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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.
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
3.
Peter Takáč 《Journal of Dynamics and Differential Equations》2006,18(3):693-765
We are concerned with the existence of a weak solution
to the degenerate quasi-linear Dirichlet boundary value problem
It is assumed that 1 < p < ∞, p ≠ 2, Ω is a bounded domain in
is a given function, and λ stands for the (real) spectral parameter near the first (smallest) eigenvalue λ1 of the positive p-Laplacian − Δ
p
, where
. Eigenvalue λ1 being simple, let φ1 denote the eigenfunction associated with it. We show the existence of a solution for problem (P) when f “nearly” satisfies the orthogonality condition ∫Ω
f φ1 dx = 0 and λ ≤ λ1 + δ (with δ > 0 small enough). Moreover, we obtain at least three distinct solutions if either p < 2 and λ1 − δ ≤ λ < λ1, or else p > 2 and λ1 < λ ≤ λ1 + δ. The proofs use a minimax principle for the corresponding energy functional performed in the orthogonal decomposition
induced by the inner product in L
2(Ω). First, the global minimum is taken over
, and then either a local minimum or a local maximum over lin {φ1}. If the latter is a local minimum, the local minimizer in
thus obtained provides a solution to problem (P). On the other hand, if it is a local maximum, one gets only a pair of sub- and supersolutions to problem (P), which is then used to obtain a solution by a topological degree argument. 相似文献
4.
Adrien Blanchet Matteo Bonforte Jean Dolbeault Gabriele Grillo Juan Luis Vázquez 《Archive for Rational Mechanics and Analysis》2009,191(2):347-385
We consider non-negative solutions of the fast diffusion equation u
t
= Δ
u
m
with m ∈ (0, 1) in the Euclidean space , d ≧ 3, and study the asymptotic behavior of a natural class of solutions in the limit corresponding to t → ∞ for m ≧ m
c
= (d − 2)/d, or as t approaches the extinction time when m < m
c
. For a class of initial data, we prove that the solution converges with a polynomial rate to a self-similar solution, for
t large enough if m ≧ m
c
, or close enough to the extinction time if m < m
c
. Such results are new in the range m ≦ m
c
where previous approaches fail. In the range m
c
< m < 1, we improve on known results. 相似文献
5.
The steady boundary-layer flow near the stagnation point on an impermeable vertical surface with slip that is embedded in
a fluid-saturated porous medium is investigated. Using appropriate similarity variables, 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 Darcy–Brinkman,
Γ, mixed convection, λ, and slip, γ, parameters, are analysed and discussed in detail for the cases of assisting and opposing
flows. It is found that dual solutions exist for assisting flows, as well as those usually reported in the literature for
opposing flows. A stability analysis of the steady flow solutions encountered for different values of the mixed convection
parameter λ is performed using a linear temporal stability analysis. This analysis reveals that for γ = 0 (slip absent)
and Γ = 1 the lower solution branch is unstable while the upper solution branch is stable. 相似文献
6.
A linear stability analysis is used to study the conditions marking the onset of secondary flow in the form of longitudinal
vortices for plane Poiseuille flow of water in the thermal entrance region of a horizontal parallel-plate channel by a numerical
method. The water temperature range under consideration is 0∼30°C and the maximum density effect at 4°C is of primary interest.
The basic flow solution for temperature includes axial heat conduction effect and the entrance temperature is taken to be
uniform at far upstream location jackie=−∞ to allow for the upstream heat penetration through thermal entrance jackie=0. Numerical results for critical Rayleigh number are obtained for Peclet numbers 1, 10, 50 and thermal condition parameters
(λ
1, λ
2) in the range of −2.0≤λ
1≤−0.5 and −1.0≤λ
2≤1.4. The analysis is motivated by a desire to determine the free convection effect on freezing or thawing in channel flow
of water. 相似文献
7.
Nicolae Tarfulea 《应用数学和力学(英文版)》2000,21(3):283-290
IntroductionInthispaper,weconsidertheellipticsystem(1λ) -Δu=f(λ,x,u)-v (inΩ),-Δv=δu-γv(inΩ),u=v=0(onΩ),whereΩisasmoothboundeddomaininRN(N≥2)andλisarealparameter.Thesolutions(u,v)ofthissystemrepresentsteadystatesolutionsofreactiondiffusionsystemsderivedfromseveralap… 相似文献
8.
In the present study we have explored the effects of thermal buoyancy on flow of a viscoelastic second grade fluid past a
vertical, continuous stretching sheet of which the velocity and temperature distributions are assumed to vary according to
a power-law form. The governing differential equations are transformed into dimensionless form using appropriate transformations
and then solved numerically. The methods here employed are (1) the perturbation method together with the Shanks transformation,
(2) the local non-similarity method with second level of truncation and (3) the implicit finite difference method for values
of ξ ( = Gr
x
/Re
x
2, defined as local mixed convection parameter) ranging in [0, 10]. The comparison between the solutions obtained by the aforementioned
methods found in excellent agreement. Effects of the elasticity parameter λ on the skin-friction and heat transfer coefficients
have been shown graphically for the fluids having the values of the Prandtl number equal to 0.72, 7.03 and 15.0. Effects of
the viscoelastic parameter and the mixed convection parameter, ξ, on the temperature and velocity fields have also been studied.
We notice that with the increase in visco-elastic parameter λ, velocity decreases whereas temperature increases and that velocity
gradient is higher than that of temperature.
On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh. 相似文献
9.
Lin Yi-han 《应用数学和力学(英文版)》1993,14(11):1063-1070
The elastostatic solutions of semi-infinite orthotropic cantilevered strips with traction free edges and loading at infinity
are governed by the differential equation φ,xyxy+(2+δ0)φ,xyzzz+φ,zzzz with δ0>-4. Based on the work of [10] for δ0>0 case, this paper completes the case δ0=0 for isotropic materials and the case 0>δ0>-4 for orthotropic materials. The solutions of the above problems have important application in the properly formulated boundary
conditions of plate theories for prescribed displacement edge data. 相似文献
10.
Kenneth R. Meyer Patrick McSwiggen Xiaojie Hou 《Journal of Dynamics and Differential Equations》2010,22(3):367-380
The search for traveling wave solutions of a semilinear diffusion partial differential equation can be reduced to the search
for heteroclinic solutions of the ordinary differential equation ü − cu̇ + f(u) = 0, where c is a positive constant and f is a nonlinear function. A heteroclinic orbit is a solution u(t) such that u(t) → γ
1 as t → −∞ and u(t) → γ
2 as t → ∞ where γ
1, γ
2 are zeros of f. We study the existence of heteroclinic orbits under various assumptions on the nonlinear function f and their bifurcations as c is varied. Our arguments are geometric in nature and so we make only minimal smoothness assumptions. We only assume that
f is continuous and that the equation has a unique solution to the initial value problem. Under these weaker smoothness conditions
we reprove the classical result that for large c there is a unique positive heteroclinic orbit from 0 to 1 when f(0) = f(1) = 0 and f(u) > 0 for 0 < u < 1. When there are more zeros of f, there is the possibility of bifurcations of the heteroclinic orbit as c varies. We give a detailed analysis of the bifurcation of the heteroclinic orbits when f is zero at the five points −1 < −θ < 0 < θ < 1 and f is odd. The heteroclinic orbit that tends to 1 as t → ∞ starts at one of the three zeros, −θ, 0, θ as t → −∞. It hops back and forth among these three zeros an infinite number of times in a predictable sequence as c is varied. 相似文献
11.
Robert McKibbin 《Transport in Porous Media》1986,1(3):271-292
The theory describing the onset of convection in a homogeneous porous layer bounded above and below by isothermal surfaces
is extended to consider an upper boundary which is partly permeable. The general boundary condition p + λ ∂p/∂n = constant is applied at the top surface and the flow is investigated for various λ in the range 0 ⩽ λ < ∞. Estimates of the magnitude and horizontal distribution of the vertical mass and heat fluxes at the surface, the horizontally-averaged
heat flux (Nusselt number) and the fraction of the fluid which recirculates within the layer are found for slightly supercritical
conditions. Comparisons are made with the two limiting cases λ → ∞, where the surface is completely impermeable, and λ = 0, where the surface is at constant pressure. Also studied are the effects of anisotropy in permeability, ξ = K
H
/K
V
, and anisotropy is thermal conductivity, η = k
H
/k
V
, both parameters being ratios of horizontal to vertical quantities. Quantitative results are given for a wide variety of
the parameters λ, ξ and η. In the limit ξ/η → 0 there is no recirculation, all fluid being converted out of the top surface, while in the limit ξ/η → ∞ there is full recirculation. 相似文献
12.
In the frame of industrial risk and propulsive application, the detonability study of JP10–air mixtures was performed. The
simulation and measurements of detonation parameters were performed for THDCPD-exo/air mixtures at various initial pressure
(1 bar < P
0 < 3 bar) and equivalence ratio (0.8 < Φ < 1.6) in a heated tube (T
0 ~ 375 K). Numerical simulations of the detonation were performed with the STANJAN code and a detailed kinetic scheme of the
combustion of THDCPD. The experimental study deals with the measurements of detonation velocity and cell size λ. The measured
velocity is in a good agreement with the calculated theoretical values. The cell size measurements show a minimum value for
Φ ~ 1.2 at every level of initial pressure studied and the calculated induction length L
i corresponds to cell size value with a coefficient k = λ/L
i = 24 at P
0 = 1 bar. Based on the comparison between the results obtained during this study and those available in the literature on
the critical initiation energy E
c, critical tube diameter d
c and deflagration to detonation transition length L
DDT, we can conclude that the detonability of THDCPD–air mixtures corresponds to that of hydrocarbon–air mixtures.
This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006. 相似文献
This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006. 相似文献
13.
郭艾 《应用数学和力学(英文版)》1999,20(6):683-689
1ProblemsandMainResultsInthispaper,westudythenonlinearvibrationsofinfiniterodswithviscoelasticity.Theconstitutionlawoftherods... 相似文献
14.
Separating oscillating flows in an internal, adverse pressure gradient geometry are studied experimentally. Simultaneous velocity
and pressure measurements demonstrate that the minor losses associated with oscillating flow in an adverse pressure gradient
geometry can be smaller or larger than those for steady flow. Separation is found to begin high in the diffuser and propagate
downward. The flow is able to remain attached further into the diffuser with larger Reynolds numbers, small displacement amplitudes,
and smaller diffuser angles. The extent of separation grows with L
0/h. The minor losses grow with increasing displacement amplitude in the measured range 10 < L
0/h < 40. Losses decrease with increasing Re
δ in the measured range of 380 < Re
δ < 740. It is found that the losses increase with increasing diffuser angle over the measured range of 12° < θ < 30°. The
nondimensional acoustic power dissipation increases with Reynolds number in the measured range and decreases with displacement
amplitude. 相似文献
15.
When a nonhomogeneous solid is melting from below, convection may be induced in a thermally–unstable melt layer. In this study,
the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance
equations. The critical Darcy–Rayleigh numbers based on the melt-layer thickness, Ra
H,c, are found numerically for various conditions. For small superheats, the present predictions show that Ra
H,c is located between 27.1 and 4π
2 and it approaches the well-known results of the original Horton–Rogers–Lapwood problem. However, for high superheats, it
is dependent on the phase change rate λ and the relation of Ra
H,c λ = 25.89 is shown. 相似文献
16.
A closed-form model for the computation of temperature distribution in an infinitely extended isotropic body with a time-dependent
moving-heat sources is discussed. The temperature solutions are presented for the sources of the forms: (i) 01(t)=0
exp(−λt), (ii) 02(t) =0(t/t
*)exp(−λt), and 03(t)=0[1+a
cos(ωt)], where λ and ω are real parameters and t
* characterizes the limiting time. The reduced (or dimensionless) temperature solutions are presented in terms of the generalized
representation of an incomplete gamma function Γ(α,x;b) and its decomposition C
Γ and S
Γ. The solutions are presented for moving, -point, -line, and -plane heat sources. It is also demonstrated that the present
analysis covers the classical temperature solutions of a constant strength source under quasi-steady state situations.
Received on 13 June 1997 相似文献
17.
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
18.
Linear and nonlinear stability analyses were performed on a fluid layer with a concentration-based internal heat source. Clear
bimodal behaviour in the neutral curve (with stationary and oscillatory modes) is observed in the region of the onset of oscillatory
convection, which is a previously unobserved phenomenon in radiation-induced convection. The numerical results for the linear
instability analysis suggest a critical value γ
c
of γ, a measure for the strength of the internal heat source, for which oscillatory convection is inhibited when γ > γ
c
. Linear instability analyses on the effect of varying the ratio of the salt concentrations at the upper and lower boundaries
conclude that the ratio has a significant effect on the stability boundary. A nonlinear analysis using an energy approach
confirms that the linear theory describes the stability boundary most accurately when γ is such that the linear theory predicts the onset of mostly stationary convection. Nevertheless, the agreement between the
linear and nonlinear stability thresholds deteriorates for larger values of the solute Rayleigh number for any value of γ. 相似文献
19.
The Darcy Model with the Boussinesq approximation is used to study natural convection in a shallow porous layer, with variable
permeability, filled with a binary fluid. The permeability of the medium is assumed to vary exponentially with the depth of
the layer. The two horizontal walls of the cavity are subject to constant fluxes of heat and solute while the two vertical
ones are impermeable and adiabatic. The governing parameters for the problem are the thermal Rayleigh number, R
T, the Lewis number, Le, the buoyancy ratio, φ, the aspect ratio of the cavity, A, the normalized porosity, ε, the variable permeability constant, c, and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained
on the basis of the parallel flow approximation. The onset of supercritical convection, or subcritical, convection are predicted by the present theory. A linear stability analysis of the parallel flow model is conducted and the
critical Rayleigh number for the onset of Hopf’s bifurcation is predicted numerically. Numerical solutions of the full governing
equations are found to be in excellent agreement with the analytical predictions. 相似文献
20.
Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the
axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR
λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized
second-order structure functions show a continuous evolution withR
λ. In particular, the scaling exponentζ
v
, corresponding to the v structure function, continues to increase with R
λ in contrast to the nearly unchanged value of ζ
u
. The Kolmogorov constant for δu shows a smaller rate of increase with R
λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR
λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the
centreline of a fully developed channel flow.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献