The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flo...The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.展开更多
Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. ...Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.展开更多
The effects of various surface roughness geometrical properties including roughness height(5%,10%,15%),number(3,6),and shape(rectangular and triangular)on the flow and heat transfer of slip-flow in trapezoidal microch...The effects of various surface roughness geometrical properties including roughness height(5%,10%,15%),number(3,6),and shape(rectangular and triangular)on the flow and heat transfer of slip-flow in trapezoidal microchannels were investigated.The effects of mentioned parameters on the heat transfer coefficient through the microchannel,average Nusselt number and pressure drop for Reynolds number of 5,10,15 and 20 were examined.The obtained results showed that increasing the roughness height and number increases the pressure drop due to higher stagnation effects before and after roughness elements and decreases the Nusselt number due to higher recirculation zones effects than obstruction effects.The most reduction in Nusselt number and the most increment in pressure drop occur at the roughness height of 15%,roughness number of 6 and Reynolds number of 20 by about 10.6%and 52.8%than the smooth microchannel respectively.展开更多
The fabrication of superhydrophobic surfaces and the studies on water flow characteristics therein are of great significance to many industrial areas as well as to science and technology development. Experiments were ...The fabrication of superhydrophobic surfaces and the studies on water flow characteristics therein are of great significance to many industrial areas as well as to science and technology development. Experiments were car- ried out to investigate slip characteristics of water flowing in circular superhydrophobic microtubes within lam- inar flow region. The superhydrophobic microtubes of stainless steel were fabricated with chemical etching- fluorination treatment. An experimental setup was designed to measure the pressure drop as function of water flow rate. For comparison, superhydrophilic tubes were also tested. Poiseuille number Po was found to be smaller for the superhydrophobic microtubes than that for superhydrophilic ones. The pressure drop reduc- tion ranges from 8% to 31%. It decreases with increasing Reynolds number when Re 〈 900, owing to the transition from Cassie state to Wenze] state. However, it is almost unchanged with further increasing Re after Re 〉 900. The slip length in superhydrophobic microtubes also exhibits a Reynolds number dependence similarly to the pressure drop reduction. The relation between slip length and Darcy friction factor is theoretically analyzed with consideration of surface roughness effect, which was testified with the experimental results.展开更多
The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow ...The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.展开更多
This problem presents the effects of thermal radiation and chemical reaction on MHD unsteady mass transfer flow past a semi-infinite vertical porous plate embedded in a porous medium in a slip flow regime with variabl...This problem presents the effects of thermal radiation and chemical reaction on MHD unsteady mass transfer flow past a semi-infinite vertical porous plate embedded in a porous medium in a slip flow regime with variable suction. A magnetic field of uniform strength is assumed to be applied transversely to the direction of the main flow. Perturbation technique is applied to transform the non-linear coupled governing partial differential equations in dimensionless form into a system of ordinary differential equations. The resulting equations are solved analytically and the solutions for the velocity, temperature and concentration fields are obtained. The effects of various flow parameters on velocity, temperature and concentration fields are presented graphically. For different values of the flow parameters involved in the problem, the numerical calculations for the Nusselt number, Sherwood number and skin-friction co-efficient at the plate are performed in tabulated form. It is seen that chemical reaction causes the velocity field and concentration field to decrease and the chemical reaction decreases the rate of viscous drag at the plate.展开更多
An analysis is made for the steady two-dimensional laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid near a stagnation point past a shrinking sheet with slip in the presence of a ...An analysis is made for the steady two-dimensional laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid near a stagnation point past a shrinking sheet with slip in the presence of a magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables and solved numerically by Shooting method. The effects of the various parameters such as velocity ratio parameter, slip parameter, Prandtl number, Eckert number and magnetic parameter for velocity and temperature distributions have been discussed in detail through graphical representation.展开更多
In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a syste...In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.展开更多
In this paper,flow of slightly rarefied compressible nitrogen in microchannels has been investigated numerically for low values of Reynolds and Mach numbers.The 2D governing equations were solved using Finite Element ...In this paper,flow of slightly rarefied compressible nitrogen in microchannels has been investigated numerically for low values of Reynolds and Mach numbers.The 2D governing equations were solved using Finite Element Method with first-order slip boundary conditions(Comsol Multiphysics software).A validation was performed by comparing with similar configuration from the literature.It was found that our model can accurately predict the pressure driven flow in microchannels.Several interesting findings are reported about the Relative pressure,longitudinal velocity,Mach number,effect of gas rarefaction and flow rate.展开更多
The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group ...The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.展开更多
Fast fluid transport on graphene has attracted a growing body of research due to a wide range of potential applications including thermal management,water desalination,energy harvesting,and lab-on-a-chip.Here,we criti...Fast fluid transport on graphene has attracted a growing body of research due to a wide range of potential applications including thermal management,water desalination,energy harvesting,and lab-on-a-chip.Here,we critically review the theoretical,simulational,and experimental progress regarding the fluid slippage on graphene.Based on the summary of the past studies,we give perspectives on future research directions towards complete understanding and practical applications of slip flow on graphene.展开更多
A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic...A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, tempera- ture and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excelle- nt correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bio- reactor diffusion flows and high-temperature chemical materials processing systems.展开更多
Recent studies on applications of the lattice Boltzmann method(LBM)and the finite-difference lattice Boltzmann method(FDLBM)to velocity slip simulations are mostly on one-dimensional(1D)problems such as a shear flow b...Recent studies on applications of the lattice Boltzmann method(LBM)and the finite-difference lattice Boltzmann method(FDLBM)to velocity slip simulations are mostly on one-dimensional(1D)problems such as a shear flow between parallel plates.Applications to a 2D problem may raise new issues.The author performed numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D problem.Two types of 2D models were used.The first were multi-speed FDLBM models proposed by the author.The second was a standard LBM,the D2Q9 model.The simulations were performed applying a finite difference scheme to both the models.The study had two objectives.The first was to investigate the accuracies of LBM and FDLBM on applications to rotational slip flow.The second was to obtain an experience on application of the cylindrical coordinate system.The FDLBM model with 8 directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation time constant or the Knudsen number was large.The FDLBM model with 24 directions showed accurate results even at large Knudsen numbers.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
An analytical approximation for the similarity solutions of the two-and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion met...An analytical approximation for the similarity solutions of the two-and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion method, but it is different from the perturbation technique, because it is independent of small physical parameters at all. Instead, it is based on a continuous mapping in topology so that it is applicable for not only weakly but also strongly nonlinear flow phenomena. Convergent [m,m] homotopy Padé approximants are obtained and compared with the numerical results and the asymptotic approximations. It is found that the homotopy Padé approximants agree well with the numerical results. The effects of the slip length and the thermal slip constant β on the heat transfer characteristics are investigated and discussed.展开更多
Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical ...Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.展开更多
An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales. The velocity profile is calculated by taking account o...An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales. The velocity profile is calculated by taking account of the micro-force between molecules and macro-force from the viscous shearing effect, as they contribute to the achieve- ment of the slip length. The calculated results are compared with those obtained from the molecular dynamics simulation, showing an excellent agreement. Further, the effect of the shear rate on the slip is investigated. The results can well predict the fluid flow behaviors on a solid substrate, but has to be proved by experiment.展开更多
This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite por...This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.展开更多
A theoretical analysis of heat transfer characteristics is presented for the fully developed laminar flow of the incompressible gas in the triangular microchannels heated unsymmetrically with constant axial heat flux....A theoretical analysis of heat transfer characteristics is presented for the fully developed laminar flow of the incompressible gas in the triangular microchannels heated unsymmetrically with constant axial heat flux. Through solving the energy equation with temperature jump boundary conditions in slip flow regime by virtue of a computation- oriented method of the orthonormal function analysis, the dimensionless temperature profiles and the average Nusselt number for various thermal boundary conditions are obtained. The effects of Knudsen number, aspect ratio, and thermal boundary conditions on the heat transfer are discussed. The calculated results show that the orthonormal function method can be used to study the heat transfer characteristics of the unsymmetrically heated triangular microchannels. The average Nusselt number in triangular microchannels is lower for slip flow than for no-slip flow, and decreases with increasing Knudsen number. The aspect ratios and thermal boundary conditions of triangular microchannels have significant influences on the change of average Nusselt numbers with the increase in the Knudsen number. For the equilateral triangular microchannels, the decrease of the Nusselt number ratio due to temperature jump is smaller at large Knudsen number and larger at small Knudsen number on the boundary condition of bottom wall heated alone as compared with the one on the boundary condition of two heated hypotenuse walls. The correlations of the average Nusselt number with the Knudsen number for equilateral triangular microchannels are obtained.展开更多
The magnetohydrodynamic（MHD） flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be appl...The magnetohydrodynamic（MHD） flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.展开更多
基金Support of National Natural Science Foundation of China under Grant Nos.11475028,11772064,and 11502117Science Challenge Project under Grant Nos.JCKY2016212A501 and TZ2016002
文摘The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.
文摘Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.
文摘The effects of various surface roughness geometrical properties including roughness height(5%,10%,15%),number(3,6),and shape(rectangular and triangular)on the flow and heat transfer of slip-flow in trapezoidal microchannels were investigated.The effects of mentioned parameters on the heat transfer coefficient through the microchannel,average Nusselt number and pressure drop for Reynolds number of 5,10,15 and 20 were examined.The obtained results showed that increasing the roughness height and number increases the pressure drop due to higher stagnation effects before and after roughness elements and decreases the Nusselt number due to higher recirculation zones effects than obstruction effects.The most reduction in Nusselt number and the most increment in pressure drop occur at the roughness height of 15%,roughness number of 6 and Reynolds number of 20 by about 10.6%and 52.8%than the smooth microchannel respectively.
基金the National Natural Science Foundation of China(20476014,51376030)
文摘The fabrication of superhydrophobic surfaces and the studies on water flow characteristics therein are of great significance to many industrial areas as well as to science and technology development. Experiments were car- ried out to investigate slip characteristics of water flowing in circular superhydrophobic microtubes within lam- inar flow region. The superhydrophobic microtubes of stainless steel were fabricated with chemical etching- fluorination treatment. An experimental setup was designed to measure the pressure drop as function of water flow rate. For comparison, superhydrophilic tubes were also tested. Poiseuille number Po was found to be smaller for the superhydrophobic microtubes than that for superhydrophilic ones. The pressure drop reduc- tion ranges from 8% to 31%. It decreases with increasing Reynolds number when Re 〈 900, owing to the transition from Cassie state to Wenze] state. However, it is almost unchanged with further increasing Re after Re 〉 900. The slip length in superhydrophobic microtubes also exhibits a Reynolds number dependence similarly to the pressure drop reduction. The relation between slip length and Darcy friction factor is theoretically analyzed with consideration of surface roughness effect, which was testified with the experimental results.
文摘The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.
文摘This problem presents the effects of thermal radiation and chemical reaction on MHD unsteady mass transfer flow past a semi-infinite vertical porous plate embedded in a porous medium in a slip flow regime with variable suction. A magnetic field of uniform strength is assumed to be applied transversely to the direction of the main flow. Perturbation technique is applied to transform the non-linear coupled governing partial differential equations in dimensionless form into a system of ordinary differential equations. The resulting equations are solved analytically and the solutions for the velocity, temperature and concentration fields are obtained. The effects of various flow parameters on velocity, temperature and concentration fields are presented graphically. For different values of the flow parameters involved in the problem, the numerical calculations for the Nusselt number, Sherwood number and skin-friction co-efficient at the plate are performed in tabulated form. It is seen that chemical reaction causes the velocity field and concentration field to decrease and the chemical reaction decreases the rate of viscous drag at the plate.
文摘An analysis is made for the steady two-dimensional laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid near a stagnation point past a shrinking sheet with slip in the presence of a magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables and solved numerically by Shooting method. The effects of the various parameters such as velocity ratio parameter, slip parameter, Prandtl number, Eckert number and magnetic parameter for velocity and temperature distributions have been discussed in detail through graphical representation.
文摘In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.
文摘In this paper,flow of slightly rarefied compressible nitrogen in microchannels has been investigated numerically for low values of Reynolds and Mach numbers.The 2D governing equations were solved using Finite Element Method with first-order slip boundary conditions(Comsol Multiphysics software).A validation was performed by comparing with similar configuration from the literature.It was found that our model can accurately predict the pressure driven flow in microchannels.Several interesting findings are reported about the Relative pressure,longitudinal velocity,Mach number,effect of gas rarefaction and flow rate.
基金Project supported by the National Natural Science Foundation of China (No. 50936003)the Open Project of State Key Laboratory for Advanced Metals and Materials and the Research Foundation of Engineering Research Institute of University of Science and Technology Beijing (No. 2009Z-02)
文摘The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.
基金the JST CREST Grant Number JPMJCR18I1,Japan,JST FOREST Program(Grant Number JPMJFR212M,Japan)JSPS KAKENHI(Grant Nos.JP20H02089,JP20H02090,and JP21K18693)。
文摘Fast fluid transport on graphene has attracted a growing body of research due to a wide range of potential applications including thermal management,water desalination,energy harvesting,and lab-on-a-chip.Here,we critically review the theoretical,simulational,and experimental progress regarding the fluid slippage on graphene.Based on the summary of the past studies,we give perspectives on future research directions towards complete understanding and practical applications of slip flow on graphene.
基金financial support from Universiti Sains Malaysia,(RU Grant No.1001/PMATHS/811252)
文摘A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, tempera- ture and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excelle- nt correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bio- reactor diffusion flows and high-temperature chemical materials processing systems.
文摘Recent studies on applications of the lattice Boltzmann method(LBM)and the finite-difference lattice Boltzmann method(FDLBM)to velocity slip simulations are mostly on one-dimensional(1D)problems such as a shear flow between parallel plates.Applications to a 2D problem may raise new issues.The author performed numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D problem.Two types of 2D models were used.The first were multi-speed FDLBM models proposed by the author.The second was a standard LBM,the D2Q9 model.The simulations were performed applying a finite difference scheme to both the models.The study had two objectives.The first was to investigate the accuracies of LBM and FDLBM on applications to rotational slip flow.The second was to obtain an experience on application of the cylindrical coordinate system.The FDLBM model with 8 directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation time constant or the Knudsen number was large.The FDLBM model with 24 directions showed accurate results even at large Knudsen numbers.
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.
基金Supported by the National Natural Science Foundation of China (Grant No.10872129)
文摘An analytical approximation for the similarity solutions of the two-and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion method, but it is different from the perturbation technique, because it is independent of small physical parameters at all. Instead, it is based on a continuous mapping in topology so that it is applicable for not only weakly but also strongly nonlinear flow phenomena. Convergent [m,m] homotopy Padé approximants are obtained and compared with the numerical results and the asymptotic approximations. It is found that the homotopy Padé approximants agree well with the numerical results. The effects of the slip length and the thermal slip constant β on the heat transfer characteristics are investigated and discussed.
文摘Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.
基金Supported by the National Natural Science Foundation of China under Grant No 51305033the Ministry of National Defense of China under Grant No 9140C340506
文摘An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales. The velocity profile is calculated by taking account of the micro-force between molecules and macro-force from the viscous shearing effect, as they contribute to the achieve- ment of the slip length. The calculated results are compared with those obtained from the molecular dynamics simulation, showing an excellent agreement. Further, the effect of the shear rate on the slip is investigated. The results can well predict the fluid flow behaviors on a solid substrate, but has to be proved by experiment.
文摘This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.
基金the National Natural Science Foundation of China (Grant No.59995550-3) the support plan for key teacher of Chongqing University.
文摘A theoretical analysis of heat transfer characteristics is presented for the fully developed laminar flow of the incompressible gas in the triangular microchannels heated unsymmetrically with constant axial heat flux. Through solving the energy equation with temperature jump boundary conditions in slip flow regime by virtue of a computation- oriented method of the orthonormal function analysis, the dimensionless temperature profiles and the average Nusselt number for various thermal boundary conditions are obtained. The effects of Knudsen number, aspect ratio, and thermal boundary conditions on the heat transfer are discussed. The calculated results show that the orthonormal function method can be used to study the heat transfer characteristics of the unsymmetrically heated triangular microchannels. The average Nusselt number in triangular microchannels is lower for slip flow than for no-slip flow, and decreases with increasing Knudsen number. The aspect ratios and thermal boundary conditions of triangular microchannels have significant influences on the change of average Nusselt numbers with the increase in the Knudsen number. For the equilateral triangular microchannels, the decrease of the Nusselt number ratio due to temperature jump is smaller at large Knudsen number and larger at small Knudsen number on the boundary condition of bottom wall heated alone as compared with the one on the boundary condition of two heated hypotenuse walls. The correlations of the average Nusselt number with the Knudsen number for equilateral triangular microchannels are obtained.
文摘The magnetohydrodynamic（MHD） flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.
