The effect of viscous dissipation in natural convection is appreciable when the induced kinetic energy becomes appreciable compared to the amount of heat transferred. This occurs when either the equivalent body force is large or when the convection region is extensive. Viscous dissipation is considered here for vertical surfaces subject to both isothermal and uniform-flux surface conditions. A perturbation method is used and the first temperature perturbation function is calculated for Prandtl numbers from 10−2 to 104. The magnitude of the effect depends upon a dissipation number, which is not expressible in terms of the Grashof or the Prandtl number.
In recent studies on small pyroelectric thermal anemometers with roughened surfaces we showed that one of the most widely used heat transfer models yielded calculated anemometer responses for flow and geometric behaviour that agreed functionally with observations, but were significantly smaller than the experimental data. As the first stage in investigating the role of small structures in heat transfer, we initiated a study of emittance from deep gratings. Here we report measurements at 400 °C of infrared (3 µm⩽λ⩽14 µm), normal, s- and p-polarized spectral emittances of 45 µm deep, near square-wave gratings of heavily phosphorus doped (110) silicon (P content ∼5 × 10 cm). The grating surface repeat scales, Λ, were 10, 14, 18 and 22µm, yielding a range of Λ/λ from 0.14 to 7.33. The s-polarization vector was parallel to the grating slots. Both s and p spectral emittances had pronounced resonant periodicities with a characteristic length of ∼42 µm. A reasonable explanation for this behaviour is the presence of standing waves in the air slots perpendicular to the silicon surface similar to those in an organ pipe. While the resonant amplitude of the s polarization does not depend significantly on Λ it does for the p polarization. No explanation for the Λ dependence of the p polarization is known.
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