The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a c...The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.展开更多
An analytical solution is obtained for the flow due to solid-body rotations an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magneti...An analytical solution is obtained for the flow due to solid-body rotations an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. Further, the flow confined between two disks is also discussed. It is found that an infinite number of solutions exist for the flow confined between two disks.展开更多
A viscous boundary layer flow of an electrically-conducting fluid over a moving flat plate in a parallel stream with a constant magnetic field applied outside the boundary layer parallel to the plate was investigated....A viscous boundary layer flow of an electrically-conducting fluid over a moving flat plate in a parallel stream with a constant magnetic field applied outside the boundary layer parallel to the plate was investigated. The goveming system of partial differential equations was transformed to ordinary differential equations using a similarity transformation. The similarity equations were then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results of the skin friction coefficient, velocity profiles, and the induced magnetic field profiles were obtained for some values of the moving parameter, magnetic parameter, and reciprocal magnetic Prandtl number. The results indicate that dual solutions exist when the plate and the fluid move in the opposite directions up to a critical value of the moving parameter, whose value depends on the value of the magnetic parameter.展开更多
This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary cond...This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations. The reduced systems are solved for convergent series solutions. The velocity, temperature, and concentration fields are discussed for different physical parameters. The results indi- cate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.展开更多
This paper presents an anisotropic adaptive finite element method （FEM） to solve the governing equations of steady magnetohydrodynamic （MHD） duct flow. A resid- ual error estimator is presented for the standard FE...This paper presents an anisotropic adaptive finite element method （FEM） to solve the governing equations of steady magnetohydrodynamic （MHD） duct flow. A resid- ual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu es- timates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.展开更多
We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations....We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.展开更多
This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructe...This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.展开更多
In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross sec- tion ...In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross sec- tion and one with annular cross section, in the presence of an applied transverse uniform magnetic field, We ob- tain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnet- ic field.展开更多
This paper deals with the magnetohydrodynamic （MHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy＇s law is used in the flow modelling. The non-line...This paper deals with the magnetohydrodynamic （MHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy＇s law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.展开更多
The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnet...The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.展开更多
The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. When an artery is exposed to a magnetic field, the blood charged particles are d...The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several biomedical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.展开更多
Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a sta...Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.展开更多
The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompres...The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.展开更多
In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an invest...In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.展开更多
The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The non...The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.展开更多
This exploration examines unsteady magnetohydrodynamic(MHD) three-dimensional flow of viscous material between rotating plates subject to radiation,Joule heating and chemical reaction.The non-linear partial differenti...This exploration examines unsteady magnetohydrodynamic(MHD) three-dimensional flow of viscous material between rotating plates subject to radiation,Joule heating and chemical reaction.The non-linear partial differential system is re-structured into the ordinary differential expressions by the implication of appropriate transformations.The developed differential equations are computed by homotopy analysis technique.Numerical consequences have been accomplished by various values of emerging parameters.Coefficients of skin friction and heat and mass transfer rates have been scrutinized.Irreversibility analysis is carried out.Influence of various prominent variables on entropy generation is presented.Moreover,the temperature increases for higher Dufour number and concentration distribution reduces against Soret number.Higher squeezing parameter enhances velocity while concentration reduces with an increment in squeezing parameter.Both entropy rate and Bejan number increase against higher diffusion parameter.展开更多
The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the model...The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.展开更多
This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distr...This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.展开更多
This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which i...This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.展开更多
The aim of this paper is two-dimensional magnetohydrodynamic viscous fluid bounded by infinite sheets to examine the Dufour and Soret effects on the （MHD） steady flow of an electrically conducting An incompressible...The aim of this paper is two-dimensional magnetohydrodynamic viscous fluid bounded by infinite sheets to examine the Dufour and Soret effects on the （MHD） steady flow of an electrically conducting An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method （HAM）. The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.展开更多
文摘The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.
文摘An analytical solution is obtained for the flow due to solid-body rotations an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. Further, the flow confined between two disks is also discussed. It is found that an infinite number of solutions exist for the flow confined between two disks.
文摘A viscous boundary layer flow of an electrically-conducting fluid over a moving flat plate in a parallel stream with a constant magnetic field applied outside the boundary layer parallel to the plate was investigated. The goveming system of partial differential equations was transformed to ordinary differential equations using a similarity transformation. The similarity equations were then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results of the skin friction coefficient, velocity profiles, and the induced magnetic field profiles were obtained for some values of the moving parameter, magnetic parameter, and reciprocal magnetic Prandtl number. The results indicate that dual solutions exist when the plate and the fluid move in the opposite directions up to a critical value of the moving parameter, whose value depends on the value of the magnetic parameter.
文摘This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations. The reduced systems are solved for convergent series solutions. The velocity, temperature, and concentration fields are discussed for different physical parameters. The results indi- cate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.
基金Project supported by the National Natural Science Foundation of China(Nos.11471329,11321061,and 91430215)the National Magnetic Confinement Fusion Science Program of China(No.2015GB110000)+1 种基金the Youth Innovation Promotion Association of Chinese Academy of Sciences(CAS)(No.2016003)the National Center for Mathematics and Interdisciplinary Sciences of CAS
文摘This paper presents an anisotropic adaptive finite element method （FEM） to solve the governing equations of steady magnetohydrodynamic （MHD） duct flow. A resid- ual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu es- timates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11171236 and 71372189)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)+1 种基金Sichuan Youth Science and Technology Foundation(Grant No.2014JQ0003)China Postdoctoral Science Foundation(Grant No.2013M542285)
文摘We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.
基金supported by the Deanship of Scientific Research (DSR) of King Abdulaziz University of Saudi Arabia
文摘This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.
文摘In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross sec- tion and one with annular cross section, in the presence of an applied transverse uniform magnetic field, We ob- tain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnet- ic field.
文摘This paper deals with the magnetohydrodynamic （MHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy＇s law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.
文摘The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.
文摘The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several biomedical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.
文摘Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.
文摘The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.
基金Supported by the National Natural Science Foundations of China under Grant Nos.21576023,51406008the National Key Research Program of China under Grant Nos.2016YFC0700601,2016YFC0700603,and 2016YFE0115500
文摘In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.
基金supported by the Fundamental Research Grant Scheme (FRGS) of the Ministry of Higher Education (MOHE) of Malaysia (No. UKM-ST-07-FRGS0036-2009)
文摘The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.
文摘This exploration examines unsteady magnetohydrodynamic(MHD) three-dimensional flow of viscous material between rotating plates subject to radiation,Joule heating and chemical reaction.The non-linear partial differential system is re-structured into the ordinary differential expressions by the implication of appropriate transformations.The developed differential equations are computed by homotopy analysis technique.Numerical consequences have been accomplished by various values of emerging parameters.Coefficients of skin friction and heat and mass transfer rates have been scrutinized.Irreversibility analysis is carried out.Influence of various prominent variables on entropy generation is presented.Moreover,the temperature increases for higher Dufour number and concentration distribution reduces against Soret number.Higher squeezing parameter enhances velocity while concentration reduces with an increment in squeezing parameter.Both entropy rate and Bejan number increase against higher diffusion parameter.
基金Project supported by the National Natural Science Foundation of China(Nos.51276014 and51476191)the Fundamental Research Funds for the Central Universities(No.FRF-BR-12-004)
文摘The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.
文摘This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.
文摘This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.
基金Project supported by the Deanship of Scientific Research (DSR) of King Abdulaziz University of Saudi Arabia (No. HiCi/40-3/1432H)
文摘The aim of this paper is two-dimensional magnetohydrodynamic viscous fluid bounded by infinite sheets to examine the Dufour and Soret effects on the （MHD） steady flow of an electrically conducting An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method （HAM）. The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.
