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
The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact soluti...The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.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
Recently, a new (2+1)-dimensional shallow water wave system, the (2+1)-dlmenslonal displacement shallow water wave system (2DDSWWS), was constructed by applying the variational principle of the analytic mechan...Recently, a new (2+1)-dimensional shallow water wave system, the (2+1)-dlmenslonal displacement shallow water wave system (2DDSWWS), was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.展开更多
In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx + (um) which is a generalized model of Boussinesq equation uts = (u2)xx + u an...In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx + (um) which is a generalized model of Boussinesq equation uts = (u2)xx + u and modified Bousinesq equation utt = (u3)xx + uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively.展开更多
The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,wa...The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual solutions exist for both cases. Moreover,numerical results show that the heat transfer rate at the surface decreases in the presence of the radiation effect.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
A suitable similarity transformation is introduced to reduce the laminarboundary layer equations of power law fluids to a class of singular nonlinear two-point boundaryvalue problems. The kin friction and shear stress...A suitable similarity transformation is introduced to reduce the laminarboundary layer equations of power law fluids to a class of singular nonlinear two-point boundaryvalue problems. The kin friction and shear stress distributions for boundary layer flow over amoving flat plate are investigated by utilizing the shooting technique. Results indicate that foreach fixed value of the power law exponent n or the velocity ratio parameter xi, the skin frictionand shear stress decrease with the increasing of n or xi respectively.展开更多
To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a powe...To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.展开更多
In this paper, the(2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional(2 D) similarity reduction equations by using the approximate symmetry method. A step-by-step proce...In this paper, the(2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional(2 D) similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.展开更多
A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this as...A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.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
The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these ...The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.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
In this paper,eight types of (1-+1)-dimensional similarity reductions which contain variable coefficient equation,are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensio...In this paper,eight types of (1-+1)-dimensional similarity reductions which contain variable coefficient equation,are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensional isospectral flows associated with the second-order scalar operators by using the direct method.In addition,the cnoidal wave solution and dromion-like solution are also derived by using the reduced nonlinear ordinary differential equations.The (1+1) dromion obtained by Lou [J.Phys.A28 (1995) 7227] and Zhang [Chin.Phys.9 (2000) 1] is only a special case of our results.Moreover,some properties of the dromion-like solutions are analyzed.展开更多
The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for...The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.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
A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion metho...A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method.The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion.It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.展开更多
A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities signifi...A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.展开更多
The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual...The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.展开更多
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.
基金Xi’an University of Architecture and Technology(Grant no.002/2040221134).
文摘The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.
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Project supported by the Natural Science Foundation of Guangdong Province of China (Grant No.10452840301004616)the National Natural Science Foundation of China (Grant No.61001018)the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (Grant No.408YKQ09)
文摘Recently, a new (2+1)-dimensional shallow water wave system, the (2+1)-dlmenslonal displacement shallow water wave system (2DDSWWS), was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.
文摘In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx + (um) which is a generalized model of Boussinesq equation uts = (u2)xx + u and modified Bousinesq equation utt = (u3)xx + uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively.
基金supported by a research grant from Universiti Kebangsaan Malaysia(No.UKM-GUP-BTT-07-25-174)
文摘The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual solutions exist for both cases. Moreover,numerical results show that the heat transfer rate at the surface decreases in the presence of the radiation effect.
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.
基金This work was financially supported by the Cross-Century Talents Projects of Educational Ministry, China and the "973" Key Item(
文摘A suitable similarity transformation is introduced to reduce the laminarboundary layer equations of power law fluids to a class of singular nonlinear two-point boundaryvalue problems. The kin friction and shear stress distributions for boundary layer flow over amoving flat plate are investigated by utilizing the shooting technique. Results indicate that foreach fixed value of the power law exponent n or the velocity ratio parameter xi, the skin frictionand shear stress decrease with the increasing of n or xi respectively.
基金Project supported by the National Natural Science Foundation of China (No.50425926)
文摘To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.
基金Project supported by the National Natural Science Foundation of China(Grant No.11505094)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20150984)
文摘In this paper, the(2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional(2 D) similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.
文摘A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.
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The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.
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.
文摘In this paper,eight types of (1-+1)-dimensional similarity reductions which contain variable coefficient equation,are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensional isospectral flows associated with the second-order scalar operators by using the direct method.In addition,the cnoidal wave solution and dromion-like solution are also derived by using the reduced nonlinear ordinary differential equations.The (1+1) dromion obtained by Lou [J.Phys.A28 (1995) 7227] and Zhang [Chin.Phys.9 (2000) 1] is only a special case of our results.Moreover,some properties of the dromion-like solutions are analyzed.
文摘The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.
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.
基金National Natural Science Foundation of China(50378063)EYTP of MOESRF for ROCS,MOE
文摘A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method.The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion.It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.
基金Supported by National Natural Science Foundation of China (50378063), Excellent Young Teachers Program of MOE and SRF for ROCS, MOE.
文摘A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.
文摘The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.