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1.
An analysis is made of heat transfer in the boundary layer of a viscoelastic fluid flowing over a stretching surface. The
velocity of the surface varies linearly with the distance x from a fixed point and the surface is held at a uniform temperature T
w
higher than the temperature T
∞ of the ambient fluid. An exact analytical solution for the temperature distribution is found by solving the energy equation
after taking into account strain energy stored in the fluid (due to its elastic property) and viscous dissipation. It is shown
that the temperature profiles are nonsimilar in marked contrast with the case when these profiles are found to be similar
in the absence of viscous dissipation and strain energy. It is also found that temperature at a point increases due to the
combined influence of these two effects in comparison with its corresponding value in the absence of these two effects. A
novel result of this analysis is that for small values of x, heat flows from the surface to the fluid while for moderate and large values of x, heat flows from the fluid to the surface even when T
w
>T
∞. Temperature distribution and the surface heat flux are determined for various values of the Prandtl number P, the elastic parameter K
1 and the viscous dissipation parameter a. Numerical solutions are also obtained through a fourth-order accurate compact finite difference scheme.
Received on 14 October 1997 相似文献
2.
The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect
in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation
as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt
number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation
on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at
wall, a critical value of Brinkman number, Br
c=−11/24, exists beyond which (−11/24<Br<0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling
effect over the viscous heating effect. On the other hand, with Br < Br
c the bulk temperature T
b will approach the wall temperature T
w at some downstream position and from there onward the bulk temperature T
b becomes less than the wall temperature T
w with T
w > B
b > T
0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br < 0 are believed to be of some interest in the design of the proposed artctic oil pipeline. 相似文献
3.
C. -H. Chen 《Heat and Mass Transfer》2000,36(1):79-86
An numerical study of the flow and heat transfer characteristics associated with a heated, continuously stretching surface
being cooled by a mixed convection flow has been carried out. The relevant heat transfer mechanisms are of interest in a wide
variety of practical applications, such as hot rolling, continuous casting, extrusion, and drawing. The surface velocity of
the continuously stretching sheet was assumed to vary according to a power-law form, that is, u
w
(x)=Cx
p
. Two conditions of surface heating were considered, a variable wall temperature (VWT) in the form T
w
(x)−T
∞=Ax
n
and a variable surface heat flux (VHF) in the form q
w
(x)=Bx
m
. The governing differential equations are transformed by introducing proper nonsimilarity variables and solved numerically
using a procedure based on finite difference approximations. Results for the local Nusselt number and the local friction coefficient
are obtained for a wide range of governing parameters, such as the surface velocity parameter p, the wall temperature exponent n, the surface heat flux exponent m, the buoyancy force parameters (ξ for the VWT case and χ for the VHF case), and Prandtl number of the fluid. It is found
that the local Nusselt number is increased with increasing the velocity exponent parameter p for the VWT case, while the opposite trend is observed for the VHF case. The local friction coefficient is increased for
a decelerated stretching surface, while it is decreased for an accelerated stretching surface. Also, appreciable effects of
the buoyancy force on the local Nusselt number and the local friction coefficient are observed for both VWT and VHF cases,
as expected.
Received on 11 January 1999 相似文献
4.
C.-H. Chen 《Heat and Mass Transfer》1998,33(5-6):471-476
The analysis of laminar mixed convection in boundary layers adjacent to a vertical, continuously stretching sheet has been
presented. The velocity and temperature of the sheet were assumed to vary in a power-law form, that is, u
w
(x)=Bx
m
and T
w
(x)−T
∞=Ax
n
. In the presence of buoyancy force effects, similarity solutions were reported for the following two cases: (a) n=0 and m=0.5, which corresponds to an isothermal sheet moving with a velocity of the form u
w
=Bx
0.5 and (b) n=1 and m=1, which corresponds to a continuous, linearly stretching sheet with a linear surface temperature distribution, i.e. T
w
−T
∞=Ax. Formulation of the present problem shows that the heat transfer characteristics depends on four governing parameters, namely,
the velocity exponent parameter m, the temperature exponent parameter n, the buoyancy force parameter G
*, and Prandtl number of the fluid. Numerical solutions were generated from a finite difference method. Results for the local
Nusselt number, the local friction coefficient, and temperature profiles are presented for different governing parameters.
Effects of buoyancy force and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.
Received on 17 July 1997 相似文献
5.
A continuous surface stretched with velocity u
w=u
w (x) and having the temperature distribution T
w=T
w (x) interacts with the viscous fluid in which it is immersed both mechanically and thermally. The thermal interaction is characterized by the surface heat flux q
w=q
w (x) and the mechanical one by the skin friction τ w=τ w (x). In the whole previous theoretical research concerned with such processes, either (u
w and T
w) or (u
w and q
w) have been prescribed as known boundary conditions. The goal of the present paper is to initiate the investigation of the boundary layer flows induced by stretching processes for which either (τ w and T
w ) or (τ w and q
w) are the prescribed quantities. The case of an isothermal surface stretched with constant skin friction, (τ w=const., T
w=const. ≠ T
∞) is worked out in detail. The corresponding flow and heat transfer characteristics are compared to those obtained for the (well known) case of a uniformly moving isothermal surface (u
w=const., T
w=const. ≠ T
∞). 相似文献
6.
Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet
Kai-Long Hsiao 《Heat and Mass Transfer》2010,46(4):413-419
In this study, an analysis has been performed for heat and mass transfer with radiation effect of a steady laminar boundary-layer
flow of a micropolar flow past a nonlinearly stretching sheet. Parameters n, K, k
0, Pr, Ec, and Sc represent the dominance of the nonlinearly effect, material effect, radiation effect, heat and mass transfer effects which
have presented in governing equations, respectively. The similar transformation, the finite-difference method and Runge–Kutta
method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature
profiles, the wall unknown values of θ′(0) and ϕ′(0) for calculating the heat and mass transfer of the similar boundary-layer flow are carried out as functions of n, Ec, k
0, Pr, Sc. The value of n, k
0, Pr and Sc parameters are important factors in this study. It will produce greater heat transfer efficiency with a larger value of those
parameters, but the viscous dissipation parameter Ec and material parameter K may reduce the heat transfer efficiency. On the other hand, for mass transfer, the value of Sc parameter is important factor in this study. It will produce greater heat transfer efficiency with a larger value of Sc. 相似文献
7.
Radiation-conduction interaction on mixed convection from a horizontal circular cylinder 总被引:1,自引:0,他引:1
A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been
studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary
layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained
employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number,
R
w the surface temperature parameter, θw and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well
as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of
R
d,θw or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the
stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters
on the formation of the flow separation are studied.
Received on 28 July 1998 相似文献
8.
The effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature
dependent viscosity past a wedge with uniform surface heat flux is considered. The governing equations for the flow are obtained
by using suitable transformations and are solved by using an implicit finite difference method. Perturbation solutions are
also obtained near the leading edge and in the downstream regime. The results are obtained in terms of the local skin friction
coefficient and the rate of heat transfer for various values of the pertinent parameters, such as the Prandtl number, Pr,
the velocity gradient parameter, m, the local suction parameter, ξ, and the viscosity variation parameter, ɛ. Perturbation solutions are compared with the finite
difference solutions and are found to be in excellent agreement. The effect of ξ, m and ɛ on the dimensionless velocity profiles and viscosity distribution are also presented graphically for Pr = 0.7 and 7.0,
which are the appropriate values for gases and water respectively.
Received on 22 July 1999 相似文献
9.
M. A. A. Mahmoud A. M. Megahed 《Journal of Applied Mechanics and Technical Physics》2009,50(5):819-825
The problem of boundary-layer flow and heat transfer of a non-Newtonian power-law fluid over a moving porous infinite flat
plate in the presence of viscous dissipation and heat generation or absorption is investigated analytically. It is assumed
that both the momentum and the energy equations are coupled by the stress friction factor, and an assumption is introduced
regarding the heat-transfer index. It is found that exact analytical solutions for velocity and temperature exist only for
pseudoplastic fluids in the presence of suction at the surface. The effects of the suction parameter, Eckert number, and the
heat generation or absorption parameter on the velocity and temperature profiles, as well as on the skin-friction coefficient
and Nusselt number are discussed. 相似文献
10.
The problem of the self-similar boundary flow of a “Darcy-Boussinesq fluid” on a vertical plate with temperature distribution
T
w(x) = T
∞+A·x
λ and lateral mass flux v
w(x) = a·x
(λ−1)/2, embedded in a saturated porous medium is revisited. For the parameter values λ = 1,−1/3 and −1/2 exact analytic solutions
are written down and the characteristics of the corresponding boundary layers are discussed as functions of the suction/ injection
parameter in detail. The results are compared with the numerical findings of previous authors.
Received on 8 March 1999 相似文献
11.
I-Chung Liu 《Transport in Porous Media》2006,64(3):375-392
The present paper deals with the flow and heat transfer of a viscous fluid saturated in a porous medium past a permeable and
non-isothermal stretching sheet with internal heat generation or absorption and radiation. Closed-form solutions to steady,
two dimensional momentum equations with neglecting quadratic inertia terms and heat transfer equation are found using a similarity
transformation. Asymptotic expressions of the temperature functions are also presented valid for both very large and very
small modified Prandtl numbers. Attention is focused on the effects of porous parameter K, suction parameter R, radiation parameter Nr, viscosity ratio Λ, internal heat parameter α and Prandtl number P to the characteristics of flow and heat transfer. 相似文献
12.
The quasi-parallel regime of a Darcy–Boussinesq boundary-layer flow over a permeable vertical flat plate adjacent to a fluid saturated porous medium is considered. Quasi-parallel means here a plane flow with a constant transversal velocity v=–v
0 directed perpendicularly towards the vertical surface, where a lateral suction with the same velocity –v
0 is applied. The plate is held at a constant temperature T
w which coincides with the ambient temperature T
of the fluid. The heat released by viscous dissipation induces a density gradient in the fluid. Thus, although T
w=T
, a thermal convection occurs. The steady regime of this self-sustaining buoyant flow has been examined in detail. Wall jet-like profiles with a continuous but finite spectrum of the momentum flow have been found. These self-sustaining buoyant jets show a universal behavior, that is, there exist certain length, velocity and temperature scales such that the flow characteristics become independent of the (constant) material properties of the fluid and the porous medium as well. 相似文献
13.
Flow and heat transfer from a continuous surface in a parallel free stream of viscoelastic second-order fluid 总被引:2,自引:0,他引:2
I. A. Hassanien 《Applied Scientific Research》1992,49(4):335-344
Boundary layer solutions are presented to investigate the steady flow and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of viscoelastic fluid. Numerical results are presented for the distribution of velocity and temperature profiles within the boundary layer. The effects of the viscoelastic parameter of the fluid on the shear stress at the wall and rate of heat transfer are studied. For the same Reynolds (based on the larger of the free stream and wall velocities) and Prandtl numbers and the same velocity difference |U
w
>|, larger skin-friction and heat transfer coefficient result for U
w
> than for U
w
<. 相似文献
14.
The momentum and heat transfer characteristics associated with the boundary layer on a continuous moving flat surface in a non-Darcian fluid have been investigated exploiting a local similarity solution procedure. The full boundary layer equations, which describe the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables, deduced from a scale analysis on the momentum and energy conservation equations. Details are provided for the effects of convective inertia and porous inertia on the velocity and temperature profiles. The resulting friction and heat transfer characteristics are found to be substantially different from those of forces convection over a stationary flat plate. Furthermore, useful asymptotic expressions for the local Nusselt number are presented in consideration of possible physical limiting conditions. 相似文献
15.
The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal
and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are
included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u
w/(u
w + u
∞), where u
w and u
∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1
it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have
been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation
technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution.
For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase
with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and
the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction
decreases as the relative velocity between the surface and free stream decreases.
Received on 17 May 1999 相似文献
16.
K. Vajravelu K. V. Prasad Robert A. Van Gorder Jinho Lee 《Transport in Porous Media》2011,90(3):977-992
Numerical solutions for the free convection heat transfer in a viscous fluid at a permeable surface embedded in a saturated
porous medium, in the presence of viscous dissipation with temperature-dependent variable fluid properties, are obtained.
The governing equations for the problem are derived using the Darcy model and the Boussinesq approximation (with nonlinear
density temperature variation in the buoyancy force term). The coupled non-linearities arising from the temperature-dependent
density, viscosity, thermal conductivity, and viscous dissipation are included. The partial differential equations of the
model are reduced to ordinary differential equations by a similarity transformation and the resulting coupled, nonlinear ordinary
differential equations are solved numerically by a second order finite difference scheme for several sets of values of the
parameters. Also, asymptotic results are obtained for large values of | f
w|. Moreover, the numerical results for the velocity, the temperature, and the wall-temperature gradient are presented through
graphs and tables, and are discussed. It is observed that by increasing the fluid variable viscosity parameter, one could
reduce the velocity and thermal boundary layer thickness. However, quite the opposite is true with the non-linear density
temperature variation parameter. 相似文献
17.
Rafael Cortell 《Meccanica》2012,47(3):769-781
An analysis is presented for the steady non-linear viscous flow of an incompressible viscous fluid over a horizontal surface
of variable temperature with a power-law velocity under the influences of suction/blowing, viscous dissipation and thermal
radiation. Numerical results are illustrated by means of tables and graphs. The governing partial differential equations are
converted into nonlinear ordinary differential equations by a similarity transformation. The effects of the stretching parameter
n, suction/blowing parameter b, Prandtl number σ, Eckert number Ec(Ec * )E_{c}(E_{c}^{ *} ) and radiation parameter N
R
are discussed. Two cases are studied, namely, (i) Prescribed surface temperature (PST case) and, (ii) Prescribed heat flux
at the sheet (PHF case). 相似文献
18.
Mohamed Abd El-Aziz 《Meccanica》2007,42(4):375-386
An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting
fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into
account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The
resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then
solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting
method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic
parameter M, the viscosity/temperature parameter θ
r
, the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number,
and the local Sherwood number are presented graphically and in tabulated form. 相似文献
19.
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
20.
The computational study of the combined effects of radiation and hydromagnetics on the natural convection flow of a viscous,incompressible,and electrically conducting fluid past a magnetized permeable vertical plate is presented.The governing non-similar equations are numerically solved by using a finite difference method for all values of the suction parameter ξ and the asymptotic solution for small and large values of ξ.The effects of varying the Prandtl number P r,the magnetic Prandtl number P r m,the magnetic force parameter S,the radiation parameter R d,and the surface temperature θ w on the coefficients of the skin friction,the rate of heat transfer,and the current density are shown graphically and in tables.An attempt is made to examine the effects of the above mentioned physical parameters on the velocity profile,the temperature distribution,and the transverse component of the magnetic field. 相似文献