Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is appl...Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.展开更多
The equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation, which needs to be solved numerically with a computer program.Neverthe...The equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation, which needs to be solved numerically with a computer program.Nevertheless, for people without access to the computer program, the conventional numerical method may be inconvenient. Thus, the objective here is to seek some method simpler than the conventional one for solving the flow problem. A commonly used model of the unidirectional methane gas flow is considered, where the methane adsorption is described by the Langmuir isotherm and the free gas is treated as real gas. By introducing the similarity solution, a simple method for solving the flow model is proposed, which can be done on a hand calculator. It is shown by two examples that the gas pressure profile obtained by the proposed method agrees well with the direct numerical solution of the flow model.展开更多
This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloc...This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.展开更多
Railway passenger flow forecasting can help to develop sensible railway schedules,make full use of railway resources,and meet the travel demand of passengers.The structure of passenger flow in railway networks and the...Railway passenger flow forecasting can help to develop sensible railway schedules,make full use of railway resources,and meet the travel demand of passengers.The structure of passenger flow in railway networks and the spatiotemporal relationship of passenger flow among stations are two distinctive features of railway passenger flow.Most of the previous studies used only a single feature for prediction and lacked correlations,resulting in suboptimal performance.To address the above-mentioned problem,we proposed the railway passenger flow prediction model called Flow-Similarity Attention Graph Convolutional Network(F-SAGCN).First,we constructed the passenger flow relations graph(RG)based on the Origin-Destination(OD).Second,the Passenger Flow Fluctuation Similarity(PFFS)algorithm is used to measure the similarity of passenger flow between stations,which helps construct the spatiotemporal similarity graph(SG).Then,we determine the weights of the mutual influence of different stations at different times through an attention mechanism and extract spatiotemporal features through graph convolution on the RG and SG.Finally,we fused the spatiotemporal features and the original temporal features of stations for prediction.The comparison experiments on a railway bureau’s accurate railway passenger flow data show that the proposed F-SAGCN method improved the prediction accuracy and reduced the mean absolute percentage error(MAPE)of 46 stations to 7.93%.展开更多
This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved a...This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.展开更多
Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses ins...Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary. The flux of the specie at the plate is proportional to specie concentration at the plate. The governing equations of continuity, momentum, energy and specie diffusion are transformed into ordinary differential equation by using the similarity transformation and solved numerically by using free parameter method along with shooting technique. The dimensionless velocity, temperature and concentration profiles are obtained and presented through figures for different parameters entering into the problem. The local Skin-friction co-efficient, Nusselt number and Sherwood number at the plate for physical interest are also discussed through tables.展开更多
Tornadoes and cyclones, as is stated in numerous literary and audiovisual works dedicated to these out of balance physical systems, are two powerful and spectacular atmospheric phenomena whose vertical and horizontal ...Tornadoes and cyclones, as is stated in numerous literary and audiovisual works dedicated to these out of balance physical systems, are two powerful and spectacular atmospheric phenomena whose vertical and horizontal profiles of winds and temperatures are not yet well known. Indeed, data and routine observations accumulated in the World Meteorological Organization (WMO) databases, regardless of their diversity and perfection of the instruments used to achieve these data (e.g. satellites, onboard cameras, wind profilers, ultra modern calculators, etc.), offer mind-blowing performances on the extent of damage caused by these disturbances, but information provided by these ground and space based observations will never allow access to real profiles of winds associated with tornadoes and cyclones both at the ground’s surface and aloft. The works recently carried out by C. Mbane Biouele allow us to discover that winds associated with tornadoes and hurricanes result from vectors addition of troposphere’s horizontal geostrophic winds and vertical movements associated with passive convection. Unfortunately, geostrophic wind and passive convection are two familiar meteorological phenomena described with much awkwardness and monumental mistakes by all scientific books written by authors who have remained loyal to Hadley principle which states (for centuries) that hot air is lighter than cold air. It is very important to know that C. Mbane Biouele’s very recent publications demonstrate that Hadley principle is not valid in the troposphere’s regions occupied by Ferrell cells. Indeed, it is urgent for the development of meteorology to highlight with great insistence to everyone that there is a Physics principle diametrically opposed to popular Hadley one which provides thermodynamic reasons of the formation of Ferrell cells. This Principle will be named Mbane Biouele Principe and be clearly stated in this paper.展开更多
The problem of aeroelasticity and maneuvering of command surface and gust wing interaction involves a starting flow period which can be seen as the flow of an airfoil attaining suddenly an angle of attack. In the line...The problem of aeroelasticity and maneuvering of command surface and gust wing interaction involves a starting flow period which can be seen as the flow of an airfoil attaining suddenly an angle of attack. In the linear or nonlinear case, compressive Mach or shock waves are generated on the windward side and expansive Mach or rarefaction waves are generated on the leeward side.On each side, these waves are composed of an oblique steady state wave, a vertically-moving onedimensional unsteady wave, and a secondary wave resulting from the interaction between the steady and unsteady ones. An analytical solution in the secondary wave has been obtained by Heaslet and Lomax in the linear case, and this linear solution has been borrowed to give an approximate solution by Bai and Wu for the nonlinear case. The structure of the secondary shock wave and the appearance of various force stages are two issues not yet considered in previous studies and has been studied in the present paper. A self-similar solution is obtained for the secondary shock wave,and the reason to have an initial force plateau as observed numerically is identified. Moreover, six theoretical characteristic time scales for pressure load variation are determined which explain the slope changes of the time-dependent force curve.展开更多
In this paper, the fluid flow differential equation based on the homogenous reservoirs model is first reviewed. Then a theorem about the formal similarity of solutions in the Laplace space with outer boundary conditio...In this paper, the fluid flow differential equation based on the homogenous reservoirs model is first reviewed. Then a theorem about the formal similarity of solutions in the Laplace space with outer boundary conditions and inner boundary condition is presented and proved. Lastly, a corollary of our theorem is given particularly on inner boundary. The obtained results are very helpful for understanding inherent laws of relevant engineering science and designing practical analysis software.展开更多
The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the dist...The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations （ODEs） are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.展开更多
Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed in...Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.展开更多
This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperat...This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x<sup>–2/3</sup>. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.展开更多
文摘Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.
基金provided by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
文摘The equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation, which needs to be solved numerically with a computer program.Nevertheless, for people without access to the computer program, the conventional numerical method may be inconvenient. Thus, the objective here is to seek some method simpler than the conventional one for solving the flow problem. A commonly used model of the unidirectional methane gas flow is considered, where the methane adsorption is described by the Langmuir isotherm and the free gas is treated as real gas. By introducing the similarity solution, a simple method for solving the flow model is proposed, which can be done on a hand calculator. It is shown by two examples that the gas pressure profile obtained by the proposed method agrees well with the direct numerical solution of the flow model.
基金supported in part by a grant from China Scholarship Councilthe National Natural Science Foundation of China(11301006)the Anhui Provincial Natural Science Foundation(1408085MA01)
文摘This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.
文摘Railway passenger flow forecasting can help to develop sensible railway schedules,make full use of railway resources,and meet the travel demand of passengers.The structure of passenger flow in railway networks and the spatiotemporal relationship of passenger flow among stations are two distinctive features of railway passenger flow.Most of the previous studies used only a single feature for prediction and lacked correlations,resulting in suboptimal performance.To address the above-mentioned problem,we proposed the railway passenger flow prediction model called Flow-Similarity Attention Graph Convolutional Network(F-SAGCN).First,we constructed the passenger flow relations graph(RG)based on the Origin-Destination(OD).Second,the Passenger Flow Fluctuation Similarity(PFFS)algorithm is used to measure the similarity of passenger flow between stations,which helps construct the spatiotemporal similarity graph(SG).Then,we determine the weights of the mutual influence of different stations at different times through an attention mechanism and extract spatiotemporal features through graph convolution on the RG and SG.Finally,we fused the spatiotemporal features and the original temporal features of stations for prediction.The comparison experiments on a railway bureau’s accurate railway passenger flow data show that the proposed F-SAGCN method improved the prediction accuracy and reduced the mean absolute percentage error(MAPE)of 46 stations to 7.93%.
文摘This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.
文摘Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary. The flux of the specie at the plate is proportional to specie concentration at the plate. The governing equations of continuity, momentum, energy and specie diffusion are transformed into ordinary differential equation by using the similarity transformation and solved numerically by using free parameter method along with shooting technique. The dimensionless velocity, temperature and concentration profiles are obtained and presented through figures for different parameters entering into the problem. The local Skin-friction co-efficient, Nusselt number and Sherwood number at the plate for physical interest are also discussed through tables.
文摘Tornadoes and cyclones, as is stated in numerous literary and audiovisual works dedicated to these out of balance physical systems, are two powerful and spectacular atmospheric phenomena whose vertical and horizontal profiles of winds and temperatures are not yet well known. Indeed, data and routine observations accumulated in the World Meteorological Organization (WMO) databases, regardless of their diversity and perfection of the instruments used to achieve these data (e.g. satellites, onboard cameras, wind profilers, ultra modern calculators, etc.), offer mind-blowing performances on the extent of damage caused by these disturbances, but information provided by these ground and space based observations will never allow access to real profiles of winds associated with tornadoes and cyclones both at the ground’s surface and aloft. The works recently carried out by C. Mbane Biouele allow us to discover that winds associated with tornadoes and hurricanes result from vectors addition of troposphere’s horizontal geostrophic winds and vertical movements associated with passive convection. Unfortunately, geostrophic wind and passive convection are two familiar meteorological phenomena described with much awkwardness and monumental mistakes by all scientific books written by authors who have remained loyal to Hadley principle which states (for centuries) that hot air is lighter than cold air. It is very important to know that C. Mbane Biouele’s very recent publications demonstrate that Hadley principle is not valid in the troposphere’s regions occupied by Ferrell cells. Indeed, it is urgent for the development of meteorology to highlight with great insistence to everyone that there is a Physics principle diametrically opposed to popular Hadley one which provides thermodynamic reasons of the formation of Ferrell cells. This Principle will be named Mbane Biouele Principe and be clearly stated in this paper.
基金supported by the Double First-Rate Project of Tsinghua University (2017) (No. 11472157)partly by the National Basic Research Program of China (No. 2012CB720205)
文摘The problem of aeroelasticity and maneuvering of command surface and gust wing interaction involves a starting flow period which can be seen as the flow of an airfoil attaining suddenly an angle of attack. In the linear or nonlinear case, compressive Mach or shock waves are generated on the windward side and expansive Mach or rarefaction waves are generated on the leeward side.On each side, these waves are composed of an oblique steady state wave, a vertically-moving onedimensional unsteady wave, and a secondary wave resulting from the interaction between the steady and unsteady ones. An analytical solution in the secondary wave has been obtained by Heaslet and Lomax in the linear case, and this linear solution has been borrowed to give an approximate solution by Bai and Wu for the nonlinear case. The structure of the secondary shock wave and the appearance of various force stages are two issues not yet considered in previous studies and has been studied in the present paper. A self-similar solution is obtained for the secondary shock wave,and the reason to have an initial force plateau as observed numerically is identified. Moreover, six theoretical characteristic time scales for pressure load variation are determined which explain the slope changes of the time-dependent force curve.
文摘In this paper, the fluid flow differential equation based on the homogenous reservoirs model is first reviewed. Then a theorem about the formal similarity of solutions in the Laplace space with outer boundary conditions and inner boundary condition is presented and proved. Lastly, a corollary of our theorem is given particularly on inner boundary. The obtained results are very helpful for understanding inherent laws of relevant engineering science and designing practical analysis software.
文摘The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations （ODEs） are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.
文摘Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.
文摘This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x<sup>–2/3</sup>. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.
