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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 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
2.
Steady two-dimensional 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 for a fluid of small kinematic viscosity, a boundary layer is formed when the stretching velocity is less than
the free stream velocity and an inverted boundary layer is formed when the stretching velocity exceeds the free stream velocity.
Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat
flux is determined.
Received on 12 July 2000 / Published online: 29 November 2001 相似文献
3.
This investigation explores the characteristics of melting heat transfer in a boundary layer flow of the Jeffrey fluid near the stagnation point on a stretching sheet subject to an applied magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by similarity transformations. Resulting nonlinear problems are solved analytically by the homotopy analysis method. It is noticed that an increase in the melting parameter decreases the dimensionless velocity and temperature, while an increase in the Deborah number increases the velocity and momentum boundary layer thickness. 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 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
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.
N. Samyuktha R. Ravindran M. Ganapathirao 《Journal of Applied Mechanics and Technical Physics》2017,58(1):116-128
An analysis is performed to study the effects of the chemical reaction and heat generation or absorption on a steady mixed convection boundary layer flow over a vertical stretching sheet with nonuniform slot mass transfer. The governing boundary layer equations with boundary conditions are transformed into the dimensionless form by a group of nonsimilar transformations. Nonsimilar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasi-linearization technique combined with an implicit finite difference scheme. The numerical computations are carried out for different values of dimensionless parameters to display the distributions of the velocity, temperature, concentration, local skin friction coefficient, local Nusselt number, and local Sherwood number. The results obtained indicate that the local Nusselt and Sherwood numbers increase with nonuniform slot suction, but nonuniform slot injection produces the opposite effect. The local Nusselt number decreases with heat generation and increases with heat absorption. 相似文献
7.
The unsteady mixed convection boundary layer flow over a vertical cone is considered to investigate the combined effects of
the buoyancy force, thermal and mass diffusion in the presence of the first order chemical reaction and surface mass transfer.
The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. The governing boundary
layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system
of coupled non-linear partial differential equations is solved numerically by the combination of quasi-linearization technique
and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display
the velocity, temperature and concentration profiles graphically. Both accelerating and decelerating free stream velocities
are considered. Numerical results are presented for the velocity, temperature and concentration profiles as well as for the
skin-friction coefficient, local Nusselt number and local Sherwood number. The obtained results are compared with previously
reported ones and are found to be in excellent agreement. 相似文献
8.
对纳米流体在伸/缩楔体上的磁流体(MHD)流动进行了数值研究。首先,通过相似变换将控制偏微分方程转化为非线性常微分方程组;然后,利用Matlab软件,借助打靶法,结合四阶五常龙格库塔迭代方案进行数值求解;最后,详细讨论了各控制参数对无量纲速度、温度、浓度、表面摩擦系数、局部Nusselt数和局部Sherwood数的影响。结果表明,楔体在拉伸情况下只有唯一解,理论上不会出现边界层分离;而在一定收缩强度范围内存在双解,边界层流动在壁面处可能会出现边界层分离,壁面抽吸会使边界层分离推迟;楔体在拉伸情况下,磁场参数对表面摩擦系数的影响较大,对局部Nusselt数和局部Sherwood数的影响较小。 相似文献
9.
Mostafa A. A. Mahmoud 《国际流体数值方法杂志》2011,67(11):1692-1701
The influence of thermal radiation on the flow and heat transfer within Newtonian liquid film over an unsteady stretching sheet with and without thermocapillarity is examined. The governing non‐linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformation, which is solved numerically for different values of the thermal radiation parameter and the thermocapillarity parameter. The results show that the dimensionless velocity, the film thickness and the local Nusselt number increase as the thermocapillarity parameter increases, while the free surface temperature decreases with increasing the thermocapillarity parameter. Also, both the dimensionless temperature and the free surface temperature increase and the local Nusselt number decreases as the thermal radiation parameter increases. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
The non-similar solution of an unsteady mixed convection laminar boundary layer flow over a vertical cone in the presence of non-uniform surface mass transfer through slot has been obtained while the axis of cone is inline with the flow. The unsteadiness is caused by the time dependent free stream velocity. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting coupled non-linear partial differential equations have been solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity and temperature profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are reported to display the effects of non-uniform single and double slot suction (injection) on skin friction and heat transfer coefficients at the wall. Further, the effects of Prandtl number, buoyancy and mass transfer (suction or injection) parameters at different stream-wise locations for various times on velocity and temperature profiles, and on skin friction and heat transfer coefficients are also presented in this paper. 相似文献
11.
Similarity solution of the laminar boundary layer equations corresponding to an unsteady stretching surface have been studied. The governing time-dependent boundary layer are transformed to ordinary differential equations containg Prandtl number and unsteadiness parameter. The effect of various govern-ing parameters such as Prandtl number and unsteadiness param-eter which determine the velocity and temperature profiles and heat transfer coefficient are studied. 相似文献
12.
Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic (MHD) flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters. 相似文献
13.
N. Siva Raman K. K. Sivagnana Prabhu R. Kandasamy 《Journal of Applied Mechanics and Technical Physics》2012,53(6):871-879
The group theoretic method is applied for solving the problem of the combined influence of the thermal diffusion and diffusion thermoeffect on magnetohydrodynamic free convective heat and mass transfer over a porous stretching surface in the presence of thermophoresis particle deposition with variable stream conditions. The application of one-parameter groups reduces the number of independent variables by one; consequently, the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The equations along with the boundary conditions are solved numerically by using the Runge-Kutta-Gill integration scheme with the shooting technique. The impact of the Soret and Dufour effects in the presence of thermophoresis particle deposition with a chemical reaction plays an important role on the flow field. 相似文献
14.
Ahmed A. Afify 《Heat and Mass Transfer》2004,40(6-7):495-500
The effect of chemical reaction on free convective flow and mass transfer of a viscous, incompressible and electrically conducting fluid over a stretching surface is investigated in the presence of a constant transverse magnetic field. The non-linear boundary layer equations with the boundary conditions are transferred by a similarity transformation into a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results of the skin friction coefficient, the local Nusselt number Nu, the local Sherwood number Sh, as will as the velocity, temperature and concentration profiles are presented for gases with a Prandtl number of 0.71 for various values of chemical reaction parameter, order of reaction, magnetic parameter and Schmidt number. 相似文献
15.
Youssef Z. Boutros Mina B. Abd-el-Malek Nagwa A. Badran Hossam S. Hassan 《Meccanica》2006,41(6):681-691
The boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at
a heated stretching sheet placed in a porous medium are considered. We apply Lie-group method for determining symmetry reductions
of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under
which the given partial differential equations are invariant. The determining equations are a set of linear differential equations,
the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables.
After the group has been determined, a solution to the given partial differential equations may be found from the invariant
surface condition such that its solution leads to similarity variables that reduce the number of independent variables of
the system. The effect of the velocity parameter λ, which is the ratio of the external free stream velocity to the stretching
surface velocity, permeability parameter of the porous medium k
1, and Prandtl number Pr on the horizontal and transverse velocities, temperature profiles, surface heat flux and the wall
shear stress, has been studied. 相似文献
16.
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
17.
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
18.
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
19.
The present paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of an incompressible
viscous fluid over an unsteady stretching sheet which is placed in a porous medium in the presence of viscous dissipation
and internal absorption or generation. Similarity transformations are used to convert the governing time dependent nonlinear
boundary layer equations into a system of non-linear ordinary differential equations containing Prandtl number, Eckert number,
heat source/sink parameter, porous parameter and unsteadiness parameter with appropriate boundary conditions. These equations
are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. Comparison of numerical results is made
with the earlier published results under limiting cases. The effects of the parameters which determine the velocity and temperature
fields are discussed in detail. 相似文献
20.
The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel
to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear
partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved
numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity
profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting
parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is
found that the problem admits dual solutions. 相似文献