Response of Wall Hot-Film Gages With Longitudinal Diffusion and Heat Conduction to the Substrate

[+] Author and Article Information
F. Sedat Tardu

Laboratoire des Ecoulements Géophysiques et Industriels, INPG, UJF,  CNRS, B.P. 53X 38041, Grenoble Cédex, Francesedat.tardu@hmg.inpg.fr

C. Thanh Pham

Laboratoire des Ecoulements Géophysiques et Industriels, INPG, UJF,  CNRS, B.P. 53X 38041, Grenoble Cédex, France

J. Heat Transfer 127(8), 812-819 (Mar 04, 2005) (8 pages) doi:10.1115/1.1928907 History: Received December 03, 2003; Revised March 04, 2005

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.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 3

Global heat flux with the longitudinal diffusion term and comparison with past studies

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Figure 5

Direct transfer to the fluid and transfer to the substrate compared with the Lévêque solution. (a) Water/glass. (b) Air/glass. Legend on (a).

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Figure 6

Effective length of the hot film gage versus the conductivity ratio for σ=30

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Figure 7

Global heat transfer rates versus the conductivity ratio. (a) Transfer to the fluid and to the substrate. (b) Transfer rates from the substrate to the fluid upstream and downstream of the hot film.

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Figure 2

Local heat flux over the film compared with the boundary layer approximation (Lévêque solution)

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Figure 1

(a) Model with a two-layer substrate and the corresponding boundary conditions. (b) Typical computational domain and mesh distribution.

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Figure 12

(a) Problem investigated by Bellhouse and Schultz (1968). (b) Comparison with the present numerical results. ∎: Air with axial diffusion. ◻: Air without axial diffusion. ●: Water with axial diffusion. 엯: Water without axial diffusion. ▵: Bellhouse and Schultz air. ◇: Bellhouse and Schultz water.

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Figure 13

Direct flux from the film to the fluid for air/glass case

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Figure 14

Total flux and indirect flux from the film to the substrate for the air/glass configuration

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Figure 15

Cyclic modulation of the direct flux for different configurations compared with the ideal Lévêque solution

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Figure 16

Modulation of the total and indirect fluxes for the water/glass configuration

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Figure 17

Frequency response of the hot-film gage in different fluid/substrate configurations. 엯: Water-glass. ◻: Helium-mylar-glass. ●: Air-mylar-glass. ▵: Air-glass.

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Figure 4

Sketch of heat transfer definitions over the hot film gage

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Figure 8

The effective length of the hot film with a double-layer substrate

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Figure 9

Global heat flux for different substrate configurations and comparison with the Lévêque solution. For legend see Fig. 8.

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Figure 10

Wall temperature distribution for several fluid/sunstrate combinations

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Figure 11

Effect of the fluid/substrate configuration on the local flux for σ¯=30



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