共查询到20条相似文献,搜索用时 15 毫秒
1.
The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water
at 4°C (maximum density) when the surface heat flux varies as x
m
and the velocity outside the boundary layer varies as x
(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions
of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions
when the mixed convection parameter λ is greater than some critical value λ
c
(dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λ
c
is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and
the limits as m → ∞ and as m → −1. 相似文献
2.
The steady boundary-layer flow near the stagnation point on a vertical flat plate embedded in a fluid-saturated porous medium
characterized by an anisotropic permeability is investigated. Using appropriate similarity transformation, the governing system
of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved
numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters,
namely, the modified mixed convection parameter Λ, and the anisotropy parameter A are analyzed and discussed. It is found that dual solutions exist for both assisting and opposing flows. Moreover, the range
of Λ for which the solution exists increases with A. 相似文献
3.
The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water
close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity
form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures
the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing
flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus
putting a finite limit on the range of existence of solutions. 相似文献
4.
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
5.
A fully developed mixed convection flow between inclined parallel flat plates filled with a porous medium is considered through
which there is a constant flow rate and with heat being supplied to the fluid by the same uniform heat flux on each plate.
The equations governing this flow are made non-dimensional and are seen to depend on two dimensionless parameters, a mixed
convection parameter λ and the Péclet number Pe, as well as the inclination γ of the plates to the horizontal. The velocity and temperature profiles are obtained in terms of λ, Pe and γ when the channel is inclined in an upwards direction as well as for horizontal channels. The limiting cases of small and
large λ and small Pe are considered with boundary-layer structures being seen to develop on the plates for large values of λ. 相似文献
6.
The problem of steady mixed convection boundary layer flow over a vertical impermeable flat plate in a porous medium saturated
with water at 4°C (maximum density) when the temperature of the plate varies as x
m
and the velocity outside boundary layer varies as x
2 m
, where x measures the distance from the leading edge of the plate and m is a constant is studied. Both cases of the assisting and the opposing flows are considered. The plate is aligned parallel
to a free stream velocity U
∞ oriented in the upward or downward direction, while the ambient temperature is T
∞ = T
m (temperature at maximum density). The mathematical models for this problem are formulated, analyzed and simplified, and further
transformed into non-dimensional form using non-dimensional variables. Next, the system of governing partial differential
equations is transformed into a system of ordinary differential equations using the similarity variables. The resulting system
of ordinary differential equations is solved numerically using a finite-difference method known as the Keller-box scheme.
Numerical results for the non-dimensional skin friction or shear stress, wall heat transfer, as well as the temperature profiles
are obtained and discussed for different values of the mixed convection parameter λ and the power index m. All the numerical solutions are presented in the form of tables and figures. The results show that solutions are possible
for large values of λ and m for the case of assisting flow. Dual solutions occurred for the case of opposing flow with limited admissible values of λ
and m. In addition, separation of boundary layers occurred for opposing flow, and separation is delayed for the case of water at
4°C (maximum density) compared to water at normal temperature. 相似文献
7.
The steady laminar magnetohydrodynamic mixed convection boundary layer flow of a nanofluid near the stagnation-point on a vertical permeable plate with prescribed external flow and surface temperature is investigated in this study. Here, both assisting and opposing flows are considered and studied. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved numerically using the Runge–Kutta scheme coupled with a conventional shooting procedure. Three different types of nanoparticles, namely copper Cu, alumina Al2O3 and titania TiO2 with water as the base fluid are considered. Numerical results are obtained for the skin-friction coefficient and Nusselt number as well as for the velocity and temperature profiles for some values of the governing parameters, namely, the volume fraction of nanoparticles ?, permeability parameter f o , magnetic parameter M and mixed convection parameter λ. It is found that dual solutions exist for both assisting and opposing flows, and the range of the mixed convection parameter for which the solution exists, increases with suction, magnetic field and volume fraction of nanoparticles. 相似文献
8.
The problem of steady laminar mixed convection boundary layer flow of an incompressible viscous fluid along vertical moving
thin needles with variable heat flux for both assisting and opposing flow cases is theoretically considered in this paper.
The governing boundary layer equations are first transformed into non-dimensional forms. The curvature effects are incorporated
into the analysis whereas the pressure variation in the axial direction has been neglected. These equations are then transformed
into similarity equations using the similarity variables, which are solved numerically using an implicit finite-difference
scheme known as the Keller-box method. The solutions are obtained for a blunt-nosed needle (m = 0). Numerical calculations are carried out for various values of the dimensionless parameters of the problem, which include
the mixed convection parameter λ, the Prandtl number Pr and the parameter a representing the needle size. It is shown from the numerical results that the skin friction coefficient, the surface (wall)
temperature and the velocity and temperature profiles are significantly influenced by these parameters. The results are presented
in graphical form and are discussed in detail. 相似文献
9.
The unsteady mixed convection of the Al2O3-Cu/H2O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed. The bvp4c technique is used to solve the resulting ordinary differential equations. The combined effects of the velocity and thermal slip are addressed. The effects of different relevant physical parameters are studied numerically. The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases, while the unsteadiness... 相似文献
10.
Leli Deswita Roslinda Nazar Anuar Ishak Rokiah Ahmad Ioan Pop 《Heat and Mass Transfer》2010,46(8-9):1013-1018
The effects of suction/injection on steady laminar mixed convection boundary layer flow over a permeable horizontal surface of a wedge in a viscous and incompressible fluid is considered in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction/injection parameter f 0, the constant exponent m of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using an implicit finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are obtained for various values of parameters considered. Dual solutions are found to exist for the case of opposing flow. 相似文献
11.
The solution to the unsteady mixed convection boundary layer flow and heat transfer problem due to a stretching vertical surface
is presented in this paper. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching
velocity and the surface temperature. The governing partial differential equations with three independent variables are first
transformed into ordinary differential equations, before they are solved numerically by a finite-difference scheme. The effects
of the unsteadiness parameter, buoyancy parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly
examined. Both assisting and opposing buoyant flows are considered. It is observed that for assisting flow, the solutions
exist for all values of buoyancy parameter, whereas for opposing flow, they exist only if the magnitude of the buoyancy parameter
is small. Comparison with known results for steady-state flow is excellent. 相似文献
12.
Steady mixed convection boundary layer flow from an isothermal horizontal circular cylinder embedded in a porous medium filled
with a nanofluid has been studied for both cases of a heated and cooled cylinder. The resulting system of nonlinear partial
differential equations is solved numerically using an implicit finite-difference scheme. The solutions for the flow and heat
transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle
volume fraction φ and the mixed convection parameter λ. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the magnitude of the skin friction coefficient decreases, and this leads to an increase in the value of the mixed
convection parameter λ which first produces no separation. On the other hand, it is also found that of all the three types
of nanoparticles considered, for any fixed values of φ and λ, the nanoparticle Cu gives the largest values of the skin friction coefficient followed by TiO2 and Al2O3. Finally, it is worth mentioning that heating the cylinder (λ > 0) delays separation of the boundary layer and if the cylinder
is hot enough (large values of λ > 0), then it is suppressed completely. On the other hand, cooling the cylinder (λ < 0) brings
the boundary layer separation point nearer to the lower stagnation point and for a sufficiently cold cylinder (large values
of λ < 0) there will not be a boundary layer on the cylinder. 相似文献
13.
Laminar mixed convection from a continuously moving vertical surface with suction or injection 总被引:1,自引:0,他引:1
The boundary layer flow over a uniformly moving vertical surface with suction or injection is studied when the buoyancy forces
assist or oppose the flow. Similarity solutions are obtained for the boundary layer equations subject to power law temperature
and velocity boundary conditions. The effect is of various governing parameters, such as Prandtl number Pr, temperature exponent
n, injection parameter d, and the mixed convection parameter λ=Gr/Re2, which determine the velocity and temperature distributions and the heat transfer coefficient, are studied. The heat transfer
coefficient increases as λ assisting the flow for all d at Pr=0.72 however, for n=−1 it decreases sharply with λ. On the other hand, increasing λ has no effect on heat transfer coefficient for Pr=10 at n=0, and 1 for almost all values of d studied. However, for n=−1 it has similar effect as for Pr=0.72. It is also found that Nusselt number increases as n increases for fixed λ and d.
Received on 26 March 1997 相似文献
14.
This article considers the problem of mixed convection stagnation-point flow towards a vertical plate embedded in a porous
medium with prescribed surface heat flux. It is assumed that the free stream velocity and the surface heat flux vary linearly
from the stagnation point. Using a similarity transformation, the governing system of partial differential equations is transformed
into a system of ordinary differential equations, before being solved numerically by a finite-difference method. The features
of the flow and the heat transfer characteristics are analyzed and discussed. It is found that dual solutions exist for both
buoyancy assisting and opposing flows. 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.
The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows. 相似文献
17.
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
18.
A. Zaib K. Bhattacharyya M. Khalid S. Shafie 《Journal of Applied Mechanics and Technical Physics》2017,58(3):419-424
The thermal radiation effect on a steady mixed convective flow with heat transfer of a nonlinear (non-Newtonian) Williamson fluid past an exponentially shrinking porous sheet with a convective boundary condition is investigated numerically. In this study, both an assisting flow and an opposing flow are considered. The governing equations are converted into nonlinear ordinary differential equations by using a suitable transformation. A numerical solution of the problem is obtained by using the Matlab software package for different values of the governing parameters. The results show that dual nonsimilar solutions exist for the opposing flow, whereas the solution for the assisting flow is unique. It is also observed that the dual nonsimilar solutions exist only if a certain amount of mass suction is applied through the porous sheet, which depends on the Williamson parameter, convective parameter, and radiation parameter. 相似文献
19.
The natural convection boundary-layer flow on a surface embedded in a fluid-saturated porous medium is discussed in the case
when the wall heat flux is related to the wall temperature through a power-law variation. The flow within the porous medium
is assumed to be described by Darcy’s law and the Boussinesq approximation is assumed for the density variations. Two cases
are discussed, (i) stagnation-point flow and (ii) flow along a vertical surface. The possible steady states are considered
first with the governing partial equations reduced to ordinary differential equations by similarity transformations and these
latter equations further transformed to previously studied free-convection problems. This identifies values of the exponent
N in the power-law wall temperature variation, N = 3/2 for stagnation-point flows and 3/2 ≤ N ≤ 3 for the vertical surface, where similarity solutions do not exist. Time development for stagnation-point flows is seen
to depend on N, for N < 3/2 the steady state is approached at large times, for N ≥ 3/2 a singularity develops at finite time leading to thermal runaway. Numerical solutions for the vertical surface, where
the temperature-dependent boundary condition becomes more significant as the solution develops, show that, for N < 3/2, the corresponding similarity solution is approached, whereas for N > 3/2 the solution breaks down at a finite distance along the surface. 相似文献
20.
The problem of melting from a vertical flat plate embedded in a porous medium is studied. The main focus is to determine the effect of mixed convection flow in the liquid phase on the melting phenomenon. Both aiding and opposing flows are considered. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The governing equations are solved numerically. Numerical results are obtained for the temperature and flow fields in the melting region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface. 相似文献