Determination of the initial temperature distribution of a body by optimal dynamic filtering

1978 ◽  
Vol 35 (4) ◽  
pp. 1237-1240 ◽  
Author(s):  
Yu. M. Matsevityi ◽  
A. V. Multanovskii
Keyword(s):  
Temperature Distribution ◽  
Initial Temperature ◽  
Initial Temperature Distribution ◽  
Optimal Dynamic ◽  
Dynamic Filtering

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.

Influence of Hot Leveling and Cooling Process on Residual Stresses of Steel Plates

2010 ◽  
Vol 168-170 ◽  
pp. 1130-1135 ◽  
Author(s):  
Ji Ping Chen ◽  
Jian Qing Qian ◽  
Sheng Zhi Li
Keyword(s):  
Residual Stress ◽  
Temperature Distribution ◽  
Residual Stresses ◽  
Initial Temperature ◽  
Steel Plate ◽  
Coupled Model ◽  
Distribution Patterns ◽  
Cooling Process ◽  
Initial Temperature Distribution ◽  
Actual Measurement

A three-dimensional thermo-mechanical coupled model of hot leveling and cooling processes of the steel plate has been conducted with MSC.Superform software. Four kinds of initial temperature distribution patterns have been determined according to literature. The effects of hot leveling and cooling processes on the transversal and longitudinal residual stresses of the steel plate have been analyzed. The results show that the initial temperature distribution patterns have significant influence on the residual stress of the plate. The more uniform temperature distribution patterns along the width of the plate, the smaller residual stress and also the smaller stress fluctuations. The cooling process has greater effect on the residual stress compared with the hot leveling process. The bigger the temperature gradient along the width of steel plate, the larger the residual stress and its fluctuation is. Through the FEM study, the value and direction of transversal and longitudinal residual stresses can be confirmed quantitatively at various positions along the width and length of plate, which can provide guidance to actual measurement of residual stress.

Formability Improvement Technique for Heated Sheet Metal Forming by Partial Cooling

2014 ◽  
Vol 622-623 ◽  
pp. 279-283 ◽  
Author(s):  
Eiichi Ota ◽  
Yasuhiro Yogo ◽  
Takamichi Iwata ◽  
Noritoshi Iwata ◽  
Kenjiro Ishida ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Sheet Metal ◽  
Deep Drawing ◽  
Initial Temperature ◽  
Hot Stamping ◽  
Local Deformation ◽  
Control Technique ◽  
Forming Limit ◽  
Forming Process ◽  
Initial Temperature Distribution

A forming process for heated sheet metal, such as hot-stamping, has limited use in deformable shapes. Higher temperature areas which have not yet come into contact with dies are more easily deformed; therefore, local deformation occurs at these areas which leads to breakage. To improve the formability of heated sheet metal, a deformation control technique utilizing the temperature dependence of flow stress is proposed. This technique can suppress local deformation by partial cooling around potential cracking areas to harden them before forming. In order to apply this technique to a variety of product shapes, a procedure to determine a suitable initial temperature distribution for deep drawing and biaxial stretching was developed with a coupled thermal structural simulation. In this procedure, finite elements exceeding forming limit strain are highlighted, and an initial temperature distribution is defined with areas of decreased temperature around the elements to increase their resistance to deformation. Subsequently, the partial cooling technique was applied to a deep drawing test with a heated steel sheet. The results of the experiment showed that the proposed technique improved 71% in the forming limit depth compared with results obtained using a uniform initial temperature distribution.

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