Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved ...Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved numerically by RKF-45 method.Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters.Furthermore,the skin friction coefficient and Nusselt number are also presented in Tabs.2 and 3.It is found that the heat transfer rates are advanced in occurrence of nonlinear radiation compered to linear radiation.Also,it is noticed that velocity and temperature profile increases by increasing Prandtl parameter.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
This Communication deals with the blood flow of Prandtl fluid through a tapered stenosed arteries having permeable walls.The governing equations of two-dimensional Prandtl fluid model are modelled in cylindrical coord...This Communication deals with the blood flow of Prandtl fluid through a tapered stenosed arteries having permeable walls.The governing equations of two-dimensional Prandtl fluid model are modelled in cylindrical coordinates.The highly nonlinear equations are simplified with the help of non-dimensional variables under the assumption of mild stenosis.The solution of reduced nonlinear equation subject to boundary condition of porous walls having the effects of Darcy's number and slip parameter are computed analytically with the help of perturbation method.Effects of emerging parameters such as impedance A,slip parameter a,stenosis height 6,magnetic parameter and stress component Srz on velocity are illustrated graphically.The streamlines have also been presented to discuss the trapping bolus discipline.展开更多
In this paper,the magnetohydrodynamic 3 D flow of Prandtl nanoliquid subject to convectively heated extendable surface has been discussed.A linear stretching surface makes the flow.Thermophoretic and Brownian motion i...In this paper,the magnetohydrodynamic 3 D flow of Prandtl nanoliquid subject to convectively heated extendable surface has been discussed.A linear stretching surface makes the flow.Thermophoretic and Brownian motion impacts are explored.Heat transfer for convective procedure is considered.Prandtl liquid is taken electrically conducted through applied magnetic field.Suitable non-dimensional variables lead to strong nonlinear ordinary differential system.The obtained nonlinear differential systems are solved through optimal homotopic technique.Physical quantities like skin friction coefficients and Nusselt number are explored via plots.It is observed that effects of Hartman parameter and Biot number on temperature and concentration are quite similar.Both temperature and concentration are enhanced for larger values of Hartman parameter and Biot number.展开更多
The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considere...The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.展开更多
This article numerically investigates the 2D, steady, laminar, incompressible fluid flow, mass and heat transfer of a non-Newtonian fluid model induced by stretching surface. A Casson fluid model is considered to stud...This article numerically investigates the 2D, steady, laminar, incompressible fluid flow, mass and heat transfer of a non-Newtonian fluid model induced by stretching surface. A Casson fluid model is considered to study the non-Newtonian behavior of the flowing fluid. The magnetic field and a porous medium are considered in the flow momentum, whereas the viscous dissipation is also taken into account in the energy transport phenomena. To see the fluid concentration, the concentration equation is used. Furthermore, the Nusselt number coefficient and skin friction are modified with the addition of nonlinear stretching and radiation parameters. With the similarity transformation, the nonlinear governing partial differential equations are transformed into a system of ordinary differential equations and then numerically solved using a fourth-order Runge-Kutta scheme with the shooting method. The relevant parameters of interest are interpreted for graphical results. The results illustrate that the fluid energy increases effectively with an increase in the Eckert number, radiation parameter, and heat source parameter, while it decreases by increasing the Prandtl number and heat sink parameter. Both the wall skin friction and the wall Nusselt number coefficient decelerate with an increase in the Casson parameter.展开更多
The major concern of proffered study based on the inquisitive analysis of entropy approach based on 3-D Prandtl fluid influenced by modified advanced heat conduction along with mass diffusion models.Moreover,influence...The major concern of proffered study based on the inquisitive analysis of entropy approach based on 3-D Prandtl fluid influenced by modified advanced heat conduction along with mass diffusion models.Moreover,influence of Hall and also slip forces and heat transmission characteristics are featured under the combined outcomes appertaining to radiations and viscous dissipation are taken into account in this investigation.This article also examined the combined impacts of thermal conductivity change together with variable mass diffusion co-efficient within the heat and mass transport in the occurrence of Prandtl fluid.Flow demeanor is examined across the bidirectional extendable sheet.Numerical simulations based on 3-D flow configured by extending surface are carried out by using OHAM.Simulated PDEs expressed as ODEs with the utilization of dimensionless variables.Simulated outcomes are validated graphically obtained by varying values of emerging constraints through previous published results and seen in desirable agreement.The influence of distinct parameters associated with this current study like Brownian and diffusion constraint,temperature and also concentration difference,Eckert number,Hall as well as ion slip parameters,Brinkman number,magnetic constraint,radiation and Prandtl fluid constraint are sketched for temperature,velocity field along xy-axes,concentration and entropy generation rate.It is noticed that velocity distribution along x-axes is an increasing function of magnetic constraint,Prandtl fluid and also elastic constraint whilst contrast impact is seen along y-axes.Moreover,temperature as well as concentration profile decays for Prandtl number,thermal and also concentration relaxation time constraint respectively whereas both profiles enhanced for distinct considered parameters.Entropy declines for ion-slip parameter whilst enhanced for Bejan number.Entropy behavior as well as Bejan number effect under various parameters is sketched graphically and enhanced behavior is depicted for entropy for considered constraint whilst Bejan number enhanced for diffusion parameter and also concentration difference constraint whereas declined behavior demonstrated for other considered parameters.The innovative component in the current study lies in the integration of multiple factors towards the Prandtl fluid model framework,forcing its boundaries beyond widespread conventional applications.Extending the Prandtl fluid model in 3D allows more comprehensive demonstration of the under consideration physical system.展开更多
A device of mercury liquid bridge of floating half-zone is designed to experimentally explore thermo-capillary convection and its instability of a low Prandtl number liquid. Noncontacted diagnostic techniques were dev...A device of mercury liquid bridge of floating half-zone is designed to experimentally explore thermo-capillary convection and its instability of a low Prandtl number liquid. Noncontacted diagnostic techniques were developed to monitor surface flow and surface deformation. The surface flow and the influence of a growing surface film (or skin) on the flow were observed It is shown that the film is a key factor in changing the behavior associated with the thermocapillary convection. The experiment indicates that the critical Marangoni number should be much higher than that expected by the numerical simulation. The condition and process of surface film growth are discussed. The surface oscillation of the mercury bridge wrapped with "dirt-film" was observed, and the characteristics and the frequency associated with this oscillation are given.展开更多
The hydrothermal wave was investigated numerically for large-Prandtl-number fluid (Pr = 105.6) in a shallow cavity with different heated sidewalls. The traveling wave appears and propagates in the direction opposite t...The hydrothermal wave was investigated numerically for large-Prandtl-number fluid (Pr = 105.6) in a shallow cavity with different heated sidewalls. The traveling wave appears and propagates in the direction opposite to the surface flow (upstream) in the case of zero gravity when the applied temperature difference grows and over the critical value. The phase relationships of the disturbed velocity,temperature and pressure demonstrate that the traveling wave is driven by the disturbed tem-perature,which is named hydrothermal wave. The hydrothermal wave is so weak that the oscillatory flow field and temperature distribution can hardly be observed in the liquid layer. The exciting mechanism of hydrothermal wave is analyzed and discussed in the present paper.展开更多
文摘Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved numerically by RKF-45 method.Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters.Furthermore,the skin friction coefficient and Nusselt number are also presented in Tabs.2 and 3.It is found that the heat transfer rates are advanced in occurrence of nonlinear radiation compered to linear radiation.Also,it is noticed that velocity and temperature profile increases by increasing Prandtl parameter.
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.
文摘This Communication deals with the blood flow of Prandtl fluid through a tapered stenosed arteries having permeable walls.The governing equations of two-dimensional Prandtl fluid model are modelled in cylindrical coordinates.The highly nonlinear equations are simplified with the help of non-dimensional variables under the assumption of mild stenosis.The solution of reduced nonlinear equation subject to boundary condition of porous walls having the effects of Darcy's number and slip parameter are computed analytically with the help of perturbation method.Effects of emerging parameters such as impedance A,slip parameter a,stenosis height 6,magnetic parameter and stress component Srz on velocity are illustrated graphically.The streamlines have also been presented to discuss the trapping bolus discipline.
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./19/40)
文摘In this paper,the magnetohydrodynamic 3 D flow of Prandtl nanoliquid subject to convectively heated extendable surface has been discussed.A linear stretching surface makes the flow.Thermophoretic and Brownian motion impacts are explored.Heat transfer for convective procedure is considered.Prandtl liquid is taken electrically conducted through applied magnetic field.Suitable non-dimensional variables lead to strong nonlinear ordinary differential system.The obtained nonlinear differential systems are solved through optimal homotopic technique.Physical quantities like skin friction coefficients and Nusselt number are explored via plots.It is observed that effects of Hartman parameter and Biot number on temperature and concentration are quite similar.Both temperature and concentration are enhanced for larger values of Hartman parameter and Biot number.
文摘The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.
文摘This article numerically investigates the 2D, steady, laminar, incompressible fluid flow, mass and heat transfer of a non-Newtonian fluid model induced by stretching surface. A Casson fluid model is considered to study the non-Newtonian behavior of the flowing fluid. The magnetic field and a porous medium are considered in the flow momentum, whereas the viscous dissipation is also taken into account in the energy transport phenomena. To see the fluid concentration, the concentration equation is used. Furthermore, the Nusselt number coefficient and skin friction are modified with the addition of nonlinear stretching and radiation parameters. With the similarity transformation, the nonlinear governing partial differential equations are transformed into a system of ordinary differential equations and then numerically solved using a fourth-order Runge-Kutta scheme with the shooting method. The relevant parameters of interest are interpreted for graphical results. The results illustrate that the fluid energy increases effectively with an increase in the Eckert number, radiation parameter, and heat source parameter, while it decreases by increasing the Prandtl number and heat sink parameter. Both the wall skin friction and the wall Nusselt number coefficient decelerate with an increase in the Casson parameter.
文摘The major concern of proffered study based on the inquisitive analysis of entropy approach based on 3-D Prandtl fluid influenced by modified advanced heat conduction along with mass diffusion models.Moreover,influence of Hall and also slip forces and heat transmission characteristics are featured under the combined outcomes appertaining to radiations and viscous dissipation are taken into account in this investigation.This article also examined the combined impacts of thermal conductivity change together with variable mass diffusion co-efficient within the heat and mass transport in the occurrence of Prandtl fluid.Flow demeanor is examined across the bidirectional extendable sheet.Numerical simulations based on 3-D flow configured by extending surface are carried out by using OHAM.Simulated PDEs expressed as ODEs with the utilization of dimensionless variables.Simulated outcomes are validated graphically obtained by varying values of emerging constraints through previous published results and seen in desirable agreement.The influence of distinct parameters associated with this current study like Brownian and diffusion constraint,temperature and also concentration difference,Eckert number,Hall as well as ion slip parameters,Brinkman number,magnetic constraint,radiation and Prandtl fluid constraint are sketched for temperature,velocity field along xy-axes,concentration and entropy generation rate.It is noticed that velocity distribution along x-axes is an increasing function of magnetic constraint,Prandtl fluid and also elastic constraint whilst contrast impact is seen along y-axes.Moreover,temperature as well as concentration profile decays for Prandtl number,thermal and also concentration relaxation time constraint respectively whereas both profiles enhanced for distinct considered parameters.Entropy declines for ion-slip parameter whilst enhanced for Bejan number.Entropy behavior as well as Bejan number effect under various parameters is sketched graphically and enhanced behavior is depicted for entropy for considered constraint whilst Bejan number enhanced for diffusion parameter and also concentration difference constraint whereas declined behavior demonstrated for other considered parameters.The innovative component in the current study lies in the integration of multiple factors towards the Prandtl fluid model framework,forcing its boundaries beyond widespread conventional applications.Extending the Prandtl fluid model in 3D allows more comprehensive demonstration of the under consideration physical system.
文摘A device of mercury liquid bridge of floating half-zone is designed to experimentally explore thermo-capillary convection and its instability of a low Prandtl number liquid. Noncontacted diagnostic techniques were developed to monitor surface flow and surface deformation. The surface flow and the influence of a growing surface film (or skin) on the flow were observed It is shown that the film is a key factor in changing the behavior associated with the thermocapillary convection. The experiment indicates that the critical Marangoni number should be much higher than that expected by the numerical simulation. The condition and process of surface film growth are discussed. The surface oscillation of the mercury bridge wrapped with "dirt-film" was observed, and the characteristics and the frequency associated with this oscillation are given.
基金Supported by the National Natural Science Foundation of China (Grant No. 10432060)
文摘The hydrothermal wave was investigated numerically for large-Prandtl-number fluid (Pr = 105.6) in a shallow cavity with different heated sidewalls. The traveling wave appears and propagates in the direction opposite to the surface flow (upstream) in the case of zero gravity when the applied temperature difference grows and over the critical value. The phase relationships of the disturbed velocity,temperature and pressure demonstrate that the traveling wave is driven by the disturbed tem-perature,which is named hydrothermal wave. The hydrothermal wave is so weak that the oscillatory flow field and temperature distribution can hardly be observed in the liquid layer. The exciting mechanism of hydrothermal wave is analyzed and discussed in the present paper.
