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.

The Formation of Stratified Combustible Mixtures in Closed Tubes by Molecular and Convective Diffusions

1985 ◽  
Vol 107 (3) ◽  
pp. 348-353 ◽  
Author(s):  
O. Badr
Keyword(s):  
Theoretical Study ◽  
Concentration Profiles ◽  
Dimensional Model ◽  
One Dimensional ◽  
Test Conditions ◽  
Experimental Justification ◽  
The One ◽  
Combustible Mixtures

This paper describes a theoretical study on the formation of stratified combustible mixtures in closed long vertical flame tubes. The concentration profiles of the fuel (methane) in air, just before ignition took place, were predicted using a one-dimensional model involving molecular and convective diffusional processes. Phenomenological and experimental justification of the one-dimensional assumption was given and some of the predicted data were compared with experiment for different test conditions. The model appears to have successfully predicted the concentration profiles in some situations where other models failed.

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.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

2018 ◽  
Vol 284 ◽  
pp. 1230-1234
Author(s):  
Mikhail V. Maisuradze ◽  
Alexandra A. Kuklina
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Differential Diffusion ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Diffusion ◽  
Simplified Algorithm ◽  
The One ◽  
Carburizing Process ◽  
Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

Gravity-induced wrinkle lines in vertical membranes

1981 ◽  
Vol 375 (1762) ◽  
pp. 307-325 ◽  
Keyword(s):  
Heat Flow ◽  
Diffusion Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Prime Objective ◽  
Flow Through ◽  
Flexible Membranes ◽  
The One

A theory is presented for the behaviour under self-weight of inextensible but perfectly flexible membranes supported in a vertical plane. Slack in the membrane manifests itself in the formation of (curved) wrinkle lines whose determination is the prime objective. The equilibrium and strain conditions are derived and solutions are given for several simple cases. It is shown that the wrinkle lines satisfy the one-dimensional diffusion equation and hence there are analogies, for example, with heat flow through a slab.

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