ON FLAME PROPAGATION IN EXPLOSIVE MIXTURES OF GASES: I. GENERAL THEORY

1956 ◽  
Vol 34 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Robert Sandri
Keyword(s):  
Temperature Distribution ◽  
Flame Propagation ◽  
Energy Equation ◽  
Approximation Formula ◽  
Flame Velocity ◽  
System Of Differential Equations ◽  
Flame Zone ◽  
Method Of Solution ◽  
Set Up ◽  
Numerical Method Of Solution

The system of differential equations of flame propagation is set up and discussed. It is shown that, without any major influences being neglected, the energy equation can be reduced to the form[Formula: see text]with the boundary conditions[Formula: see text]Some qualities of the solutions of this equation are discussed and a simple numerical method of solution is described. The flame velocity V0 is found as an eigenvalue of the energy equation. The temperature distribution in the flame zone can then be found by an ordinary quadrature. Further, an approximation formula for finding V0 directly is derived[Formula: see text]where F(η) is proportional to [Formula: see text]and has a maximum for η = ηm.

ON FLAME PROPAGATION IN EXPLOSIVE MIXTURES OF GASES: III. FLAME PROPAGATION IN MIXTURES OF METHANE AND NITROGEN AIR, HELIUM AIR, AND ARGON AIR

1956 ◽  
Vol 34 (3) ◽  
pp. 331-337 ◽  
Author(s):  
Robert Sandri
Keyword(s):  
Temperature Distribution ◽  
General Theory ◽  
Oxygen Atom ◽  
Flame Propagation ◽  
Flame Velocity ◽  
Flame Zone ◽  
End Products ◽  
Atom Chain ◽  
Experimental Values ◽  
Good Agreement

The general theory developed in an earlier paper of the author is applied to the combustion of mixtures of methane and nitrogen air, helium air, and argon air where dissociation of the end products is negligible. The oxygen atom chain is assumed to be rate-determining. Absolute values of the flame velocity are computed for mixtures containing 8% of methane and for the stoichiometric mixtures. The results are found to be in very good agreement with experimental values. Dependence on pressure is likewise found to be in very good agreement with experiments. The temperature distribution in the flame zone is also computed.

The numerical solution of certain integral equations with non-integrable kernels arising in the theory of crack propagation and elastic wave diffraction

1969 ◽  
Vol 265 (1163) ◽  
pp. 353-381 ◽  
Keyword(s):  
Integral Equation ◽  
Elastic Wave ◽  
Numerical Solution ◽  
Wave Diffraction ◽  
Crack Surface ◽  
Relative Displacement ◽  
Method Of Solution ◽  
Set Up ◽  
Prestressed State ◽  
Numerical Method Of Solution

An infinite elastic medium is initially at rest in a prestressed state of plane- or anti-plane strain. At time t = 0 a plane crack comes into existence which occupies a strip parallel to the y axis and whose width varies in time. Assuming that the components of the traction are known on the crack surface it is possible to set up an integral equation on the area of the crack for the relative displacement across the crack. Although the kernel of this integral equation is non-integrable a method is found for discretizing it and a numerical method of solution is carried out. The results, which in some cases are the solutions of diffraction problems, are presented graphically.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

Temperature Distribution of Hot Air Flow in Heating Zone for Drying Application

2014 ◽  
Vol 627 ◽  
pp. 153-157
Author(s):  
Nawadee Srisiriwat ◽  
Chananchai Wutthithanyawat
Keyword(s):  
Temperature Distribution ◽  
Air Temperature ◽  
Power Supply ◽  
Air Flow ◽  
Heating Zone ◽  
Velocity Control ◽  
Rectangular Duct ◽  
Air Velocity ◽  
Hot Air ◽  
Set Up

The temperature distribution of hot air flow in heating zone of a rectangular duct has been investigated for drying application. The experimental set-up consists of a heater and a fan to generate the hot air flow in the range of temperature from 40 to 100°C and the range of air velocity between 1.20 and 1.57 m/s. An increase of the heater power supply increases the hot air temperature in the heating zone while an increase of air velocity forced by fan decreases the initial temperature at the same power supply provided to generate the hot air flow. The temperature distribution shows that the hot air temperature after transferring through air duct decreases with an increase of the length of the rectangular duct. These results are very important for the air flow temperature and velocity control strategy to apply for heating zone design in the drying process.

Temperature Distribution in a Cylindrical Rod Moving From a Chamber at One Temperature to a Chamber at Another Temperature

1964 ◽  
Vol 86 (2) ◽  
pp. 265-270 ◽  
Author(s):  
G. Horvay ◽  
M. Dacosta
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Arbitrary Constant ◽  
Families Of Curves ◽  
Special Cases ◽  
Method Of Solution ◽  
Lower Chamber ◽  
Higher Temperature ◽  
Hopf Method ◽  
The Heat Transfer Coefficient

When an infinitely long cylindrical rod travels from a chamber at one temperature ϑa to a chamber (insulated from the first) at a higher temperature ϑf, then heat will leak out along the rod from the second chamber to the first, whose amount decreases as the speed of the rod increases. Using the Wiener-Hopf method of solution, we determine the temperature distribution in the rod for the case where in the second chamber the heat-transfer coefficient h+ is infinite, while in the first chamber it has an arbitrary constant value h. Families of curves illustrate the temperature distribution in the two special cases where h = ∞ (isothermal boundary conditions in lower chamber) and where h = 0 (rod is insulated in lower chamber).

AC Magnetic Measurements on Superconductors

2013 ◽  
pp. 208-222
Author(s):  
Philippe Laurent ◽  
Jean-François Fagnard ◽  
Philippe Vanderbemden
Keyword(s):  
Magnetic Properties ◽  
Temperature Distribution ◽  
Magnetic Measurements ◽  
Sampling Rate ◽  
Data Acquisition System ◽  
Magnetic Data ◽  
Magnetic Characterization ◽  
Set Up ◽  
Cryogenic Conditions

This work describes the design and realisation of an apparatus to measure simultaneously the AC magnetic properties and the temperature distribution on the top surface of bulk superconducting samples (up to 32 mm in diameter) in cryogenic conditions (temperature range 78-120 K). First the authors describe the experimental set-up used for simultaneous thermal and magnetic characterization of the sample. Next, the authors describe the practical considerations required for generating the large AC magnetic fields, possibly in the presence of DC fields. Then the authors present the data acquisition system allowing both temperature and magnetic data to be recorded at high a sampling rate.” The performances and limitations of the system are discussed.

Effect of viscous dissipation in stokes flow between rotating cylinders using BEM

2019 ◽  
Vol 30 (4) ◽  
pp. 2121-2136 ◽  
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Nusselt Number ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Stokes Flow ◽  
Energy Equation ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Content Type ◽  
Dissipation Term ◽  
Cylinder Diameter

Purpose The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters. Design/methodology/approach The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders. Findings As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases. Originality/value The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

AC Magnetic Measurements on Superconductors

2011 ◽  
Vol 1 (3) ◽  
pp. 53-66
Author(s):  
Philippe Laurent ◽  
Jean-François Fagnard ◽  
Philippe Vanderbemden
Keyword(s):  
Magnetic Properties ◽  
Temperature Distribution ◽  
Magnetic Measurements ◽  
Sampling Rate ◽  
Data Acquisition System ◽  
Magnetic Data ◽  
Magnetic Characterization ◽  
Set Up ◽  
Cryogenic Conditions

This work describes the design and realisation of an apparatus to measure simultaneously the AC magnetic properties and the temperature distribution on the top surface of bulk superconducting samples (up to 32 mm in diameter) in cryogenic conditions (temperature range 78-120 K). First the authors describe the experimental set-up used for simultaneous thermal and magnetic characterization of the sample. Next, the authors describe the practical considerations required for generating the large AC magnetic fields, possibly in the presence of DC fields. Then the authors present the data acquisition system allowing both temperature and magnetic data to be recorded at high a sampling rate." The performances and limitations of the system are discussed.

Analysis of Shells of Revolution Subjected to Symmetrical and Nonsymmetrical Loads

1964 ◽  
Vol 31 (3) ◽  
pp. 467-476 ◽  
Author(s):  
A. Kalnins
Keyword(s):  
Direct Integration ◽  
Shells Of Revolution ◽  
Natural Boundary ◽  
First Order ◽  
Rotationally Symmetric ◽  
Dependent Variables ◽  
Method Of Solution ◽  
Natural Boundary Conditions ◽  
Numerical Method Of Solution ◽  
Theory Of Shells

The boundary-value problem of deformation of a rotationally symmetric shell is stated in terms of a new system of first-order ordinary differential equations which can be derived for any consistent linear bending theory of shells. The dependent variables contained in this system of equations are those quantities which appear in the natural boundary conditions on a rotationally symmetric edge of a shell of revolution. A numerical method of solution which combines the advantages of both the direct integration and the finite-difference approach is developed for the analysis of rotationally symmetric shells. This method eliminates the loss of accuracy encountered in the usual application of the direct integration approach to the analysis of shells. For the purpose of illustration, stresses and displacements of a pressurized torus are calculated and detailed numerical results are presented.

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