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Numerical Analysis of Fluid Flow and Heat Transfer Based on the Cylindrical Coordinate System
Mohammad Hassan Mohammadi
Issue:
Volume 4, Issue 1, March 2018
Pages:
1-13
Received:
18 October 2017
Accepted:
8 December 2017
Published:
15 January 2018
Abstract: In this work we will apply the three-dimensional mathematical modelling of fluid flow and heat transfer inside the furnaces based on the cylindrical coordinate system to describe the behavior of the transport phenomena. This modelling is constructed by using the mass, momentum, and energy conservation laws to achieve the continuity equation, the Navier-Stokes equations, and the energy conservation equation. Due to the moving boundary between the solid and melted materials inside of the furnaces we will impose the Stefan condition to describe the behavior of the free boundary between two phases. We will derive the variational formulation of the system of transport phenomena, then we will discrete the domain to complete the finite element method stages and we will obtain the system of nonlinear equations in 256 equations in 256 unknowns. To get the numerical solution of the large-scale system we will prepare a convenient mathematical work and gain some diagrams where they would be applicable in the design process of the furnaces shapes.
Abstract: In this work we will apply the three-dimensional mathematical modelling of fluid flow and heat transfer inside the furnaces based on the cylindrical coordinate system to describe the behavior of the transport phenomena. This modelling is constructed by using the mass, momentum, and energy conservation laws to achieve the continuity equation, the Na...
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Modeling an Ascending Nitrogen Gas Bubble in a Medium Crude Oil by Lattice Boltzmann Method
Carolina del Valle Silva,
Luque Montilla Jesús Miguel
Issue:
Volume 4, Issue 1, March 2018
Pages:
14-19
Received:
20 October 2017
Accepted:
19 December 2017
Published:
19 January 2018
Abstract: The study and modeling of oil biphasic systems, liquid-liquid and liquid-gas, focus mainly on the details of the modifications and application of the numerical methods itself. The correspondence between theoretical and experimental results and the information needed to apply a certain numerical method, usually remain in the background. On the other hand, in the particular case of the prediction of minimum miscibility pressure, extremely important parameter in oil exploration, references that show qualitative and numerical data associated with the characterization of the systems are scarce. The above reasons motivated the realization of this work. We used the Lattice Boltzmann Equation method to model a two-dimensional system of the displacement of a nitrogen gas bubble through a medium crude oil, under different pressure conditions keeping the temperature constant. According to experimental data, the bubble is not miscible by the crude, under a pressure range of 5000 psi to 6500 psi; nevertheless, the bubble is miscible in the range of 7000 psi to 7500 psi. Throughout simulations performed under similar conditions, we showed that it can be inferred the critical pressure range of miscibility of a medium crude oil.
Abstract: The study and modeling of oil biphasic systems, liquid-liquid and liquid-gas, focus mainly on the details of the modifications and application of the numerical methods itself. The correspondence between theoretical and experimental results and the information needed to apply a certain numerical method, usually remain in the background. On the other...
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Numerical Solution of Burger’s_Fisher Equation in One - Dimensional Using Finite Differences Methods
Abdulghafor M. Al-Rozbayani,
Karam A. Al-Hayalie
Issue:
Volume 4, Issue 1, March 2018
Pages:
20-26
Received:
24 October 2017
Accepted:
4 January 2018
Published:
1 February 2018
Abstract: In this paper the Burger’s_Fisher equation inone dimension has been solved by using three finite differences methods which are the explicit method, exponential method and DuFort_Frankel method After comparing the numerical results of those methods with the exact solution for the equation, there has been found an excellent approximation between exact solution and Numerical solutions for those methods, the DuFort_Frankel method was the best method in one dimension.
Abstract: In this paper the Burger’s_Fisher equation inone dimension has been solved by using three finite differences methods which are the explicit method, exponential method and DuFort_Frankel method After comparing the numerical results of those methods with the exact solution for the equation, there has been found an excellent approximation between exac...
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Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate
Taha Zakaraia Abdel Wahid
Issue:
Volume 4, Issue 1, March 2018
Pages:
27-37
Received:
21 September 2017
Accepted:
26 October 2017
Published:
15 March 2018
Abstract: The extension of the previous paper [Can. J. Phys. Vol. 88, (2010), 501–511] has been made. Therefore, the effect of the neutral atoms collisions with electrons and with positive ions is taken into consideration, which was ignored, for the sake of simplicity, in the earlier work. Thus, we will have multi-collision terms (electron–electron, electron–ion, electron– neutral) instead of one term, as was studied before for the sake of facilitation. These collision terms are needed to obtain the real physical situation. The new procedures will increase the ability of the research applications. This study is based on the solution of the BGK (Bhatnager–Gross–Krook) model of the nonlinear partial differential Boltzmann equations coupled with Maxwell’s partial differential equations. The initial-boundary value problem of the Rayleigh flow problem applied to the system of the plasma (positive ions + electrons+ neutral atoms), bounded by a moving plate, is solved. For this purpose, the traveling wave solution method is used to get the exact solution of the nonlinear partial differential equations system. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both dia-magnetic and para-magnetic plasma. The results are applied to a typical model of laboratory argon plasma. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.
Abstract: The extension of the previous paper [Can. J. Phys. Vol. 88, (2010), 501–511] has been made. Therefore, the effect of the neutral atoms collisions with electrons and with positive ions is taken into consideration, which was ignored, for the sake of simplicity, in the earlier work. Thus, we will have multi-collision terms (electron–electron, electron...
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