materials that are typically in the thickness range of 0.1–5 mm. In addition, localized conductance measurements are now possible with a spatial resolution of about four times the thickness of the solid and can be used to detect interfacial voids and defects.

The thermoelastic stress field in a functionally graded curved beam, where the elastic stiffness varies in the radial direction, is considered. An analytical solution is obtained where the radial variation of the stiffness is represented by a fairly general form. The stress fields corresponding to two different cases for the elastic properties are examined: first, the elastic properties representing a coating on the outer surfaces of the curved beam; secondly, the elastic properties obtained from experimental data. The flexural stress in the curved beam is then compared with that of a solid ring. Finally, a relatively simple approximate solution is developed and this is shown to be in good agreement with the analytical results.

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