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1.
An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a viscoelastic fluid of short memory (obeying Walters’ B′ model), a boundary layer is formed when the stretching velocity of the surface is less than the inviscid free-stream velocity and velocity at a point increases with increase in the elasticity of the fluid. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the velocity of the free stream and the velocity decreases with increase in the elasticity of the fluid. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when the surface stretching velocity is equal to the velocity of the free stream. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined. It is found that temperature at a point decreases with increase in the elasticity of the fluid. 相似文献
2.
An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat
deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point.
It is shown that for a viscoelastic conducting fluid of short memory (obeying Walters’ Bʹ model), a boundary layer is formed
when the stretching velocity of the surface is less than the inviscid free-stream velocity and velocity at a point increases
with increase in the Hartmann number. On the other hand an inverted boundary layer is formed when the surface stretching velocity
exceeds the velocity of the free stream and the velocity decreases with increase in the Hartmann number. A novel result of
the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when
the surface stretching velocity is equal to the velocity of the free stream. Temperature distribution in the boundary layer
is found when the surface is held at constant temperature and surface heat flux is determined. It is found that in the absence
of viscous and Ohmic dissipation and strain energy in the flow, temperature at a point decreases with increase in the Hartmann
number. 相似文献
3.
This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method(HAM). It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters. 相似文献
4.
An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity cx, where x is the distance from the stagnation-point and c is a positive constant. It is shown that for a viscoelastic fluid of short memory (obeying Walters’ B model), a boundary layer is formed when the stretching velocity of the surface is less than ax, where ax+2by is the inviscid free-stream velocity and y is the distance normal to the plate, a and b being constants and the velocity at a point increases with increase in the elasticity of the fluid. On the other hand an inverted boundary layer is formed when the surface stretching velocity exceeds ax and the velocity decreases with increase in the elasticity of the fluid. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when a=c. Temperature distribution in the boundary layer is found in three cases, namely: (i) the sheet with constant surface temperature (CST); (ii) the sheet with variable surface temperature (VST) and (iii) the sheet with prescribed quadratic power law surface heat flux (PHF) for various values of non-dimensional parameters. It is found that in all the three cases when a/c>1, temperature at a point decreases with increase in the elasticity of the fluid and when a/c<1, temperature at a point increases with increase in the elasticity of the fluid. Further temperature at a point decreases with increase in the radiation parameter and wall temperature parameter. 相似文献
5.
Swati Mukhopadhyay 《Meccanica》2013,48(7):1717-1730
Similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet subject to suction. Fluid viscosity is assumed to vary as a linear function of temperature. Thermal radiation term is considered in the energy equation. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. With the help of them the partial differential equations corresponding to momentum and energy equations are transformed into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing values of the ratio of the free stream velocity to the stretching velocity. Velocity increases with the increasing temperature dependent fluid viscosity parameter when the free-stream velocity is less than the stretching velocity but opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. Temperature at a point of the surface is found to decrease with increasing thermal radiation. 相似文献
6.
Steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet is investigated
when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is
shown that the flow has a boundary layer structure for values of a/c (> 1), where ax+2by and cx are the x-component of the free stream velocity and the stretching velocity of the plate respectively, x being the distance from the stagnation-point. On the other hand when a/c < 1, the flow has an inverted boundary layer structure. It is also observed that the velocity at a point increases with increase
in the free stream shear. For a fixed value of a/c, the streamlines becomes more and more oblique towards the left of the stagnation-point with increase in b/c where b > 0. On the other hand the streamlines become increasingly oblique to the right of the stagnation-point with increase in
|b/c| when b < 0. For a fixed value of the Prandtl number Pr, temperature at a point decreases with increase in a/c. Further for a given value of a/c, the surface heat flux increases with increase in Pr. 相似文献
7.
Steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface is investigated when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. We have discussed the uniqueness of the solution except when the ratio of free stream velocity and stretching velocity is equal to 1. The effect of magnetic field on the flow characteristic is explored numerically and it is concluded that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. It is further observed that for a given value of magnetic parameter M, the dimensionless shear stress coefficient |F″(0)| increases with increase in power-law index n when the value of the ratio of free stream velocity and stretching velocity is close to 1 but not equal to 1. But when the value of this ratio further differs from 1, the variation of |F″(0)| with n is non-monotonic. 相似文献
8.
This letter is concerned with the plane and axisymmetric stagnation-point flows and heat transfer of an electrically-conducting
fluid past a stretching sheet in the presence of the thermal radiation and heat generation or absorption. The analytical solutions
for the velocity distribution and dimensionless temperature profiles are obtained for the various values of the ratio of free
stream velocity and stretching velocity, heat source parameter, Prandtl number, thermal radiation parameter, the suction and
injection velocity parameter and magnetic parameter and dimensionality index in the series form with the help of homotopy
analysis method (HAM). Convergence of the series is explicitly discussed. In addition, shear stress and heat flux at the surface
are calculated. 相似文献
9.
T. HAYAT M.MUSTAFA Z.IQBAL A.ALSAEDI 《应用数学和力学(英文版)》2013,34(2):167-176
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. 相似文献
10.
In this article, a similarity solution of the steady boundary layer flow near the stagnation-point flow on a permeable stretching
sheet in a porous medium saturated with a nanofluid and in the presence of internal heat generation/absorption is theoretically
studied. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary
differential equations with the appropriate boundary conditions via Lie-group analysis. Copper (Cu) with water as its base
fluid has been considered and representative results have been obtained for the nanoparticle volume fraction parameter f{\phi} in the range 0 £ f £ 0.2{0\leq \phi \leq 0.2} with the Prandtl number of Pr = 6.8 for the water working fluid. Velocity and temperature profiles as well as the skin friction coefficient and the local
Nusselt number are determined numerically. The influence of pertinent parameters such as nanofluid volume fraction parameter,
the ratio of free stream velocity and stretching velocity parameter, the permeability parameter, suction/blowing parameter,
and heat source/sink parameter on the flow and heat transfer characteristics is discussed. Comparisons with published results
are also presented. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change
the flow pattern. 相似文献
11.
Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet 总被引:1,自引:0,他引:1
An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation-point. Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent. 相似文献
12.
The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid over a stretching
sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations
are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations
are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl
numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity,
and the temperature profiles are presented graphically and discussed in detail. 相似文献
13.
Thermophoresis particle deposition with chemical reaction on Magnetohydrodynamic flow of an electrically conducting fluid over a porous stretching sheet in the presence of a uniform transverse magnetic field with variable stream conditions is investigated using scaling group transformation. Starting from Navier-Stokes equations and using scaling group transformations, the governing equations are obtained in the form of differential equations. The fluid viscosity is assumed to vary as a linear function of temperature. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. Impact of thermophoresis particle deposition in the presence of chemical reaction plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed. 相似文献
14.
This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point
on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external
flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations
are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method.
The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and
discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions
exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the
velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it. 相似文献
15.
F. M. ALI R. NAZAR N. M. ARIFIN I.POP 《应用数学和力学(英文版)》2014,35(2):155-166
The problem of steady laminar magnetohydrodynamic (MHD) mixed con- vection stagnation-point flow of an incompressible viscous fluid over a vertical stretch- ing sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an exter- nally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A 〉 1 and A ~ 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow. 相似文献
16.
An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer of an incompressible viscous fluid over a porous shrinking sheet in the presence of thermal radiation. A set of similarity transformations reduce the boundary layer equations to a set of non-linear ordinary differential equations which are solved numerically using fourth order Runge-Kutta method with shooting technique. The analysis of the result obtained shows that as the porosity parameter β increases, the range of region of existence of similarity solution increases. It is also observed that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on β. We then discuss the stability of the unsteady solutions about each steady solution, showing that one steady state solution corresponds to a stable solution whereas the other corresponds to an unstable solution. The stable solution corresponds to the physically relevant solution. Further we obtain numerical results for each solution, which enable us to discuss the features of the respective solutions. 相似文献
17.
Swati Mukhopadhyay Iswar Chandra Mondal Rama Subba Reddy Gorla 《Heat and Mass Transfer》2012,48(6):915-921
The aim of this paper is to present the boundary layer flow of viscous incompressible fluid due to a porous vertical stretching surface with a power-law stretching velocity in a thermally stratified medium. Using a special form of Lie group transformations viz. scaling group of transformations, similarity solutions for this problem are obtained. The equations are then solved numerically. With increasing values of the stratification parameter, the velocity as well as temperature decreases. At a particular point of the porous stretching sheet, the velocity decreases with the increasing suction parameter. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The findings of this study reveal that stratification and suction can be used as means of cooling the boundary layer flow region. 相似文献
18.
This present analysis discusses the mixed convection boundary layer flow of a magnetohydrodynamic second grade fluid over an unsteady permeable stretching sheet. The time‐dependent stretching velocity and the surface temperature are chosen. Series solutions of the governing boundary value problems are obtained by employing homotopy analysis method. Convergence of the obtained solution is explicitly discussed. The dependence of velocity and temperature profiles on the various quantities is shown and discussed by plotting graphs. Skin friction coefficient and the local Nusselt number tabulated and analyzed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
Dulal Pal 《Meccanica》2009,44(2):145-158
In this paper an analysis has been made to study heat and mass transfer in two-dimensional stagnation-point flow of an incompressible
viscous fluid over a stretching vertical sheet in the presence of buoyancy force and thermal radiation. The similarity solution
is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential
equations containing Prandtl number, Schmidt number and Sherwood number which are solved numerically with appropriate boundary
conditions for various values of the dimensionless parameters. Comparison of the present numerical results are found to be
in excellent with the earlier published results under limiting cases. The effects of various physical parameters on the boundary
layer velocity, temperature and concentration profiles are discussed in detail for both the cases of assisting and opposing
flows. The computed values of the skin friction coefficient, local Nusselt number and Sherwood number are discussed for various
values of physical parameters. The tabulated results show that the effect of radiation is to increase skin friction coefficient,
local Nusselt number and Sherwood number. 相似文献