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Numerical Solution of the Coupled viscous Burgers’ Equation Using Differential Quadrature Method Based on Fourier Expansion Basis

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Applied Mathematics 2018年第7期9卷 821-835页

作者： Masho Jima Alemayehu Shiferaw Ali Tsegaye Department of Mathematics Jimma University Jimma Ethiopia

The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Differential quadrature method based on Fourier expansion basis to obtain a system of ordinary differential equation (ODE) then we implement the numerical scheme by computer programing and perform numerical solution. Finally the validation of the present scheme is demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produces a good result as compared to other researcher’s result and even generates a value at the nodes or mesh points that the results have not seen yet.

关键词： Differential Quadrature Method Fourier Expansion Coupled viscous Coupled viscous Burgers’ Equation Initial and Boundary Conditions

Thermal Radiation, Joule Heating, and viscous Dissipation Effects on MHD Forced Convection Flow with Uniform Surface Temperature

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Open Journal of Fluid Dynamics 2014年第2期4卷 125-132页

作者： M. Y. Abdollahzadeh Jamalabadi Jae Hyun Park Department of Aerospace and System Engineering Research Center for Aircraft Parts Technology Gyeongsang National University Jinju South Korea Maritime University of Chabahar Chabahar Iran

In this paper, we studied the effects of thermal radiation, Joule heating and viscous dissipation on forced convection flow in a magnetohydrodynamics (namely MHD) pump in rectangular channel with uniform surface temperature. Numerical results were obtained by solving the nonlinear governing momentum and energy equations with steady state fully developed assumptions by finite difference method. The Lorentz force in momentum and Joule heating, and viscous dissipation in energy equation with the Rossel and approximation are assumed to increase the knowledge of the details of the temperature and flow field in order to design a MHD pump. The purpose of this study is the parametric study of a Newtonian fluid in a MHD pump. The values of maximum velocity, fully developed Nusselt number for different values of magnetic density flux, Brinkman number, viscous heating and radiation number are obtained. However, the maximum temperature stays almost constant with magnetic field, as current increases, the velocity and the temperature increase too. Besides, the increase of thermal radiation number causes the increase in effective thermal conductivity and decrease in thermal boundary layer and the Nusselt number at wall.

关键词： Forced Convection Thermal Radiation Magnetohydrodynamic Pump Internal Heating viscous Dissipation Roseland Model

The Application of the Generalized Differential Formulation of the First Law of Thermodynamics for Evidence of the Tidal Mechanism of Maintenance of the Energy and viscous-Thermal Dissipative Turbulent Structure of the Mesoscale Oceanic Eddies

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Journal of Modern Physics 2018年第3期9卷 357-386页

作者： Sergey V.Simonenko Vyacheslav B.Lobanov V.I.Il'ichev Pacific Oceanological Institute Far Eastern Branch of Russian Academy of SciencesVladivostokRussia

The practical significance of the established generalized differential formula-tion of the first law of thermodynamics (formulated for the rotational coor-dinate system) is evaluated (for the first time and for the mesoscale oceanic eddies) by deriving the general (viscous-compressible-thermal) and partial (incompressible, viscous-thermal) local conditions of the tidal maintenance of the quasi-stationary energy and dissipative turbulent structure of the mesoscale eddy located inside of the individual fluid region of the ther-mally heterogeneous viscous (compressible and incompressible, respective-ly) heat-conducting stratified fluid over the two-dimensional bottom topog-raphy characterized by the horizontal coordinate x along a horizon-tal axis X. Based on the derived partial (incompressible) local condition (of the tidal maintenance of the quasi-stationary energy and viscous-thermal dis-sipative turbulent structure of the mesoscale eddy) and using the calculated vertical distributions of the mean viscous dissipation rate per unit mass and the mean thermal dissipation rate per unit mass in four regions near the observed mesoscale (periodically topographically trapped by nearly two-dimensional bottom topography h(x) eddy located near the northern region of the Yamato Rise in the Japan Sea, the combined analysis of the energy structure of the eddy and the viscous-thermal dissipative structure of turbulence is presented. The convincing evidence is presented of the tidal mechanism of maintenance of the eddy energy and viscous-thermal dissipa-tive structure of turbulence (produced by the breaking internal gravity waves generated by the eddy) in three regions near the Yamato Rise subjected to the observed mesoscale eddy near the northern region of the Yamato Rise of the Japan Sea.

关键词： Generalized Formulation of the First Law of Thermodynamics Cosmic Gravitation Small-Scale Dissipative Turbulence viscous and Thermal Dissipation Rates Mesoscale Oceanic Eddies Internal Tide

MHD Free Convection Flow past an Inclined Stretching Sheet with Considering viscous Dissipation and Radiation

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Open Journal of Fluid Dynamics 2017年第2期7卷 152-168页

作者： Maruf Hasan Enamul Karim Abdus Samad Department of Mathematics Comilla University Comilla Bangladesh Department of Applied Mathematics University of Dhaka Dhaka Bangladesh

The present study concentrates on the analysis of MHD free convection flow past an inclined stretching sheet. The viscous dissipation and radiation effects are assumed in the heat equation. Approximation solutions have been derived for velocity, temperature, concentration, Nusselt number, skin friction and Sherwood number using Nachtsheim-Swigert shooting iteration technique along with the six-order Runge-Kutta iteration scheme. Graphs are plotted to find out the characteristics of different physical parameters. The variations of physical parameters on skin friction coefficient, Nusselt number and Sherwood number are displayed via table.

关键词： viscous Dissipation Magnetic Field Skin Friction Eckert Number

Prospects of viscous Crude Development in Liaohe Oilfields

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China Oil & Gas 1997年第2期4卷 68-70页

作者： Zhang Xiuwen Rong Jiashu Chief Geologist Research Institute of Liaohe Petroleum Exploration Bureau

Liaohe oil area has developed viscous crude for 20 years. The annual output reached 8.46 million tons in 1995, of which 6.77 million tons were produced by steam injection, accounting for 56% of crude output by the met... 详细信息

关键词： viscous oil recovcry Steam soaking Development project

Axial power flow distributions of ultrasonic guided waves in viscous liquid-filled pipes

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声学技术 2004年第S1期23卷 18-22页

作者： TA Dean (Department of Electronic Engineering, Fudan University, Shanghai 200433, China) Department of Electronic Engineering Fudan University Shanghai 200433 China

The axial power flow (APF) magnitude and attenuation distributions of ultrasonic longitudinal guided waves in viscous liquid-filled elastic pipes are investigated. The optimal location, optimal mode and its frequency-thickness product (fd) for the test of pipes filled with viscous liquid are chosen according to APF and attenuation distributions. The results show that the APF magnitude distribution is an important parameter in choosing the modes and parameters. A particular mode has weak dispersion in ranges of fd values with large group velocity, while other modes with smaller group velocity in the same fd ranges have stronger dispersion. It has been observed that, within these ranges, the chosen mode has a larger APF on the (pipe’s) wall. Therefore, in the region of fd values where a particular mode has a large group velocity, this mode will be effective to be used in testing elastic pipes filled with viscous liquid. The results obtained from both the APF analysis and attenuation distribution are consistent.

关键词： guided waves viscous liquid-filled elastic pipes axial power flow (APF) attenuation

MHD Flow, and Heat Transfer with Effects of Buoyancy, viscous and Joules Dissipation over a Nonlinear Vertical Stretching Porous Sheet with Partial Slip

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Engineering（科研） 2011年第3期3卷 285-291页

作者： M. Subhas Abel Kulkarni Anant Kumar R. Ravikumara 不详

In this paper, the problem of steady laminar two-dimensional boundary layer MHD flow and heat transfer of an incompressible viscous fluid with the presence of buoyancy force and viscous dissipation over an vertical nonlinear stretching sheet with partial slip is investigated numerically. Numerical solutions of the resulting nonlinear boundary value problem in the case when the sheet stretches with a velocity varying nonlinearly with the distance is carried out. The effects of for various values of suction parameter, magnetic parameter, Prandtl number, Eckert number, buoyancy parameter, nonlinear stretching parameter and slip parameter on flow and heat transfer characteristics is investigated.

关键词： MHD Nonlinear Stretching Parameter Joules Dissipation viscous Dissipation Eckert Number Slip Parameter

Asymptotic Stability of Combination of Contact Discontinuity with Rarefaction Waves for the One-Dimensional viscous Micropolar Fluid Model

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Journal of Applied Mathematics and Physics 2019年第9期7卷 2089-2111页

作者： Lishuang Peng College of Science University of Shanghai for Science and Technology Shanghai China

In this paper, we consider with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible micropolar fluid model, where the far field states are prescribed. When the corresponding Riemann problem for the Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is shown that the combination wave corresponding to the contact discontinuity, with rarefaction waves is asymptotically stable provided that the strength of the combination wave and the initial perturbation are suitably small. This result is proved by using elementary L2-energy methods.

关键词： Contact Discontinuity Rarefaction Waves viscous Micropolar Fluid Model Asymptotic Stability Energy Estimates

Mechanism for strong normal velocity fluctuations in viscous sublayer

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Science China Mathematics 1996年第5期39卷 520-527页

作者：许春晓 F.T.M.Nieuwstadt 张兆顺 Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China Lab for Aero- and Hydro-dynamics Faculty of Mechanical Engineering and Marine Technology Technical University of Delft Netherlands

The spike phenomena,namely strong normal velocity fluctuations,in the viscous sublayer have been discovered through detailed investigation of the databank of the direct numerical simulation of a turbulent channel *** characteristic features are disclosed and their effects on the generation of turbulence,and correlation with the vortex structures are studied.

关键词： viscous sublayer spike turbulence.