The spread of flame across a liquid surface II. Steady-state conditions

1968 ◽  
Vol 308 (1492) ◽  
pp. 55-68 ◽  
Keyword(s):  
Steady State ◽  
Gas Phase ◽  
Flame Spread ◽  
Initial Temperature ◽  
Liquid Surface ◽  
Flash Point ◽  
One Dimensional ◽  
Flammable Liquids ◽  
The One ◽  
Qualitative Picture

The one-dimensional spread of flame along the surface of flammable liquids confined in a parallel-sided channel has been studied and the effects of physical dimensions and initial temperature upon its rate established. When the initial temperature of the liquid is below the closed flash point, flame spread depends upon the transfer of heat to the liquid sufficient to raise its surface temperature to the flash-point value and a qualitative picture of the mechanism by which this takes place is developed. When the initial temperature is above the flash point, flame spread is dependent upon conditions in the gas phase above the liquid and these are defined.

On a Class of Models for the Yielding Behavior of Continuous and Composite Systems

1967 ◽  
Vol 34 (3) ◽  
pp. 612-617 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Bauschinger Effect ◽  
Three Dimensions ◽  
Cyclic Behavior ◽  
One Dimensional ◽  
Composite Systems ◽  
Yielding Behavior ◽  
Nonsteady State ◽  
The One ◽  
Incremental Theory Of Plasticity

A class of one-dimensional models for the yielding behavior of materials and structures is presented. This class of models leads to stress-strain relations which exhibit a Bauschinger effect of the Massing type, and both the steady-state and nonsteady-state cyclic behavior are completely specified if the initial monotonic loading behavior is known. The concepts of the one-dimensional class of models are extended to three-dimensions and lead to a subsequent generalization of the customary concepts of the incremental theory of plasticity.

SPATIAL DISORDER OF CNN — WITH ASYMMETRIC OUTPUT FUNCTION

2001 ◽  
Vol 11 (08) ◽  
pp. 2085-2095 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
KAI-PING CHIEN ◽  
SONG-SUN LIN ◽  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Steady State ◽  
Three Dimensional ◽  
Cellular Neural Networks ◽  
Output Function ◽  
One Dimensional ◽  
Spatial Entropy ◽  
The One ◽  
Steady State Solutions

This investigation will describe the spatial disorder of one-dimensional Cellular Neural Networks (CNN). The steady state solutions of the one-dimensional CNN can be replaced as an iteration map which is one dimensional under certain parameters. Then, the maps are chaotic and the spatial entropy of the steady state solutions is a three-dimensional devil-staircase like function.

scholarly journals Non-steady-state heat conduction in composite walls

2014 ◽  
Vol 470 (2165) ◽  
pp. 20130605 ◽  
Author(s):  
Bernard Deconinck ◽  
Beatrice Pelloni ◽  
Natalie E. Sheils
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Composite Materials ◽  
Solution Method ◽  
One Dimensional ◽  
Infinite Domains ◽  
Steady State Heat ◽  
The One ◽  
Composite Walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Air Temperature Distribution Inside of a Longitudinal Highway Tunnel: A Case Study

2012 ◽  
Vol 433-440 ◽  
pp. 6384-6389 ◽  
Author(s):  
Xing Han ◽  
Xu Zhang
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Air Temperature ◽  
State Theory ◽  
One Dimensional ◽  
Highway Tunnel ◽  
Temperature Enhancement ◽  
The One ◽  
General Method

With the development of tunneling technology and the increase of transportation, the mobiles are discharging more and more heat into the tunnel nowadays, which will cause the temperature enhancement. In this paper, general method of calculating the heat discharge is studied, and temperature distribution in the tunnels, which use different ventilation systems, is studied according to the one-dimensional steady state theory. One tunnel is taken for example to calculate the temperature distribution. The result can b e used in the relevant design and research.

scholarly journals A computational method to solve for the heat conduction temperature field based on data-driven approach

2021 ◽  
pp. 165-165
Author(s):  
Kun Li ◽  
Shiquan Shan ◽  
Qi Zhang ◽  
Xichuan Cai ◽  
Zhou Zhijun
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Steady State ◽  
Transient State ◽  
Absolute Error ◽  
Computational Method ◽  
Data Driven ◽  
One Dimensional ◽  
Data Driven Approach ◽  
The One

In this paper, a computational method for solving for the one-dimensional heat conduction temperature field is proposed based on a data-driven approach. The traditional numerical solution requires algebraic processing of the heat conduction differential equations, and necessitates the use of a complex mathematical derivation process to solve for the temperature field. In this paper, a temperature field solution model called HTM (Hidden Temperature Method) is proposed. This model uses an artificial neural network to establish the correspondence relationship of the node temperature values during the iterative process, so as to obtain the "Data to Data" solution. In this work, one example of one-dimensional steady state and three examples of one-dimensional transient state are selected, and the calculated values are compared to those obtained by traditional numerical methods. The mean-absolute error(MAE)of the steady state is only 0.2508, and among the three transient cases, the maximum mean-square error(MSE) is only 2.6875, indicating that the model is highly accurate in both steady-state and transient conditions. This shows that the HTM simulation can be applied to the solution of the heat conduction temperature field. This study provides a basis for the further optimization of the HTM algorithm.

scholarly journals Investigation of the semi-strip’s stress state in the case of steady-state oscillations

2019 ◽  
pp. 54-57
Author(s):  
N. D. Vaysfeld ◽  
Z. Yu. Zhuravlova ◽  
O. P. Moyseenok ◽  
V. V. Reut
Keyword(s):  
Integral Equation ◽  
Steady State ◽  
General Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Partial Solution ◽  
Initial Problem ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

The elastic semi-strip under the dynamic load concentrated at the centre of the semi-strip’s short edge is considered. The lateral sides of the semi-strip are fixed. The case of steady-state oscillations is considered. The initial problem is reduced to the one-dimensional problem with the help of the semi-infinite sin-, cos-Fourier’s transform. The one-dimensional problem is formulated in the vector form. Its solution is constructed as a superposition of the general solution for the homogeneous equation and the partial solution for the inhomogeneous equation. The general solution for the homogeneous vector equation is found with the help of the matrix differential calculations. The partial solution is expressed through Green’s matrixfunction, which is constructed as the bilinear expansion. The inverse Fourier’s transform is applied to the derived expressions for the displacements. The solving of the initial problem is reduced to the solving of the singular integral equation. Its solution is searched as the series of the orthogonal Chebyshev polynomials of the second kind. The orthogonalization method is used for the solving of the singular integral equation. The stress-deformable state of the semi-strip is investigated regarding both the frequency of the applied load, and the load segment’s length.

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