arXiv subjects

Aubrey G. Jaffer

Publications and source records attributed to Aubrey G. Jaffer.

5 recordsLinked to original sources

arXiv2026

Natural Convection Heat Transfer from an Inclined Cylinder

Based on Jaffer's (2023) heat engine analysis of natural convection, this investigation mathematically derives a novel, comprehensive formula predicting the natural convective heat transfer from an inclined cylinder given its length, diameter, angle, and Rayleigh number, and the fluid's Prandtl number and thermal conductivity. The present formula was tested with 116 inclined cylinder measurements having length-to-diameter ratios between 1.48 and 12500 in ten data-sets from four peer-reviewed studies, yielding (data-set) root-mean-squared relative error values between 1.0% and 4.7%.

physics.flu-dyn↗

arXiv2024

Mixed Convection From an Isothermal Rough Plate

This investigation derives formulas to predict the mixed convective surface conductance of a flat isotropic surface roughness having a convex perimeter in a Newtonian fluid with a steady forced flow in the plane of that roughness. Heat transfer measurements of a 30.5 cm square rough plate with forced air velocities between 0.1 m/s and 2.5 m/s were made by the present apparatus in two inclined and all five orthogonal orientations. The present work's formulas are compared with 104 measurements in twelve data-sets. The twelve data-sets have root-mean-square relative error (RMSRE) values between 1.3% and 4% relative to the present theory. The present work's formulas are also compared with 78 measurements in 28 data-sets on five vertical rough surfaces in horizontal flow from Rowley, Algren, and Blackshaw (1930). The five stucco data-sets have RMSRE values between 2.5% and 6.5%; the other data-sets have RMSRE values between 0.2% and 5%.

physics.flu-dyn↗

arXiv2024

Skin-Friction and Forced Convection from Rough and Smooth Plates

Since the 1930s, theories of skin-friction drag from plates with rough surfaces have been based by analogy to turbulent flow in pipes with rough interiors. Failure of this analogy at slow velocities has frustrated attempts to create a comprehensive theory. Utilizing the concept of a self-similar roughness which disrupts the boundary layer at all scales, this investigation derives formulas for a rough or smooth plate's skin-friction coefficient and forced convection heat transfer given its characteristic length, root-mean-squared (RMS) height-of-roughness, isotropic spatial period, Reynolds number, and the fluid's Prandtl number. This novel theory was tested with 456 heat transfer and friction measurements in 32 data-sets from one book, six peer-reviewed studies, and the present apparatus. Compared with the present theory, the RMS relative error (RMSRE) values of the 32 data-sets span 0.75% through 8.2%, with only four data-sets exceeding 6%. Prior work formulas have smaller RMSRE on only four of the data-sets.

physics.flu-dyn↗

arXiv2018

The Lamb-Oseen Vortex and Paint Marbling

The displacement pattern arising from the decay of a two-dimensional Lamb-Oseen vortex in a Newtonian fluid can be closely modeled by the closed-form expression presented here. This formula enables Lamb-Oseen vortex simulation orders of magnitude faster than can be accomplished using finite-element methods, and without the accumulation of errors. "French Curl" marbling patterns look as though they are created by a vortex. Analysis and simulation of a nineteenth century example of French Curl finds that the pattern was created without a vortex. True vortexes are rarely seen in paint marbling because, in order to reach Reynolds numbers larger than 90, viscosity of the fluid bath must be much lower than is customarily used.

cs.CG↗

arXiv2018

Fractal Scaling of Population Counts Over Time Spans

Attributes which are infrequently expressed in a population can require weeks or months of counting to reach statistical significance. But replacement in a stable population increases long-term counts to a degree determined by the probability distribution of lifetimes. If the lifetimes are in a Pareto distribution with shape factor $1-r$ between 0 and 1, then the expected counts for a stable population are proportional to time raised to the $r$ power. Thus $r$ is the fractal dimension of counts versus time for this population. Furthermore, the counts from a series of consecutive measurement intervals can be combined using the $L^p$-norm where $p=1/r$ to approximate the population count over the combined time span. Data from digital advertising support these assertions and find that fractal scaling is useful for early estimates of reach, and that the largest reachable fraction of an audience over a long time span is about $1-r$.

cs.CG↗