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Skin-Friction and Forced Convection from an Isothermal Rough Plate


Abstract

Developed are new correlations for skin-friction and forced convection from an isothermal plate having RMS height-of-roughness εq. Corresponding to Prandtl and Schlichting's "fully-developed roughness" region, the skin-friction correlation is independent of Reynolds number; the convection correlation is a linear function of Reynolds number (versus an exponent of 4/5 for turbulent convection from a smooth plate).

Measurements taken with the apparatus built for this purpose match the convection correlation within 4% at Reynolds numbers from 5500 to 40000. A model addressing the transition from fully-rough turbulent to smooth turbulent convection extends that range to Re=95000.

Full Article

Skin-Friction and Forced Convection from an Isothermal Rough Plate

Supplementary Data

In the temperature versus time graphs in the supplementary files, the green, blue, and black traces are the plate, (insulated) back, and ambient temperatures respectively. The upper red trace is a simulation of the plate temperature with the back and average ambient temperatures as inputs. The middle red trace is a simulation of the back temperature with the plate and ambient temperatures as inputs. The lower red line is the ambient temperature averaged over the final 3/4 of the measurement period.

The diamonds on the plate temperature trace mark the beginning and end of the measurement period, the ending temperature difference with ambient being at most half of the peak temperature difference with ambient. The simulated plate temperature is reset to the real plate temperature at the first diamond.

Underneath each temperature graph is a graph of the air velocity versus time for mixed convection runs and Raleigh number versus time for natural convection runs.

Natural Convection
natural.pdfNatural Convection at a dozen Raleigh numbers in vertical and horizontal orientations.
angles.pdfNatural Convection at angles from −90 to +90
Mixed Convection
mixed-up.pdf3mm roughness face up; horizontal forced flow
mixed-aid.pdf3mm roughness face vertical; upward forced flow
mixed-vt.pdf3mm roughness face vertical; horizontal forced flow
mixed-opp.pdf3mm roughness face vertical; downward forced flow
mixed-dn.pdf3mm roughness face down; horizontal forced flow
mixed-dn.pdf1mm roughness face down; horizontal forced flow
mixed-aid+84.pdf1mm roughness face down inclined +84
mixed-opp+95.pdf1mm roughness face down inclined +95
Zip of Supplementary Files
supplementary.zipZip Archive of All Files

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Copyright © 2016, 2017 Aubrey Jaffer

I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.  My actions and comments do not reflect in any way on MIT.
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