The effects of heat transfer into a substrate and axial diffusion are analyzed through numerical simulations in order to elucidate the frequency response of wall hot-film gages. The ratio of the conductivities of the substrate and fluid plays an important role in steady flows when it is larger than 5 and the Péclet number is smaller than 50. The equivalent film length increases considerably with the conductivity ratio, and it decreases when a thin film of low conductivity is sandwiched between the hot-film gage and the substrate, showing a net improvement of the heat transfer conditions. The frequency response in unsteady flows is highly attenuated in the presence of heat transfer into the substrate. The cutoff frequency is strongly dependent on the conductivity ratio. Improved response is obtained with the two-layer substrate configuration. It is further shown that axial diffusion considerably affects the frequency response when the shear and/or the streamwise length of the film are small.
Response of Wall Hot-Film Gages With Longitudinal Diffusion and Heat Conduction to the Substrate
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Tardu, F. S., and Pham, C. T. (March 4, 2005). "Response of Wall Hot-Film Gages With Longitudinal Diffusion and Heat Conduction to the Substrate." ASME. J. Heat Transfer. August 2005; 127(8): 812–819. https://doi.org/10.1115/1.1928907
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