In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solutio...This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.展开更多
An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transvers...An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.展开更多
Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic diffe...Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.展开更多
Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes.Water is utilized as base liquid while carbon nanotubes are considered nanomaterial.An exponential stretchable curved surface flow is origin...Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes.Water is utilized as base liquid while carbon nanotubes are considered nanomaterial.An exponential stretchable curved surface flow is originated.Heat source is present.Xue relation of nanoliquid is employed to explore the feature of CNTs (single and multi-wall).Transformation technique is adopted in order to achieve non-linear ordinary differential systems.The governing systems are solved numerically.Effects of involved parameters on flow,temperature,concentration,heat transfer rate (Nusselt number) with addition of skin friction coefficient are illustrated graphically.Decay in velocity is noted with an increment in Forchheimer number and porosity parameter while opposite impact is seen for temperature.Moreover,role of MWCNTs is prominent when compared with SWCNTs.展开更多
This article gives a numerical report to two dimensional(2D)Darcy-Forchheimer flow of carbon-water nanofluid.Flow is instigated by exponential extending curved surface.Viscous liquid in permeable space is described by...This article gives a numerical report to two dimensional(2D)Darcy-Forchheimer flow of carbon-water nanofluid.Flow is instigated by exponential extending curved surface.Viscous liquid in permeable space is described by Darcy-Forchheimer.The subsequent arrangement of partial differential equations is changed into ordinary differential framework through proper transformations.Numerical arrangements of governing frameworks are set up by NDSolve procedure.Outcomes of different sundry parameters on temperature and velocity are examined.Skin friction and heat transfer rate are also shown and inspected.展开更多
Three-dimensional Darcy-Forchheimer nanoliquid flow in the presence of rotating frame and activation energy is inspected.Flow is developed through linearly stretching of the surface.Convection of heat and mass exchang...Three-dimensional Darcy-Forchheimer nanoliquid flow in the presence of rotating frame and activation energy is inspected.Flow is developed through linearly stretching of the surface.Convection of heat and mass exchange is given due consideration.The novel characteristics in regards to Brownian dispersion and thermophoresis are retained.The variation in partial differential framework (PDEs) to nonlinear ordinary differential framework (ODEs) is done through reasonable transformations.Governing differential frameworks have been computed in edge of NDSolve.Discussion regarding thermal field and concentration distribution for several involved parameters is pivotal part.Physical amounts like surface drag coefficients,transfer of heat and mass rates are portrayed by numeric esteems.It is noticed that impacts of porosity parameter and Forchheimer number on the thermal and concentration fields are quite similar.Both temperature and associated thermal layer thickness are enhanced for larger porosity parameter and Forchheimer number.Temperature and concentration fields exhibit similar trend for the higher values of rotational parameter.Effects of thermal and concentration Biot numbers on the temperature and concentration fields are qualitatively similar.Higher Prandtl and Schmidt numbers correspond to stronger temperature and concentration fields.Larger nondimensional activation energy,temperature difference parameter and fitted rate constant yield weaker concentration field.Brownian motion parameter for temperature and concentration has reverse effects while similar trend is observed via thermophoresis parameter.展开更多
The underbalanced drilling has been widely used due to its advantages of high drilling efficiency and low cost etc., especially for hard formation drilling. These advantages, however, are closely related to the stress...The underbalanced drilling has been widely used due to its advantages of high drilling efficiency and low cost etc., especially for hard formation drilling. These advantages, however, are closely related to the stress state of the bottom-hole rock; therefore, it is significant to research the stress distribution of bottom-hole rock for the correct understanding of the mechanism of rock fragmentation and high penetration rate. The stress condition of bottom-hole rock is very complicated while under the co-action of overburden pressure, horizontal in-situ stresses, drilling mud pressure, pore pressure and temperature etc. In this paper, the fully coupled simulation model is established and the effects of overburden pressure, horizontal in-situ stresses, drilling mud pressure, pore pressure and temperature on stress distribution of bottom-hole rock are studied. The research shows that： in air drilling, as the well depth increases, the more easily the bottom-hole rock is broken; the mud pressure has a great effect on the bottom hole rock. The bigger the mud pressure is, the more difficult to break the bottom-hole rock; the max principle stress of the bottom-hole increased with the increasing of mud pressure, well depth and temperature difference. The bottom-hole rock can be divided into 3 regions respectively according to the stress state, 3 direction stretch zone, 2 direction compression area and 3 direction compression zone; the corresponding fragmentation degree of difficulty is easily, normally and hardly.展开更多
This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical m...This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.展开更多
In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice o...In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.展开更多
In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system inv...In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system involving multiple parameters was carried out,and a new type oscillation heat transfer dynamic model of the CLOHP was set up based on conservation laws of mass,momentum and energy.Application results indicate that its oscillation heat transfer dynamics features depend largely on the filling rate,pipe diameter and difference in temperature.Besides,oscillation intensity and transfer performance can be improved to a large extent by increasing the temperature difference properly and enlarging the pipe diameter within a certain range under a certain filling rate.展开更多
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.
文摘An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.
基金Project(06JJ30024) supported by the Natural Science Foundation of Hunan Province, ChinaProject(2004CB619206) supported by the Major State Basic Research and Development Program of China+1 种基金Project(50321402) supported by the National Science Fund for Innovative Research Groups of ChinaProject(06B052) supported by the Scientific Research Fund of Hunan Provincial Education Department of China
文摘Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.
文摘Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes.Water is utilized as base liquid while carbon nanotubes are considered nanomaterial.An exponential stretchable curved surface flow is originated.Heat source is present.Xue relation of nanoliquid is employed to explore the feature of CNTs (single and multi-wall).Transformation technique is adopted in order to achieve non-linear ordinary differential systems.The governing systems are solved numerically.Effects of involved parameters on flow,temperature,concentration,heat transfer rate (Nusselt number) with addition of skin friction coefficient are illustrated graphically.Decay in velocity is noted with an increment in Forchheimer number and porosity parameter while opposite impact is seen for temperature.Moreover,role of MWCNTs is prominent when compared with SWCNTs.
文摘This article gives a numerical report to two dimensional(2D)Darcy-Forchheimer flow of carbon-water nanofluid.Flow is instigated by exponential extending curved surface.Viscous liquid in permeable space is described by Darcy-Forchheimer.The subsequent arrangement of partial differential equations is changed into ordinary differential framework through proper transformations.Numerical arrangements of governing frameworks are set up by NDSolve procedure.Outcomes of different sundry parameters on temperature and velocity are examined.Skin friction and heat transfer rate are also shown and inspected.
文摘Three-dimensional Darcy-Forchheimer nanoliquid flow in the presence of rotating frame and activation energy is inspected.Flow is developed through linearly stretching of the surface.Convection of heat and mass exchange is given due consideration.The novel characteristics in regards to Brownian dispersion and thermophoresis are retained.The variation in partial differential framework (PDEs) to nonlinear ordinary differential framework (ODEs) is done through reasonable transformations.Governing differential frameworks have been computed in edge of NDSolve.Discussion regarding thermal field and concentration distribution for several involved parameters is pivotal part.Physical amounts like surface drag coefficients,transfer of heat and mass rates are portrayed by numeric esteems.It is noticed that impacts of porosity parameter and Forchheimer number on the thermal and concentration fields are quite similar.Both temperature and associated thermal layer thickness are enhanced for larger porosity parameter and Forchheimer number.Temperature and concentration fields exhibit similar trend for the higher values of rotational parameter.Effects of thermal and concentration Biot numbers on the temperature and concentration fields are qualitatively similar.Higher Prandtl and Schmidt numbers correspond to stronger temperature and concentration fields.Larger nondimensional activation energy,temperature difference parameter and fitted rate constant yield weaker concentration field.Brownian motion parameter for temperature and concentration has reverse effects while similar trend is observed via thermophoresis parameter.
基金Projects(U1562212,51525404)supported by the National Natural Science Foundation of ChinaProject(JYBFX-YQ-1)supported by the Research Project of Key Laboratory Machinery and Power Machinery(Xihua University),Ministry of Education,China
文摘The underbalanced drilling has been widely used due to its advantages of high drilling efficiency and low cost etc., especially for hard formation drilling. These advantages, however, are closely related to the stress state of the bottom-hole rock; therefore, it is significant to research the stress distribution of bottom-hole rock for the correct understanding of the mechanism of rock fragmentation and high penetration rate. The stress condition of bottom-hole rock is very complicated while under the co-action of overburden pressure, horizontal in-situ stresses, drilling mud pressure, pore pressure and temperature etc. In this paper, the fully coupled simulation model is established and the effects of overburden pressure, horizontal in-situ stresses, drilling mud pressure, pore pressure and temperature on stress distribution of bottom-hole rock are studied. The research shows that： in air drilling, as the well depth increases, the more easily the bottom-hole rock is broken; the mud pressure has a great effect on the bottom hole rock. The bigger the mud pressure is, the more difficult to break the bottom-hole rock; the max principle stress of the bottom-hole increased with the increasing of mud pressure, well depth and temperature difference. The bottom-hole rock can be divided into 3 regions respectively according to the stress state, 3 direction stretch zone, 2 direction compression area and 3 direction compression zone; the corresponding fragmentation degree of difficulty is easily, normally and hardly.
基金supported by the National Natural Science Foundation of China(6127312660904032)the Natural Science Foundation of Guangdong Province(10251064101000008)
文摘This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.
基金Project(NRF-2016R1A2B4011009)supported by National Research Foundation of KoreaProject(KSTePS/VGST-KFIST(L1)/2017)supported by Vision Group of Science and Technology,Government of Karnataka,India
文摘In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.
基金Project(531107040300)supported by the Fundamental Research Funds for the Central Universities in ChinaProject(51176045)supported by the National Natural Science Foundation of China
文摘In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system involving multiple parameters was carried out,and a new type oscillation heat transfer dynamic model of the CLOHP was set up based on conservation laws of mass,momentum and energy.Application results indicate that its oscillation heat transfer dynamics features depend largely on the filling rate,pipe diameter and difference in temperature.Besides,oscillation intensity and transfer performance can be improved to a large extent by increasing the temperature difference properly and enlarging the pipe diameter within a certain range under a certain filling rate.
