An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS...An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS equations and physical analysis and relevant discussions are then presented.展开更多
In this research,the three-dimensional(3D)steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed.The disturbance in the porous medium has been characterized ...In this research,the three-dimensional(3D)steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed.The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation.The slip for viscous fluid is considered.The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate.The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method.Dual solutions are obtained for the velocity,skin friction coefficient,temperature,and Nusselt number subject to sundry flow parameters,magnetic parameter,Darcy-Forchheimer number,thermal radiation parameter,suction parameter,and dimensionless slip parameter.In this research,the main consideration is given to the engineering interest like skin friction coefficient(velocity gradient or surface drag force)and Nusselt number(temperature gradient or heat transfer rate)and discussed numerically through tables.In conclusion,it is noticed from the stability results that the upper branch solution(UBS)is more reliable and physically stable than the lower branch solution(LBS).展开更多
The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is invest...The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.展开更多
The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching she...The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.展开更多
Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorpti...Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.展开更多
The present study inspects the non-aligned stagnation point nano fluid over a convective surface in the presence of partial slip. Two types of base fluids namely water and kerosene are selected with Cu nanoparticles. ...The present study inspects the non-aligned stagnation point nano fluid over a convective surface in the presence of partial slip. Two types of base fluids namely water and kerosene are selected with Cu nanoparticles. The governing physical problem is presented and transformed into a system of coupled nonlinear differential equations using suitable similarity transformations. These equations are then solved numerically using midpoint integration scheme along with Richardson extrapolation via Maple. Impact of relevant physical parameters on the dimensionless velocity and temperature profiles are portrayed through graphs. Physical quantities such as local skin frictions co-efficient and Nusselt numbers are tabularized.It is detected from numerical computations that kerosene-based nano fluids have better heat transfer capability compared with water-based nanofluids. Moreover it is found that water-based nanofluids offer less resistance in terms of skin friction than kerosene-based fluid. In order to authenticate our present study, the calculated results are compared with the prevailing literature and a considerable agreement is perceived for the limiting case.展开更多
In this study,the stagnation point transport of second grade fluid with linear stretching under the effects of variable thermal conductivity is considered.Induced magnetic field impact is also incorporated.The nonline...In this study,the stagnation point transport of second grade fluid with linear stretching under the effects of variable thermal conductivity is considered.Induced magnetic field impact is also incorporated.The nonlinear set of particle differential equations is converted into set of ordinary differential equations through appropriate transformation.The resulting equations are then resolved by optimal homotopy analysis method.The effect of pertinent parameters of interest on skin friction coefficient,temperature,induced magnetic field,velocity and local Nusselt number is inspected by generating appropriate plots.For numerical results,the built-in bvp4 c technique in computational software MATLAB is used for the convergence and residual errors of obtained series solution.It is perceived that the induced magnetic field is intensified by increasing β.It can also be observed that skin friction coefficient enhances with increasing value of magnetic parameter depending on the stretching ratio a/c.For the validness of the obtained results,a comparison has been made and an excellent agreement of current study with existing literature is found.展开更多
This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching sheet.The influence of thermophoresis and Brownian motion is also considered in transport equations...This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching sheet.The influence of thermophoresis and Brownian motion is also considered in transport equations.The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations.The numerical experiments are performed using the Galerkin scheme.A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme(RK-4)is available to show the credibility of the Galerkin method.The numerical exploration is carried out for various governing parameters,namely,Brownian motion,steadiness,thermophoresis,stretching ratio,velocity slip,concentration slip,thermal slip,and fluid parameters,and Hartmann,Prandtl and Schmidt numbers.The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing,but the behavior is reversed for assisting cases.The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases(assisting and opposing).The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter.All the outcomes and the behavior of emerging parameters are illustrated graphically.The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method.It is concluded that said method could be extended to other problems of a complex nature.展开更多
The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and conve...The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and convective boundary condition are also taken into account.The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis.The resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity transformations.Numerical solutions have been obtained for the velocity,temperature and nanoparticle fraction profles.The influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.展开更多
The heat transfer of Homann flow in the stagnation region of the Al2 O3-Cu/water hybrid nanofluid is investigated by adopting the Tiwari-Das model over a cylindrical disk.The effects of the nanoparticle shape,the visc...The heat transfer of Homann flow in the stagnation region of the Al2 O3-Cu/water hybrid nanofluid is investigated by adopting the Tiwari-Das model over a cylindrical disk.The effects of the nanoparticle shape,the viscous dissipation,and the nonlinear radiation are considered.The governing equations are obtained by using similarity transformations,and the numerical outcomes for the flow and the temperature field are noted by bvp4 c on MATLAB.The numerical solutions of the flow field are compared with the asymptotic behaviors of large shear-to-strain-rate ratio.The effects of variations of parameters involved are inspected for both nanofluid and hybrid nanofluid flows,temperature profiles,local Nusselt numbers,and skin frictions.It is concluded that the velocity and temperature fields in the hybrid nanophase function more rapidly than those in the nanofluid phase.展开更多
The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into ac...The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into account. Two explicit cases, i.e., the prescribed surface temperature （PST） and the prescribed heat flux （PHF）, are discussed. The boundary layer flow and energy equations are solved by employing the homotopy analysis method. The quantities of physical interest are examined through the presenta- tion of plots/tabulated values. It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.展开更多
In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suit...In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.展开更多
Single cell trapping in vitro by microfluidic device is an emerging approach for the study of the relationship between single cells and their dynamic biochemical microenvironments. In this paper, a hydrodynamic-based ...Single cell trapping in vitro by microfluidic device is an emerging approach for the study of the relationship between single cells and their dynamic biochemical microenvironments. In this paper, a hydrodynamic-based microfluidic device for single cell trapping is designed using a combination of stagnation point flow and physical barrier.The microfluidic device overcomes the weakness of the traditional ones, which have been only based upon either stagnation point flows or physical barriers, and can conveniently load dynamic biochemical signals to the trapped cell. In addition, it can connect with a programmable syringe pump and a microscope to constitute an integrated experimental system.It is experimentally verified that the microfluidic system can trap single cells in vitro even under flow disturbance and conveniently load biochemical signals to the trapped cell. The designed micro-device would provide a simple yet effective experimental platform for further study of the interactions between single cells and their microenvironments.展开更多
Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transfor...Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by finite difference technique known as Keller Box method. The various parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic parameter (M), Casson parameter (β) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Casson fluid parameter (β) decreased both the fluid velocity and temperature whereas an increase in (β) increased both the heat transfer rate and wall skin-friction coefficient.展开更多
The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of Williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretc...The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of Williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretching cylinder. Further the effects of variable thermal conductivity and thermal stratification are also considered. The governing partial differential equations are converted to ordinary differential equations with the help of similarity transformation.The system of coupled non-linear ordinary differential equations is then solved by shooting technique. MATLAB shooting code is validated by comparison with the previously published work in limiting case. Results are further strengthened when the present results are compared with MATLAB built-in function bvp4c. Effects of prominent parameters are deliberated graphically for the velocity, temperature and concentration profiles. Skin-friction coefficient and Nusselt number for the different parameters are investigated with the help of tables.展开更多
This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell nanofluid.The Buongiorno’s theory has been established to picture the induce...This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell nanofluid.The Buongiorno’s theory has been established to picture the inducement of Brownian and thermophrotic diffusions effects.Additionally,the aspect of heat sink/source is reported.The homotopic analysis method(HAM)has been worked out for the solution of nonlinear ODEs.The behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and discussed.The attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration fields.It is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion parameter.Moreover,for the confirmation of our study comparison tables are reported.展开更多
The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional(3D)stagnation point body is studied under a microgravity environment.The effects of g-jitter and thermal radiation e...The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional(3D)stagnation point body is studied under a microgravity environment.The effects of g-jitter and thermal radiation exist under the microgravity environment,where there is a gravitational field with fluctuations.The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition.With the semi-similar transformation technique,the dimensional system of equations is reduced into a dimensionless system of equations,where the dependent variables of the problem are lessened.A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method,which is an implicit finite difference approach.The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics,the heat transfer properties,and the concentration distributions.The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body,where the stagnation point is located.The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied,where the fluctuating range becomes smaller when the oscillation frequency increases.Moreover,the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux,and the thermal radiation could increase the heat transfer properties.展开更多
This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic(MHD)stagnation point flow across a stretchable surface.The heat transport process is investigated with respect to the viscou...This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic(MHD)stagnation point flow across a stretchable surface.The heat transport process is investigated with respect to the viscous dissipation and thermal radiation,whereas the mass transport is observed under the influence of a chemical reaction.The irreversibe factor is measured through the application of the second law of thermodynamics.The established non-linear partial differential equations(PDEs)have been replaced by acceptable ordinary differential equations(ODEs),which are solved numerically via the bvp4 c method(built-in package in MATLAB).The numerical analysis of the resulting ODEs is carried out on the different flow parameters,and their effects on the rate of heat transport,friction drag,concentration,and the entropy generation are considered.It is determined that the concentration estimation and the Sherwood number reduce and enhance for higher values of the chemical reaction parameter and the Schmidt number,although the rate of heat transport is increased for the Eckert number and heat generation/absorption parameter,respectively.The entropy generation augments with boosting values of the Brinkman number,and decays with escalating values of both the radiation parameter and the Weissenberg number.展开更多
The unsteady mixed convection of the Al_(2)O_(3)-Cu/H_(2)O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed.The bvp4c technique is used to solve the resulting ordinary differential equ...The unsteady mixed convection of the Al_(2)O_(3)-Cu/H_(2)O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed.The bvp4c technique is used to solve the resulting ordinary differential equations.The combined effects of the velocity and thermal slip are addressed.The effects of different relevant physical parameters are studied numerically.The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases,while the unsteadiness parameter has an opposite effect in the opposing flow.The presence of the slip parameter is proven to increase the skin friction coefficient while reduce the local Nusselt number in the buoyancy opposing flow.A contradictory result is observed in the buoyancy assisting flow.Meanwhile,the heat transfer rate is reduced in the buoyancy of the assisting and opposing flows when the thermal slip effect is considered.展开更多
In order to evaluate uncertainties in computational fluid dynamics （CFD） computations of the stagnation point heat flux, a physical criterion is developed. Based on a quasi-one-dimensional hypothesis along the stagn...In order to evaluate uncertainties in computational fluid dynamics （CFD） computations of the stagnation point heat flux, a physical criterion is developed. Based on a quasi-one-dimensional hypothesis along the stagnation line, a new stagnation flow model is applied to obtain the governing equations of the flow near the stagnation point at hypersonic speeds. From the above equations, the compatibility relations are given at the stagnation point and along the stagnation line, which consist of the physical criterion for checking the accuracy in the stagnation point heat flux computations. The verification of the criterion is made with various numerical results.展开更多
文摘An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS equations and physical analysis and relevant discussions are then presented.
基金Project supported by the National Natural Science Foundation of China(Nos.11971142,11871202,61673169,11701176,11626101,and 11601485)。
文摘In this research,the three-dimensional(3D)steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed.The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation.The slip for viscous fluid is considered.The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate.The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method.Dual solutions are obtained for the velocity,skin friction coefficient,temperature,and Nusselt number subject to sundry flow parameters,magnetic parameter,Darcy-Forchheimer number,thermal radiation parameter,suction parameter,and dimensionless slip parameter.In this research,the main consideration is given to the engineering interest like skin friction coefficient(velocity gradient or surface drag force)and Nusselt number(temperature gradient or heat transfer rate)and discussed numerically through tables.In conclusion,it is noticed from the stability results that the upper branch solution(UBS)is more reliable and physically stable than the lower branch solution(LBS).
文摘The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.
文摘The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.
文摘Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
文摘The present study inspects the non-aligned stagnation point nano fluid over a convective surface in the presence of partial slip. Two types of base fluids namely water and kerosene are selected with Cu nanoparticles. The governing physical problem is presented and transformed into a system of coupled nonlinear differential equations using suitable similarity transformations. These equations are then solved numerically using midpoint integration scheme along with Richardson extrapolation via Maple. Impact of relevant physical parameters on the dimensionless velocity and temperature profiles are portrayed through graphs. Physical quantities such as local skin frictions co-efficient and Nusselt numbers are tabularized.It is detected from numerical computations that kerosene-based nano fluids have better heat transfer capability compared with water-based nanofluids. Moreover it is found that water-based nanofluids offer less resistance in terms of skin friction than kerosene-based fluid. In order to authenticate our present study, the calculated results are compared with the prevailing literature and a considerable agreement is perceived for the limiting case.
文摘In this study,the stagnation point transport of second grade fluid with linear stretching under the effects of variable thermal conductivity is considered.Induced magnetic field impact is also incorporated.The nonlinear set of particle differential equations is converted into set of ordinary differential equations through appropriate transformation.The resulting equations are then resolved by optimal homotopy analysis method.The effect of pertinent parameters of interest on skin friction coefficient,temperature,induced magnetic field,velocity and local Nusselt number is inspected by generating appropriate plots.For numerical results,the built-in bvp4 c technique in computational software MATLAB is used for the convergence and residual errors of obtained series solution.It is perceived that the induced magnetic field is intensified by increasing β.It can also be observed that skin friction coefficient enhances with increasing value of magnetic parameter depending on the stretching ratio a/c.For the validness of the obtained results,a comparison has been made and an excellent agreement of current study with existing literature is found.
基金the support of Peking University through the Boya Post-Doctoral Fellowshipsupported by China Postdoctoral Science Foundation(No.2020M681135)the financial support from the Thousand Talents Plan for the Introduction of High-level Talents at Home and Abroad in Sichuan Province。
文摘This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching sheet.The influence of thermophoresis and Brownian motion is also considered in transport equations.The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations.The numerical experiments are performed using the Galerkin scheme.A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme(RK-4)is available to show the credibility of the Galerkin method.The numerical exploration is carried out for various governing parameters,namely,Brownian motion,steadiness,thermophoresis,stretching ratio,velocity slip,concentration slip,thermal slip,and fluid parameters,and Hartmann,Prandtl and Schmidt numbers.The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing,but the behavior is reversed for assisting cases.The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases(assisting and opposing).The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter.All the outcomes and the behavior of emerging parameters are illustrated graphically.The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method.It is concluded that said method could be extended to other problems of a complex nature.
文摘The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and convective boundary condition are also taken into account.The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis.The resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity transformations.Numerical solutions have been obtained for the velocity,temperature and nanoparticle fraction profles.The influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.
文摘The heat transfer of Homann flow in the stagnation region of the Al2 O3-Cu/water hybrid nanofluid is investigated by adopting the Tiwari-Das model over a cylindrical disk.The effects of the nanoparticle shape,the viscous dissipation,and the nonlinear radiation are considered.The governing equations are obtained by using similarity transformations,and the numerical outcomes for the flow and the temperature field are noted by bvp4 c on MATLAB.The numerical solutions of the flow field are compared with the asymptotic behaviors of large shear-to-strain-rate ratio.The effects of variations of parameters involved are inspected for both nanofluid and hybrid nanofluid flows,temperature profiles,local Nusselt numbers,and skin frictions.It is concluded that the velocity and temperature fields in the hybrid nanophase function more rapidly than those in the nanofluid phase.
基金Project supported by the Higher Education Commission (HEC) of Pakistan (No. 106-1396-Ps6-004)
文摘The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into account. Two explicit cases, i.e., the prescribed surface temperature （PST） and the prescribed heat flux （PHF）, are discussed. The boundary layer flow and energy equations are solved by employing the homotopy analysis method. The quantities of physical interest are examined through the presenta- tion of plots/tabulated values. It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.
文摘In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.
基金supported by the National Natural Science Foundation of China (Grants 11172060 and 31370948)
文摘Single cell trapping in vitro by microfluidic device is an emerging approach for the study of the relationship between single cells and their dynamic biochemical microenvironments. In this paper, a hydrodynamic-based microfluidic device for single cell trapping is designed using a combination of stagnation point flow and physical barrier.The microfluidic device overcomes the weakness of the traditional ones, which have been only based upon either stagnation point flows or physical barriers, and can conveniently load dynamic biochemical signals to the trapped cell. In addition, it can connect with a programmable syringe pump and a microscope to constitute an integrated experimental system.It is experimentally verified that the microfluidic system can trap single cells in vitro even under flow disturbance and conveniently load biochemical signals to the trapped cell. The designed micro-device would provide a simple yet effective experimental platform for further study of the interactions between single cells and their microenvironments.
文摘Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by finite difference technique known as Keller Box method. The various parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic parameter (M), Casson parameter (β) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Casson fluid parameter (β) decreased both the fluid velocity and temperature whereas an increase in (β) increased both the heat transfer rate and wall skin-friction coefficient.
文摘The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of Williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretching cylinder. Further the effects of variable thermal conductivity and thermal stratification are also considered. The governing partial differential equations are converted to ordinary differential equations with the help of similarity transformation.The system of coupled non-linear ordinary differential equations is then solved by shooting technique. MATLAB shooting code is validated by comparison with the previously published work in limiting case. Results are further strengthened when the present results are compared with MATLAB built-in function bvp4c. Effects of prominent parameters are deliberated graphically for the velocity, temperature and concentration profiles. Skin-friction coefficient and Nusselt number for the different parameters are investigated with the help of tables.
基金the Deanship of Scientific Research at King Khalid University for funding this work through Research Groups Program under Grant number (R.G. P2. /26/40)
文摘This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell nanofluid.The Buongiorno’s theory has been established to picture the inducement of Brownian and thermophrotic diffusions effects.Additionally,the aspect of heat sink/source is reported.The homotopic analysis method(HAM)has been worked out for the solution of nonlinear ODEs.The behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and discussed.The attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration fields.It is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion parameter.Moreover,for the confirmation of our study comparison tables are reported.
基金Project supported by the Ministry of Education(MOE)and Research Management Centre,Universiti Teknologi Malaysia(Nos.5F166,5F004,07G70,07G72,07G76,and 07G77)。
文摘The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional(3D)stagnation point body is studied under a microgravity environment.The effects of g-jitter and thermal radiation exist under the microgravity environment,where there is a gravitational field with fluctuations.The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition.With the semi-similar transformation technique,the dimensional system of equations is reduced into a dimensionless system of equations,where the dependent variables of the problem are lessened.A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method,which is an implicit finite difference approach.The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics,the heat transfer properties,and the concentration distributions.The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body,where the stagnation point is located.The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied,where the fluctuating range becomes smaller when the oscillation frequency increases.Moreover,the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux,and the thermal radiation could increase the heat transfer properties.
文摘This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic(MHD)stagnation point flow across a stretchable surface.The heat transport process is investigated with respect to the viscous dissipation and thermal radiation,whereas the mass transport is observed under the influence of a chemical reaction.The irreversibe factor is measured through the application of the second law of thermodynamics.The established non-linear partial differential equations(PDEs)have been replaced by acceptable ordinary differential equations(ODEs),which are solved numerically via the bvp4 c method(built-in package in MATLAB).The numerical analysis of the resulting ODEs is carried out on the different flow parameters,and their effects on the rate of heat transport,friction drag,concentration,and the entropy generation are considered.It is determined that the concentration estimation and the Sherwood number reduce and enhance for higher values of the chemical reaction parameter and the Schmidt number,although the rate of heat transport is increased for the Eckert number and heat generation/absorption parameter,respectively.The entropy generation augments with boosting values of the Brinkman number,and decays with escalating values of both the radiation parameter and the Weissenberg number.
基金funded by the Research University Grant(GUP-2019034)from the Universiti Kebangsaan Malaysia。
文摘The unsteady mixed convection of the Al_(2)O_(3)-Cu/H_(2)O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed.The bvp4c technique is used to solve the resulting ordinary differential equations.The combined effects of the velocity and thermal slip are addressed.The effects of different relevant physical parameters are studied numerically.The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases,while the unsteadiness parameter has an opposite effect in the opposing flow.The presence of the slip parameter is proven to increase the skin friction coefficient while reduce the local Nusselt number in the buoyancy opposing flow.A contradictory result is observed in the buoyancy assisting flow.Meanwhile,the heat transfer rate is reduced in the buoyancy of the assisting and opposing flows when the thermal slip effect is considered.
基金supported by the National Natural Science Foundation of China (Nos.90716011,10902119)
文摘In order to evaluate uncertainties in computational fluid dynamics （CFD） computations of the stagnation point heat flux, a physical criterion is developed. Based on a quasi-one-dimensional hypothesis along the stagnation line, a new stagnation flow model is applied to obtain the governing equations of the flow near the stagnation point at hypersonic speeds. From the above equations, the compatibility relations are given at the stagnation point and along the stagnation line, which consist of the physical criterion for checking the accuracy in the stagnation point heat flux computations. The verification of the criterion is made with various numerical results.
