Thiswork investigates an oblique stagnation point flowof hybrid nanofluid over a rigid surface with power lawfluidas lubricated layers. Copper (Cu) and Silver (Ag) solid particles are used as hybrid particles acting i...Thiswork investigates an oblique stagnation point flowof hybrid nanofluid over a rigid surface with power lawfluidas lubricated layers. Copper (Cu) and Silver (Ag) solid particles are used as hybrid particles acting in water H2O asa base fluid. The mathematical formulation of flow configuration is presented in terms of differential systemthat isnonlinear in nature. The thermal aspects of the flow field are also investigated by assuming the surface is a heatedsurface with a constant temperature T. Numerical solutions to the governing mathematical model are calculatedby the RK45 algorithm. The results based on the numerical solution against various flow and thermal controllingparameters are presented in terms of line graphs. The specific results depict that the heat flux increases over thelubricated-indexed parameter.展开更多
The Kom-Ombo and Nuqra basins in southern Egypt have recently been discovered as potential hydrocarbon basins. The lack of information about the geothermal gradient and heat flow in the study area gives importance to ...The Kom-Ombo and Nuqra basins in southern Egypt have recently been discovered as potential hydrocarbon basins. The lack of information about the geothermal gradient and heat flow in the study area gives importance to studying the heat flow and the geothermal gradient. Several studies were carried out to investigate the geothermal analyses of the northwestern desert, as well as the west and east of the Nile River, using density, compressive wave velocity, and bottom hole temperature (BHT) measured from deep oil wells. This research relies on spectral analysis of airborne magnetic survey data in the Kom-Ombo and Nuqra basins in order to estimate the geothermal gradient based on calculating the depth to the bottom of the magnetic source that caused the occurrence of these magnetic deviations. This depth is equal to the CPD, at which the material loses its magnetic polarisation. This method is fast and gives satisfactory results. Usually, it can be applied as a reconnaissance technique for geothermal exploration targets due to the abundance of magnetic data. The depth of the top (Z<sub>t</sub>) and centroid (Z<sub>0</sub>) of the magnetic source bodies was calculated for the 32 windows representing the study area using spectral analysis of airborne magnetic data. The curie-isotherm depth, geothermal gradient, and heat flow maps were constructed for the study area. The results showed that the CPD in the study area ranges from 13 km to 20 km. The heat flow map values range from 69 to 109 mW/m<sup>2</sup>, with an average of about 80 mW/m<sup>2</sup>. The calculated heat flow values in the assigned areas (A, B, C, and D) of the study area are considered to have high heat flow values, reaching 109 mW/m<sup>2</sup>. On the other hand, the heat flow values in the other parts range from 70 to 85 mW/m<sup>2</sup>. Since heat flow plays an essential role in the maturation of organic matter, it is recommended that hydrocarbon accumulations be located in places with high heat flow values, while deep drilling of hydrocarbon wells is recommended in places with low to moderate heat flow values.展开更多
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
This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy ...This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.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 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 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 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
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
Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the vel...Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.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
The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation ef...The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.展开更多
The present article investigates the dual nature of the solution of the magneto- hydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary dif...The present article investigates the dual nature of the solution of the magneto- hydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting: method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions (the classical Newtonian fluid model) is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.展开更多
In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct pow...In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.展开更多
The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. Th...The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensionM axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter β and the rotating parameter Ω. However, the lower branch solution breaks down at some moderate values of β The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β. The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.展开更多
The problem of steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid towards a stretching surface is reexamined. Here the surface is stretched with a velocity proportional to the dist...The problem of steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid towards a stretching surface is reexamined. Here the surface is stretched with a velocity proportional to the distance from a fixed point. Previous studies on this problem are reviewed and the errors in the boundary conditions at infinity are rectified. It is found that for a very small value of shear in the free stream, the flow has a boundary layer structure when , where and are the free stream stagnation-point velocity and the stretching velocity of the sheet, respectively, being the distance along the surface from the stagnation-point. On the other hand, the flow has an inverted boundary layer structure when . It is also observed that for given values of and free stream shear, the horizontal velocity at a point decreases with increase in the pressure gradient parameter.展开更多
By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that...By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of ' mufti- layer structure' in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories .展开更多
With the aid of a slip-disentanglemnt theory, a rheological equation has been deduced about the composite system of solid-state low melting point metal and polymer. By measuring some rheological properties of the comp...With the aid of a slip-disentanglemnt theory, a rheological equation has been deduced about the composite system of solid-state low melting point metal and polymer. By measuring some rheological properties of the composite system composed of low melt point metal and polypropylene (LMPM/PP), the results show that LMPM has a promoter flow action upon PP when using a small amount of LMPM and, if some coupled agents are added, the promoter flow action will be remarkable. Moreover, while LMPM being added into the composite, the temperature sensitivity of system will go rip. This indicates that the system's viscosity will drop further if its temperature is increased.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
文摘Thiswork investigates an oblique stagnation point flowof hybrid nanofluid over a rigid surface with power lawfluidas lubricated layers. Copper (Cu) and Silver (Ag) solid particles are used as hybrid particles acting in water H2O asa base fluid. The mathematical formulation of flow configuration is presented in terms of differential systemthat isnonlinear in nature. The thermal aspects of the flow field are also investigated by assuming the surface is a heatedsurface with a constant temperature T. Numerical solutions to the governing mathematical model are calculatedby the RK45 algorithm. The results based on the numerical solution against various flow and thermal controllingparameters are presented in terms of line graphs. The specific results depict that the heat flux increases over thelubricated-indexed parameter.
文摘The Kom-Ombo and Nuqra basins in southern Egypt have recently been discovered as potential hydrocarbon basins. The lack of information about the geothermal gradient and heat flow in the study area gives importance to studying the heat flow and the geothermal gradient. Several studies were carried out to investigate the geothermal analyses of the northwestern desert, as well as the west and east of the Nile River, using density, compressive wave velocity, and bottom hole temperature (BHT) measured from deep oil wells. This research relies on spectral analysis of airborne magnetic survey data in the Kom-Ombo and Nuqra basins in order to estimate the geothermal gradient based on calculating the depth to the bottom of the magnetic source that caused the occurrence of these magnetic deviations. This depth is equal to the CPD, at which the material loses its magnetic polarisation. This method is fast and gives satisfactory results. Usually, it can be applied as a reconnaissance technique for geothermal exploration targets due to the abundance of magnetic data. The depth of the top (Z<sub>t</sub>) and centroid (Z<sub>0</sub>) of the magnetic source bodies was calculated for the 32 windows representing the study area using spectral analysis of airborne magnetic data. The curie-isotherm depth, geothermal gradient, and heat flow maps were constructed for the study area. The results showed that the CPD in the study area ranges from 13 km to 20 km. The heat flow map values range from 69 to 109 mW/m<sup>2</sup>, with an average of about 80 mW/m<sup>2</sup>. The calculated heat flow values in the assigned areas (A, B, C, and D) of the study area are considered to have high heat flow values, reaching 109 mW/m<sup>2</sup>. On the other hand, the heat flow values in the other parts range from 70 to 85 mW/m<sup>2</sup>. Since heat flow plays an essential role in the maturation of organic matter, it is recommended that hydrocarbon accumulations be located in places with high heat flow values, while deep drilling of hydrocarbon wells is recommended in places with low to moderate heat flow values.
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.
文摘This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.
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.
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.
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 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.
基金supported by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.
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Project supported by the National Natural Science Foundation of China(Nos.51709191,51706149,and 51606130)the Key Laboratory of Advanced Reactor Engineering and Safety,Ministry of Education of China(No.ARES-2018-10)the State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University of China(No.Skhl1803)
文摘The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.
文摘The present article investigates the dual nature of the solution of the magneto- hydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting: method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions (the classical Newtonian fluid model) is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.
基金the National Board for Higher Mathematics(NBHM),DAE,Mumbai,India
文摘In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.
文摘The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensionM axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter β and the rotating parameter Ω. However, the lower branch solution breaks down at some moderate values of β The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β. The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.
文摘The problem of steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid towards a stretching surface is reexamined. Here the surface is stretched with a velocity proportional to the distance from a fixed point. Previous studies on this problem are reviewed and the errors in the boundary conditions at infinity are rectified. It is found that for a very small value of shear in the free stream, the flow has a boundary layer structure when , where and are the free stream stagnation-point velocity and the stretching velocity of the sheet, respectively, being the distance along the surface from the stagnation-point. On the other hand, the flow has an inverted boundary layer structure when . It is also observed that for given values of and free stream shear, the horizontal velocity at a point decreases with increase in the pressure gradient parameter.
基金Foundation items : the National Natural Science Foundation of China ( NSFC grant No.90205024) the Russian Foundation for Basic Research (RFBR grant No. 02-01-00770) RFBR-NSFC grant No.99-01-39020)
文摘By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of ' mufti- layer structure' in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories .
文摘With the aid of a slip-disentanglemnt theory, a rheological equation has been deduced about the composite system of solid-state low melting point metal and polymer. By measuring some rheological properties of the composite system composed of low melt point metal and polypropylene (LMPM/PP), the results show that LMPM has a promoter flow action upon PP when using a small amount of LMPM and, if some coupled agents are added, the promoter flow action will be remarkable. Moreover, while LMPM being added into the composite, the temperature sensitivity of system will go rip. This indicates that the system's viscosity will drop further if its temperature is increased.
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.