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

Exact Analytical Solution for the Peristaltic Flow of Nanofluids in an Asymmetric Channel with Slip Effect of the Velocity, Temperature and Concentration

2014 ◽  
Vol 30 (4) ◽  
pp. 411-422 ◽  
Author(s):  
E. H. Aly ◽  
A. Ebaid
Keyword(s):  
Brownian Motion ◽  
Temperature Distribution ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Rise Velocity ◽  
Nanoparticle Concentration ◽  
Homotopy Perturbation

AbstractThe peristaltic flow of nanofluids under the effect of slip conditions was theoretically investigated. The mathematical model was governed by a system of linear and non-linear partial differential equations with prescribed boundary conditions. Then, the exact solutions were successfully obtained and reported for the first time in the present work. These exact solutions were then used for studying the effects of the slip, thermophoresis, Brownian motion parameters and many others on the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and pressure gradient. In addition, it is proved that the obtained exact solutions are reduced to the literature results in the special cases.In the general case, it was found that on comparing the current solutions with the approximate ones obtained using the homotopy perturbation method in literature, remarkable differences have been detected for behaviour of the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and finally the pressure gradient. An example of these differences is about effect of the Brownian motion parameter on the velocity profile; where it was shown in this paper that the small values of this parameter have not a significant effect on the velocity, while this situation was completely different in the published work. Many other significant differences have been also discussed. Therefore, these observed differences recommend the necessity of including the convergence issue when applying the homotopy perturbation method or any other series solution method to solve a physical model. In conclusion. The current results may be considered as a base for any future analysis and/or comparisons.

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.

scholarly journals Solving Fractional-Order Logistic Equation Using a New Iterative Method

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Iterative Method ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Logistic Equation ◽  
Series Solutions ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
New Iterative Method

A fractional version of logistic equation is solved using new iterative method proposed by Daftardar-Gejji and Jafari (2006). Convergence of the series solutions obtained is discussed. The solutions obtained are compared with Adomian decomposition method and homotopy perturbation method.

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.

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