Theoretical frequency response of stagnation-region thin-film thermometers

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Abstract
A thin-film resistance thermometer is assumed to be at or near the stagnation point on the rounded tip of a towed probe. The velocity field that carries the temperature fluctuations in the free stream toward the film is replaced by one of the exact solutions of the Navier-Stokes equations for stagnation flow toward flat walls. Two-dimensional and axisymmetric stagnation flows are considered. The frequency response in stagnation flow is taken as the ratio of temperature-fluctuation amplitudes of the film (on the fluid-substrate interface) and the outer flow at infinite distance from the wall. For the case of one-dimensional, harmonic temperature distribution, the problem reduces to a Ricatti-type equation with an interface boundary condition. For parameter ranges of interest, one- and two-term series expansions in frequency are useful approximations of the exact stagnation-flow solutions. The stagnation-flow frequency-response results are expected to apply to stagnation-region films on glass probes in water. The available experimental data support this conclusion.

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