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51.
In this paper the free convection flow through a thin rigid hot sheet moving horizontally out of a slot is considered. It is found that there is a similarity formulation of the boundary-layer equations so that the problem reduces to solving a system of coupled ordinary differential equations with suitable boundary conditions. This system of equations is solved numerically for various values of the Prandtl number,Pr, namely 0.45≤Pr≤10000. It is found that for the flow under the sheet there is a reverse flow region near the sheet for small values ofPr, whilst in the case of the flow above the sheet there is no reverse flow region for any value ofPr we have investigated. For the flow under the sheet an asymptotic behaviour, which is valid near the minimum value of the Prandtl number for which it is possible to obtain a numerical solution, is proposed. 相似文献
52.
Higher-order boundary-layer effects for natural convection flow along inclined flat plates (of both positive and negative inclinations) with a uniform heat flux surface condition in a saturated porous medium are studied. Using the method of matched asymptotic expansions the three terms in inner and outer expansions have been obtained. It is shown that the first eigenfunction for this considered problem coincides with 0(? 2)-term in the inner expansion. 相似文献
53.
The flow and heat transfer from a heated semi-infinite horizontal circular cylinder which is moving with a constant speed into a porous medium is considered. It is assumed that the Grashof and Reynolds numbers are large so that the governing equations are the three dimensional boundary-layer equations. A numerical procedure for solving these equations is described and the asymptotic solutions which are valid both near and distant from the leading edge of the cylinder are presented. The range of validity of these asymptotic solutions is discussed and the results are compared in detail with the full numerical solution. The problem is of practical importance, for example in the drilling of pipes into a geothermal reservoir.
Nomenclature a radius of cylinder - Gr Grashof number (=g(Tw-Ta/2) - g acceleration due to gravity - permeability in the porous medium - Nu local Nusselt number - total heat flux from cylinder - q w heat flux from cylinder - r radial co ordinate - Ra Rayleigh number (=g (Tw - Tt8) a/ ) - Re Reynolds number (=U t8 a/) - T temperature - u, v, w speeds inx, , r directions - x axial co ordinate - equivalent thermal diffusivity - thermal expansion coefficient - ratioGr/Re - similarity variable - dimensionless temperature (=(T- T)/(T w- T) - kinematic viscosity - azimuthal co ordinate - w cylinder surface - free stream 相似文献
Freie erzwungene Konvektion von einem beheizten schlanken horizontalen Zylinder, eingebettet in ein poröses Medium
Zusammenfassung Es wird die Strömung und der Wärmeübergang an einem beheizten, halbunendlichen horizontalen Kreiszylinder betrachtet, der mit konstanter Geschwindigkeit sich in ein poröses Medium bewegt. Dabei wird angenommen, daß die Grashof- und Reynolds-Zahlen groß sind, so daß die Bestimmungsgleichungen von den dreidimensionalen Grenzschichtgleichungen gebildet werden. Es wird ein numerisches Verfahren zur Lösung dieser Gleichungen beschrieben und eine asymptotische Lösung präsentiert, die sowohl in der Nähe als auch in großem Abstand von dem vorderen Ende des Zylinders gültig ist. Der Gültigkeitsbereich dieser asymptotischen Lösungen wird diskutiert und die Ergebnisse werden im Detail mit vollständigen numerischen Lösungen verglichen. Das Problem ist z.B. beim Eindringen von Rohrleitungen in geothermische Reservoire von praktischer Wichtigkeit.
Nomenclature a radius of cylinder - Gr Grashof number (=g(Tw-Ta/2) - g acceleration due to gravity - permeability in the porous medium - Nu local Nusselt number - total heat flux from cylinder - q w heat flux from cylinder - r radial co ordinate - Ra Rayleigh number (=g (Tw - Tt8) a/ ) - Re Reynolds number (=U t8 a/) - T temperature - u, v, w speeds inx, , r directions - x axial co ordinate - equivalent thermal diffusivity - thermal expansion coefficient - ratioGr/Re - similarity variable - dimensionless temperature (=(T- T)/(T w- T) - kinematic viscosity - azimuthal co ordinate - w cylinder surface - free stream 相似文献
54.
The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for timet<0 the plate is hotter than its surroundings and at timet=0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely
- an analytical solution which is valid for small time,
- an asymptotic analytical solution which is valid for large time, and
- a numerical solution which matches these two limiting analytical solutions.
55.
On natural convection from a vertical plate with a prescribed surface heat flux in porous media 总被引:1,自引:0,他引:1
This paper presents a theoretical and numerical investigation of the natural convection boundary-layer along a vertical surface, which is embedded in a porous medium, when the surface heat flux varies as (1 +x
2)), where is a constant andx is the distance along the surface. It is shown that for > -1/2 the solution develops from a similarity solution which is valid for small values ofx to one which is valid for large values ofx. However, when -1/2 no similarity solutions exist for large values ofx and it is found that there are two cases to consider, namely < -1/2 and = -1/2. The wall temperature and the velocity at large distances along the plate are determined for a range of values of .Notation
g
Gravitational acceleration
-
k
Thermal conductivity of the saturated porous medium
-
K
Permeability of the porous medium
-
l
Typical streamwise length
-
q
w
Uniform heat flux on the wall
- Ra
Rayleigh number, =gK(q
w
/k)l/(v)
-
T
Temperature
- Too
Temperature far from the plate
-
u, v
Components of seepage velocity in the x and y directions
-
x, y
Cartesian coordinates
-
Thermal diffusivity of the fluid saturated porous medium
-
The coefficient of thermal expansion
-
An undetermined constant
-
Porosity of the porous medium
-
Similarity variable, =y(1+x
)
/3/x
1/3
-
A preassigned constant
-
Kinematic viscosity
-
Nondimensional temperature, =(T – T
)Ra1/3
k/qw
-
Similarity variable, = =y(loge
x)1/3/x
2/3
-
Similarity variable, =y/x
2/3
-
Stream function 相似文献
56.
A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values 总被引:3,自引:0,他引:3
In this paper a unified mathematical theory for the viscous dissipation term in the governing Brinkman equation is derived. This term has, unlike other models, the correct asymptotic behaviour in both the fully Darcy and Newtonian fluid flow limits. 相似文献
57.
A Systems Approach towards an Intelligent and Self‐Controlling Platform for Integrated Continuous Reaction Sequences
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Richard J. Ingham Dr. Claudio Battilocchio Daniel E. Fitzpatrick Dr. Eric Sliwinski Dr. Joel M. Hawkins Prof. Steven V. Ley 《Angewandte Chemie (International ed. in English)》2015,54(1):144-148
Performing reactions in flow can offer major advantages over batch methods. However, laboratory flow chemistry processes are currently often limited to single steps or short sequences due to the complexity involved with operating a multi‐step process. Using new modular components for downstream processing, coupled with control technologies, more advanced multi‐step flow sequences can be realized. These tools are applied to the synthesis of 2‐aminoadamantane‐2‐carboxylic acid. A system comprising three chemistry steps and three workup steps was developed, having sufficient autonomy and self‐regulation to be managed by a single operator. 相似文献
58.
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
59.
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
60.