THEORETICAL FUNDAMENTALS OF THE METHOD FOR THERMAL-DIFFUSIVITY MEASUREMENTS FROM AUTOOSCILLATION PARAMETERS IN A SYSTEM WITH A THERMAL FEEDBACK

Theoretical fundamentals of the method to determine thermal diffusivity from auto-oscillation parameters in a control system, CS, with thermal feedback through the test specimen, are developed. The equation of a CS with a flat specimen and proportional controller (nonlinear boundary value problem of nonstationary heat conduction) is considered. Periodic solutions of the boundary value problem, which is linearized in the vicinity of the stationary solution, are analyzed. It is proved that, with a certain value of CS gain factor, excitation of auto-oscillations occurs. Their frequency omega(c) is related to the thermal diffusivity alpha as alpha = Comega(c), where C is constant. By nonlinear analysis, it is revealed that the auto-oscillation excitation mode is soft and the frequency depends on the gain factor to a very weak degree. Formulas for calculation of the thermal diffusivity and the specimen temperature field are obtained.