Formation of Flammable Zones Due to the Action of Diffusional Mass Transfer—A Simplified Approach

1992 ◽  
Vol 114 (4) ◽  
pp. 267-273
Author(s):  
O. Badr ◽  
G. A. Karim
Keyword(s):  
Convective Diffusion ◽  
Approximate Solutions ◽  
Concentration Profiles ◽  
Mathematical Form ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Simplified Approach ◽  
Accuracy Comparison ◽  
Diffusional Mass ◽  
Experimental Values

The transient concentration profiles of a fuel or a toxic gas were examined following its release into air within a long confined volume with either an open or a closed end. The exact one-dimensional solution with its limitations for cases of molecular and convective diffusion was presented and discussed. Two approximate solutions simplifying the exact one were developed. Their results were compared to those of the exact one and an error analysis was given. It was shown that despite its simple mathematical form, the second approximate solution would predict the concentration profiles with a reasonable accuracy. Comparison of some of the calculated values of the concentration with the corresponding experimental values was also made.

Examination of the Formation of Combustible Mixtures by Diffusional Mass Transfer

1989 ◽  
Vol 111 (3) ◽  
pp. 194-199 ◽  
Author(s):  
O. A. Badr ◽  
G. A. Karim
Keyword(s):  
Constant Pressure ◽  
Convective Diffusion ◽  
Eddy Diffusivity ◽  
Concentration Profiles ◽  
Confined Space ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Diffusional Mass ◽  
The One ◽  
Combustible Mixtures

The approximate prediction of the concentration profiles following the release of a fuel into air, typically within a confined space at constant pressure and temperature is presented using generalized charts based on the one-dimensional diffusion equation and an effective eddy diffusivity. It is suggested that such generalized plots can be employed to establish the size and changes with time of the associated flammable zones, including when convective diffusion may be involved. Examples for some typical common fuels are presented.

Selection of one-dimensional sedimentation: models for on-line use

1995 ◽  
Vol 31 (2) ◽  
pp. 193-204 ◽  
Author(s):  
Koen Grijspeerdt ◽  
Peter Vanrolleghem ◽  
Willy Verstraete
Keyword(s):  
Steady State ◽  
Selection Criteria ◽  
Data Sets ◽  
Concentration Profiles ◽  
A Posteriori ◽  
One Dimensional ◽  
On Line ◽  
Dynamic Concentration ◽  
Selection Of ◽  
Modelling Task

A comparative study of several recently proposed one-dimensional sedimentation models has been made. This has been achieved by fitting these models to steady-state and dynamic concentration profiles obtained in a down-scaled secondary decanter. The models were evaluated with several a posteriori model selection criteria. Since the purpose of the modelling task is to do on-line simulations, the calculation time was used as one of the selection criteria. Finally, the practical identifiability of the models for the available data sets was also investigated. It could be concluded that the model of Takács et al. (1991) gave the most reliable results.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals Markov chain approximation of one-dimensional sticky diffusions

2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang
Keyword(s):  
Markov Chain ◽  
Approximate Solutions ◽  
Price Model ◽  
One Dimensional ◽  
Markov Chain Approximation ◽  
Alternative Approaches ◽  
Second Order Convergence ◽  
Chain Approximation ◽  
Matrix Exponentials ◽  
Interior Points

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

INHOMOGENEOUS LARGE DEFORMATION KINETICS OF POLYMERIC GELS

2013 ◽  
Vol 05 (01) ◽  
pp. 1350001 ◽  
Author(s):  
WILLIAM TOH ◽  
ZISHUN LIU ◽  
TENG YONG NG ◽  
WEI HONG
Keyword(s):  
Large Deformation ◽  
Soft Matter ◽  
Inner Core ◽  
Kinetic Studies ◽  
Fe Model ◽  
One Dimensional ◽  
Simplified Approach ◽  
Deformation Kinetics ◽  
Polymeric Gels ◽  
Kinetics Of

This work examines the dynamics of nonlinear large deformation of polymeric gels, and the kinetics of gel deformation is carried out through the coupling of existing hyperelastic theory for gels with kinetic laws for diffusion of small molecules. As finite element (FE) models for the transient swelling process is not available in commercial FE software, we develop a customized FE model/methodology which can be used to simulate the transient swelling process of hydrogels. The method is based on the similarity between diffusion and heat transfer laws by determining the equivalent thermal properties for gel kinetics. Several numerical examples are investigated to explore the capabilities of the present FE model, namely: a cube to study free swelling; one-dimensional constrained swelling; a rectangular block fixed to a rigid substrate to study swelling under external constraints; and a thin annulus fixed at the inner core to study buckling phenomena. The simulation results for the constrained block and one-dimensional constrained swelling are compared with available experimental data, and these comparisons show a good degree of similarity. In addition to this work providing a valuable tool to researchers for the study of gel kinetic deformation in the various applications of soft matter, we also hope to inspire works to adopt this simplified approach, in particular to kinetic studies of diffusion-driven mechanisms.

The combined effect of lattice’s uniaxial strains and electron–phonon interaction’s screening on TBEC of the intersite bipolarons

2016 ◽  
Vol 30 (26) ◽  
pp. 1650186
Author(s):  
B. Yavidov ◽  
SH. Djumanov ◽  
T. Saparbaev ◽  
O. Ganiyev ◽  
S. Zholdassova ◽  
...  
Keyword(s):  
Ideal Gas ◽  
Einstein Condensation ◽  
Chain Model ◽  
One Dimensional ◽  
Electron Phonon Interaction ◽  
Model Lattice ◽  
Experimental Values ◽  
Bose Einstein ◽  
Derivatives Of ◽  
The Ideal

Having accepted a more generalized form for density-displacement type electron–phonon interaction (EPI) force we studied the simultaneous effect of uniaxial strains and EPI’s screening on the temperature of Bose–Einstein condensation [Formula: see text] of the ideal gas of intersite bipolarons. [Formula: see text] of the ideal gas of intersite bipolarons is calculated as a function of both strain and screening radius for a one-dimensional chain model of cuprates within the framework of Extended Holstein–Hubbard model. It is shown that the chain model lattice comprises the essential features of cuprates regarding of strain and screening effects on transition temperature [Formula: see text] of superconductivity. The obtained values of strain derivatives of [Formula: see text] [Formula: see text] are in qualitative agreement with the experimental values of [Formula: see text] [Formula: see text] of La[Formula: see text]Sr[Formula: see text]CuO4 under moderate screening regimes.

Corrosion initiation time of steel reinforcement in a chloride environment—A one dimensional solution

1997 ◽  
Vol 39 (4) ◽  
pp. 739-759 ◽  
Author(s):  
P. Arora ◽  
B.N. Popov ◽  
B. Haran ◽  
M. Ramasubramanian ◽  
S. Popova ◽  
...  
Keyword(s):  
Steel Reinforcement ◽  
Initiation Time ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Corrosion Initiation ◽  
Corrosion Initiation Time ◽  
Chloride Environment

Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Subrata K. Ghosh ◽  
R. K. Sahoo ◽  
Sunil K. Sarangi
Keyword(s):  
Pressure Ratio ◽  
Expansion Ratio ◽  
Flow Conditions ◽  
Flow Properties ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Design Performance ◽  
Fluid Properties ◽  
The Mean ◽  
Inlet Conditions

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

scholarly journals CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

2021 ◽  
Vol 7 (1(37)) ◽  
pp. 9-22
Author(s):  
E.G. Yakubovsky
Keyword(s):  
Speed Of Sound ◽  
Added Mass ◽  
Navier Stokes ◽  
Speed Of Light ◽  
Attached Mass ◽  
Additional Mass ◽  
Navier Stokes Equation ◽  
Dimensional Solution ◽  
Jet Engine ◽  
One Dimensional

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

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