scholarly journals Initiation of combustion waves in solids, and the effects of geometry

2001 ◽  
Vol 43 (1) ◽  
pp. 149-163 ◽  
Author(s):  
J. Brindley ◽  
J. F. Griffiths ◽  
A. C. McIntosh ◽  
J. Zhang
Keyword(s):  
Initial Temperature ◽  
Solid Medium ◽  
Boundary Surface ◽  
Critical Conditions ◽  
Main Concern ◽  
Initial Temperature Distribution ◽  
Combustion Waves ◽  
Finite Systems ◽  
The Waves ◽  
Central Sphere

AbstractIn a recent paper Weber et al. [9] examined the propagation of combustion waves in a semi-infinite gaseous or solid medium. Whereas their main concern was the behaviour of waves once they had been initiated, we concentrate here on the initiation of such waves in a solid medium and have not examined in detail the steadiness or otherwise of the waves subsequent to their formation. The investigation includes calculations for finite systems. The results for a slab, cylinder and sphere are compared.Critical conditions for initiation of ignition by a power source are established. For a slab the energy input is spread uniformly over one boundary surface. In the case of cylindrical or spherical symmetry it originates from a cylindrical core or from a small, central sphere, respectively. The size of source and reactant body is important in the last two cases. With the exception of the initial temperature distribution, the equations investigated are similar in form to those of Weber et al. [5,9] and, as a prelude to the present study, with very simple adaptation, it has been possible to reproduce the results of the earlier work. We then go on to report the result of calculations for the initiation of ignition under different geometries with various initial and boundary conditions.

On the Effect of Hull Girder Flexibility on the Vertical Wave Bending Moment for Ultra Large Container Vessels

2012 ◽  
Author(s):  
Ingrid Marie Vincent Andersen ◽  
Jørgen Juncher Jensen
Keyword(s):  
Bending Moment ◽  
Main Concern ◽  
Hull Girder ◽  
Numerical Predictions ◽  
Strip Theory ◽  
Reliability Method ◽  
Non Linear ◽  
Large Container ◽  
The Waves ◽  
Good Agreement

Currently, a number of very large container ships are being built and more are on order, and some concerns have been expressed about the importance of the reduced hull girder stiffness to the wave-induced loads. The main concern is related to the fatigue life, but also a possible increase in the global hull girder loads as consequence of the increased hull flexibility must be considered. This is especially so as the rules of the classification societies do not explicitly account for the effect of hull flexibility on the global loads. In the present paper an analysis has been carried out for the 9,400 TEU container ship used as case-ship in the EU project TULCS (Tools for Ultra Large Container Ships). A non-linear time-domain strip theory is used for the hydrodynamic analysis of the vertical bending moment amidships in sagging and hogging conditions for a flexible and a rigid modelling of the ship. The theory takes into account non-linear radiation forces (memory effects) through the use of a set of higher order differential equations. The non-linear hydrostatic restoring forces and non-linear Froude-Krylov forces are determined accurately at the instantaneous position of the ship in the waves. Slamming forces are determined by a standard momentum formulation. The hull flexibility is modelled as a non-prismatic Timoshenko beam. Generally, good agreement with experimental results and more accurate numerical predictions has previously been obtained in a number of studies. The statistical analysis is done using the First Order Reliability Method (FORM) supplemented with Monte Carlo simulations. Furthermore, strip-theory calculations are compared to model tests in regular waves of different wave lengths using a segmented, flexible model of the case-ship and good agreement is obtained for the longest of the waves. For the shorter waves the agreement is less good. The discrepancy in the amplitudes of the bending moment can most probably be explained by an underestimation on the effect of momentum slamming in the strip-theory applied.

COMPUTATIONAL SOLUTION OF TEMPERATURE DISTRIBUTION IN A THIN ROD OVER A GIVEN INTERVAL I={x├|0

2021 ◽  
Vol 5 (1) ◽  
pp. 608-618
Author(s):  
Falade Kazeen Iyanda ◽  
Ismail Baoku ◽  
Gwanda Yusuf Ibrahim
Keyword(s):  
Temperature Distribution ◽  
Homotopy Perturbation Method ◽  
Initial Temperature ◽  
Applied Mathematics ◽  
Numerical Algorithms ◽  
Initial Temperature Distribution ◽  
Related Field ◽  
Homotopy Perturbation ◽  
Numerical Tools ◽  
New Iterative Method

In this paper, two analytical–numerical algorithms are formulated based on homotopy perturbation method and new iterative method to obtain numerical solution for temperature distribution in a thin rod over a given finite interval. The effects of different parameters such as the coefficient  which accounts for the heat loss and the diffusivity constant  are examined when initial temperature distribution  (trigonometry and algebraic functions) are considered. The error in both algorithms approaches to zero as the computational length  increases. The proposed algorithms have been demonstrated to be quite flexible, robust and accurate. Thus, the algorithms are established as good numerical tools to solve several problems in applied mathematics and other related field of sciences

scholarly journals Field Observations and Experimental and Theoretical Studies on the Superimposed Ice of McCall Glacier, Alaska

1976 ◽  
Vol 16 (74) ◽  
pp. 135-149 ◽  
Author(s):  
Gorow Wakahama ◽  
Daisuke Kuroiwa ◽  
Tatsuo Hasemi ◽  
Carl S. Benson
Keyword(s):  
Growth Rate ◽  
Temperature Distribution ◽  
Laboratory Experiment ◽  
Observational Data ◽  
Initial Temperature ◽  
Field Observations ◽  
Snow Melting ◽  
Initial Temperature Distribution ◽  
Run Off ◽  
Melt Water

AbstractThe formation of superimposed ice in the accumulation area of sub-polar glaciers plays an important role in the heat and mass balance of the glaciers. In order to study the process of superimposed ice formation in detail, field observations were conducted on McCall Glacier, a sub-polar glacier in Arctic Alaska. It was found that the approximate thickness of superimposed ice formed in a whole summer was 20 cm in the upper region and 30—40 cm in the lower region of the accumulation area of the glacier. This difference in thickness may be attributed to the difference in the temperature of the underlying ice and the rate of supply of melt water. The ratio of the amount of superimposed ice formed in the accumulation area from May to July in 1972 to the total amount of melt was determined. Approximately 50% of the total melt water was discharged from the glacier as run-off water, and the remainder contributed to the formation of superimposed ice.An experimental study on the artificial formation of superimposed ice was conducted in the cold laboratory to obtain the ratio of superimposed ice, that of run-off water, and that of free water suspended between snow grains, to the total amount of melt water produced in the snow. The ratios obtained in the laboratory experiment agree fairly well with those derived from the observational data on McCall Glacier.Numerical calculations were conducted to examine the relationship between the growth rate of superimposed ice, the rale of snow melting, the rate of discharge of excess melt-water, and the temperature of the underlying ice. Calculations were made in reference to both the laboratory experiment and the field observations on McCall Glacier. It was found that the predominant factors controlling the growth rate or the total amount of superimposed ice in a sub-polar glacier are the rate of supply of melt water to the snow-ice interface and the initial temperature distribution in the underlying ice. By using the present calculation, it may be possible to estimate the growth rate, the total amount of superimposed ice, and the ratio of superimposed ice to the total amount of melting in the accumulation area of any sub-polar glacier, if observational data on the initial temperature distribution in ice and the rate of snow melting at the snow surface are available.

scholarly journals Porous medium combustion: ignition, temporal evolution, and parameter dependence

1991 ◽  
Vol 33 (1) ◽  
pp. 16-26
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Porous Medium ◽  
Temperature Distribution ◽  
Initial Data ◽  
Initial Temperature ◽  
Temporal Evolution ◽  
Parameter Dependence ◽  
Initial Temperature Distribution ◽  
Infinite Slab

AbstractA model for the combustion of a porous medium is considered for an infinite slab. The case of ignition by an initial temperature distribution is considered first. The influence of the initial data and parameters on the solution is inferred from the solution of a related ordinary differential equation. The case of ignition by heating on one side of the slab is then considered in the same manner.

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