arXiv subjects

Martin S. Jaffer

Publications and source records attributed to Martin S. Jaffer.

3 recordsLinked to original sources

arXiv2025

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↗

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↗