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Skin-Friction and Mixed Convection from an Isothermal Rough Plate


Presented are new correlations for skin-friction and forced convection from an isothermal plate having RMS height-of-roughness ε. Corresponding to Prandtl and Schlichting's "fully-developed roughness" region, the skin-friction correlation is independent of Reynolds number; the convection correlation is linear in Reynolds number.

Measurements taken with a new apparatus match the convection correlation within ±4% at Reynolds numbers from 4000 to 40000. The full mixed convection model extends that range to 2400<Re<95000.

Natural convection measurements made at plate angles from −90° to +90° are close to values predicted by established (smooth plate) formulas from Fujii and Imura, Churchill and Chu, and Schulenberg; and showed no significant dependence on surface roughness.

Mixing natural convection with horizontal forced flow is successfully modeled by the L2-norm for vertical and upward-facing plates and the L4-norm for downward-facing plates. With vertical flow on a vertical plate, mixing transitions between the L4-norm and the L2-norm for both upward and downward flows.

The mixed convection model is generalized to any inclination of a rectangular plate having at least one horizontal edge. Comprehensive formulas are presented along with their graphs and corresponding measurements.

Full Article

Skin-Friction and Mixed 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-dnnt.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.
agj @ alum.mit.edu
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