Valid Range Of Parameters Research Articles

Exact Insulated-Tip Fin Length Correction for Tip Convection Compensation

Abstract This study details the derivation of a length correction term for computing the heat transfer performance of one-dimensional, straight, convecting-tip fins using the insulated-tip fin solution. Use of this corrected length in the insulated-tip fin solution produces the identical heat transfer rate and temperature profile as those computed using the more complex convecting-tip fin equations. The analysis derives the length correction equation from fundamental principles and produces a simple, closed-form expression valid for all fin cross-sectional shapes. Furthermore, the valid parameter range where this length correction is applicable, and outside of which no exact length correction is possible, is quantified.

Correlations of Heat Transfer and Fluid Flow Data for Lattice Brick Settings in Tunnel Kilns

This paper proposes correlation equations of heat transfer and pressure drop for the design and operation of tunnel kilns loaded with lattice brick settings of different geometrical parameters in the form of Nusselt number and friction factor. The developed correlation equations considered parameters that were not investigated in previous studies, such as the relative roughness of the bricks and the stack channels, and they also extended the Reynolds numbers to a practical range that was not covered before in a simple, practical form. The correlation equations are valid for Reynolds number between 125 and 10,200, Prandtl number between 0.68 and 0.73, brick’s relative roughness between 0.23 and 0.93, voidage fraction between 0.48 and 0.653, and the geometrical parameters of the tested lattice brick settings. The achieved correlations of the Nusselt number and the friction factor are well compared with the available correlations in the literature in their valid range of parameters. It is found that Nusselt numbers and the friction factors for low-density are higher than those of high-density settings for all considered parameters except the voidage fraction. The effect of the considered parameters confirms that Nusselt numbers increase and the friction factors decrease substantially with the Reynolds number and slightly with the Prandtl number. At a constant Reynolds number, both the Nusselt number and the friction factor increase as the brick’s relative roughness is increased. Moreover, as the stack channel spacing is increased, the Nusselt number decreases, and the friction factor increases. The voidage fraction of the setting has a monotonic effect on both Nusselt numbers and friction factors. Nusselt numbers for high-density are higher than those for low-density settings as the voidage fraction varies.

The TIME Table: rotation and ages of cool exoplanet host stars

ABSTRACT Age is a stellar parameter that is both fundamental and difficult to determine. Among middle-aged M dwarfs, the most prolific hosts of close-in and detectable exoplanets, gyrochronology is the most promising method to assign ages, but requires calibration by rotation-temperature sequences (gyrochrones) in clusters of known ages. We curated a catalogue of 249 late K- and M-type (Teff = 3200–4200 K) exoplanet host stars with established rotation periods, and applied empirical, temperature-dependent rotation–age relations based on relevant published gyrochrones, including one derived from observations of the 4-Gyr-old open cluster M67. We estimated ages for 227 of these stars, and upper limits for eight others, excluding 14 which are too rapidly rotating or are otherwise outside the valid parameter range of our gyrochronology. We estimated uncertainties based on observed scatter in rotation periods in young clusters, error in the gyrochrones, and uncertainties in temperature and non-solar metallicity. For those stars with measured metallicities, we provide but do not incorporate a correction for the effects of deviation from solar-metallicity. The age distribution of our sample declines to near zero at 10 Gyr, the age of the Galactic disc, with the handful of outliers explainable by large uncertainties. Continued addition or extension of cluster rotation sequences to more thoroughly calibrate the gyrochronology in time and temperature space, more precise and robust measurement of rotation periods, and more accurate stellar parameter measurements will enable continued improvements in the age estimates of these important exoplanet host stars.

Comprehensive kinetic theory of inverse sheath for a strong electron-emitting electrode in a low-pressure isotropic plasma

The basic kinetic theory of an electron emitting inverse sheath was presented in T Gyergyek, J Kovačič, I Gomez, J P Gunn, S Costea and M Mozetič (2020 Phys. of Plasmas 27, 023 520). Here we extend this theory to find the potential profile and kinetic energy flux in inverse sheath for floating and current carrying electron emitting electrode/wall. The values of emitted-electron temperature, number and current densities are explored for the existence and nonexistence of inverse sheath for floating and current carrying electrode/wall. For this we consider half Maxwellian velocity distribution functions of species (emitted-electron, plasma-electron and ions) at their respective emerging boundaries. The species charge densities are calculated self-consistently from the prior assumed positive sheath structure. The Poisson’s equation is then solved numerically for floating and current carrying electrode/wall with varying normalized emitted-electron and ion temperatures. The resulting inverse sheath solution is valid for limited range of emitted-electron and ion temperatures in case of floating electrode/wall. The kinetic energy flux relations for each species are derived in inverse sheath. The numerical solutions of these relations for floating and current carrying electrode/wall are presented for valid range of parameters. These solutions shows that the total or kinetic flux received by floating electrode/wall surface decreases with increasing of emitted-electron temperature and even approaches to zero for equal values of emitted-electron and plasma-electron temperatures.

A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment's movies

<p style='text-indent:20px;'>We propose a simple and accurate procedure how to extract the values of model parameters in a flame/smoldering evolution equation from 2D movie images of real experiments. The procedure includes a novel method of image segmentation, which can detect an expanding smoldering front as a plane polygonal curve. The evolution equation is equivalent to the so-called Kuramoto-Sivashinsky (KS) equation in a certain scale. Our results suggest a valid range of parameters in the KS equation as well as the validity of the KS equation itself.

Magnetic torque-driven deformation of Ni-nanorod/hydrogel nanocomposites

Abstract Nickel (Ni) nanorods were prepared by the anodized aluminum oxide (AAO) template method and dispersed in poly(acrylamide) (PAM) hydrogels. The deformation of the magnetoresponsive composites was studied with particular attention to the consequences of finite magnetic shape anisotropy as compared to rigid dipoles on the field-dependent torque. For comparison with experiments, the composite was described as an elastic continuum with a local magnetic torque density, applied by discrete particles and determined by the local orientation of their magnetic anisotropy axis with respect to the magnetic field. The mean magnetic moment of the single domain particles m and their volume density in the composite φ vol were derived from the static field-dependent optical transmission (SFOT) of linear polarized light. The mechanical coupling between the particles and their viscoelastic environment was retrieved from the rotational dynamics of the nanorods using oscillating field-dependent optical transmission (OFOT) measurements. Field- and orientation-dependent magnetization measurements were analyzed using the Stoner–Wohlfarth (SW) model and a valid parameter range was identified by introducing an effective anisotropy constant K A as a new empirical model parameter. This adapted SW-model for quantitative description of the field- and orientation dependence of the magnetic torque was validated by measuring the local rotation of nanorods in a soft elastic hydrogel. Finally, torsional and bending deformation of thin magnetically textured composite filaments were computed and compared with experiments.

Analytical solutions for weak black hole kicks

The black hole is modelled by a combined gravitational potential of the bulge, disk and halo and is subjected to an initial weak kick. The resulting differential equations are set up, and shown to possess analytical solutions. The effects of black hole accretion and dynamical friction are also incorporated into this analytical framework. The resultant frequencies and amplitudes are computed, and are compared with the ones obtained from numerical simulations. Within the valid range of parameters of the analytical model, the two sets of results are shown to be in reasonable agreement. It is shown that this model reproduces the linear dependence of the amplitude on the initial kick velocity, and the constant of proportionality is close to that obtained from the simulations. The analytical treatment presented is quite general, and its applications to other areas are also indicated.

A Film-Cooling Correlation for Shaped Holes on a Flat-Plate Surface

A common method of optimizing coolant performance in gas turbine engines is through the use of shaped film-cooling holes. Despite widespread use of shaped holes, existing correlations for predicting performance are limited to narrow ranges of parameters. This study extends the prediction capability for shaped holes through the development of a physics-based empirical correlation for predicting laterally averaged film-cooling effectiveness on a flat-plate downstream of a row of shaped film-cooling holes. Existing data were used to determine the physical relationship between film-cooling effectiveness and several parameters, including blowing ratio, hole coverage ratio, area ratio, and hole spacing. Those relationships were then incorporated into the skeleton form of an empirical correlation, using results from the literature to determine coefficients for the correlation. Predictions from the current correlation, as well as existing shaped-hole correlations and a cylindrical hole correlation, were compared with the existing experimental data. Results show that the current physics-based correlation yields a significant improvement in predictive capability, by expanding the valid parameter range and improving agreement with experimental data. Particularly significant is the inclusion of higher blowing ratio conditions (up to M=2.5) into the current correlation, whereas the existing correlations worked adequately only at lower blowing ratios (M≈0.5).

Valid parameter range analyses for chemical reaction kinetic models

The present work quantifies the relations between the structure of a chemical reaction kinetic model, its valid parameter range, and the truncation error tolerance of the model. General methods are presented to solve the three important problems of valid parameter range analysis: (1) identification of the valid parameter range of a kinetic model, (2) estimation of the error tolerance required when applying a kinetic model over a specified parameter range, and (3) improvement of existing model generation algorithms to construct more robust models. Finally, the relationship between a model's structure, its valid parameter range, and the truncation error tolerance are illustrated by the flexibility–tolerance–model graph. The new methods are applied to pyrolysis of methane/ethane mixtures.