共查询到20条相似文献,搜索用时 328 毫秒
1.
H. Watanabe Tomohiro Sato Motoyuki Hirose Kunihiro Osaki Ming-Long Yao 《Rheologica Acta》1998,37(6):519-527
Dielectric relaxation behavior was examined for 4-4′-n-pentyl-cyanobiphenyl (5CB) and 4-4′-n-heptyl-cyanobiphenyl (7CB) under flow. In quiescent states at all temperatures examined, both 5CB and 7CB exhibited dispersions
in their complex dielectric constant ε*(ω) at characteristic frequencies ω
c
above 106 rad s–1. This dispersion reflected orientational fluctuation of individual 5CB and 7CB molecules having large dipoles parallel to
their principal axis (in the direction of C≡N bond). In the isotropic state at high temperatures, these molecules exhibited no detectable changes of ε*(ω) under flow at
shear rates . In contrast, in the nematic state at lower temperatures the terminal relaxation intensity of ε*(ω) as well as the static
dielectric constant ε′(0) decreased under flow at . This rheo-dielectric change was discussed in relation to the flow effects on the nematic texture (director distribution)
and anisotropy in motion of individual molecules with respect to the director.
Received: 14 April 1998 Accepted: 29 July 1998 相似文献
2.
A numerical investigation of the steady-state, laminar, axi-symmetric, mixed convection heat transfer in the annulus between
two concentric vertical cylinders using porous inserts is carried out. The inner cylinder is subjected to constant heat flux
and the outer cylinder is insulated. A finite volume code is used to numerically solve the sets of governing equations. The
Darcy–Brinkman–Forchheimer model along with Boussinesq approximation is used to solve the flow in the porous region. The Navier–Stokes
equation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on several flow
and geometric parameters is investigated. These include: convective parameter, λ, Darcy number, Da, thermal conductivity ratio,
K
r, and porous-insert thickness to gap ratio (H/D). It is found that, in general, the heat transfer enhances by the presence of porous layers of high thermal conductivity
ratios. It is also found that there is a critical thermal conductivity ratio on which if the values of Kr are higher than
the critical value the average Nusselt number starts to decrease. Also, it found that at low thermal conductivity ratio (K
r ≈ 1) and for all values of λ the porous material acts as thermal insulation. 相似文献
3.
Hiroshi Watanabe Tomohiro Sato Motoyuki Hirose Kunihiro Osaki Ming-Long Yao 《Rheologica Acta》1999,38(2):100-107
Rheo-dielectric behavior was examined for 4−4′−n-octyl-cyanobiphenyl (8CB) having large dipoles parallel to its principal axis (in the direction of the C≡N bond). In the
quiescent state at all temperatures (T) examined, orientational fluctuation of the 8CB molecules was observed as dielectric dispersions at characteristic frequencies
ωc>106 s−1. In the isotropic state at high T, no detectable changes of the complex dielectric constant ɛ*(ω) were found under slow flow at shear rates ˙γ≫ωc. In the nematic state at intermediate T, the terminal relaxation intensity of ɛ*(ω) was decreased under such slow flow. In the smectic state at lower T, the flow effect became much less significant. These results were related to the flow-induced changes of the liquid crystalline
textures in the nematic and smectic states, and the differences of the rheo-dielectric behavior in these states are discussed
in relation to a difference of the symmetry of molecular arrangements in the nematic and smectic textures.
Received: 1 October 1998 Accepted: 13 January 1999 相似文献
4.
M. P. Escudier A. Abdel-Hameed M. W. Johnson C. J. Sutcliffe 《Experiments in fluids》1998,25(5-6):491-502
Experimental results are reported for the response of an initially turbulent boundary layer (Re
θ≈1700) to a favourable pressure gradient with a peak value of K≡(−υ/ρU
3
E
) dp/dx equal to 4.4×10-6. In the near-wall region of the boundary layer (y/δ<0.1) the turbulence intensity u′ scales roughly with the free-stream velocity U
E
until close to the location where K is a maximum whereas in the outer region u′ remains essentially frozen. Once the pressure gradient is relaxed, the turbulence level increases throughout the boundary
layer until K falls to zero when the near wall u′ levels show a significant decrease. The intermittency γ is the clearest indicator of a fundamental change in the turbulence
structure: once K exceeds 3×10-6, the value of γ in the immediate vicinity of the wall γ
s
falls rapidly from unity, reaches zero at the location where K again falls below 3×10-6 and then rises back to unity. Although γ is practically zero throughout the boundary layer in the vicinity of γ
s
=0, the turbulence level remains high. The explanation for what appears to be a contradiction is that the turbulent frequencies
are too low to induce turbulent mixing. The mean velocity profile changes shape abruptly where K exceeds 3×10-6. Values for the skin friction coefficient, based upon hot-film measurements, peak at the same location as K and fall to a minimum close to the location where K drops back to zero.
Received: 28 January 1998/Accepted: 8 April 1998 相似文献
5.
The unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder is considered with combined buoyancy
force effects, for the situation in which the surface temperature T
′
w(x) and C
′
w(x) are subjected to the power-law surface heat and mass flux as K(T
′/r) = −ax
n
and D(C
′/r) = −bx
m
. The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results are
obtained for different values of Prandtl number, Schmidt number ‘n’ and ‘m’. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt and Sherwood numbers are
shown graphically. The local Nusselt and Sherwood number of the present study are compared with the available result and a
good agreement is found to exist.
Received on 7 July 1998 相似文献
6.
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
7.
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
8.
Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local
Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically
fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations
is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on
velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn),
Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio
(K
R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C
f
Re
*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer
number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or
K
R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases. 相似文献
9.
Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system
with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse
uniform magnetic field. A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow
rate distributions, for a wide range of the governing parameters. Asymptotic behavior of the solution is analyzed for large
M
2 (Hartmann number squared) and K
2 (rotation parameter). The heat transfer aspect is considered also with Joule and viscous heating effects present. Boundary
layers arise close to the channel walls for large K
2, i.e. strong rotation of the channel. For slowly rotating systems (small K
2), Hall current parameter (m) reduces primary mass flow rate (Q
x
/R
ρ
v). Heat transfer rate at the upper plate (d
θ/d
η)
η=1 decreases, while at the lower plate (d
θ/d
η)
η=−1 increases, with increase in either K
2 or m. For constant values of the rotation parameter, K
2, heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m. The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field
components to the control parameters is also studied graphically. Applications of the study arise in rotating MHD induction
machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing
systems, hybrid magnetic propulsion systems for space travel etc. 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.
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
12.
C. Tunç 《Nonlinear Oscillations》2006,9(4):536-551
We consider the equation X
(4) + Φ(X″)X‴ + F(X,X′)X″ + G(X′) + H(X) = P(t,X,X′,X″,X‴) in two cases: P ≡ 0 and P ≠ 0. In the case P ≡ 0, the asymptotic stability of the zero solution X = 0 of the equation is investigated; in the case P ≠ 0, the boundedness of all solutions of the equation is proved.
Published in Neliniini Kolyvannya, Vol. 9, No. 4, pp. 548–563, October–December, 2006. 相似文献
13.
The flow of fluids in heterogeneous porous media is modelled by regarding the hydraulic conductivity as a stationary random space function. The flow variables, the pressure head and velocity field are random functions as well and we are interested primarily in calculating their mean values. The latter had been intensively studied in the past for flows uniform in the average. It has been shown that the average Darcy's law, which relates the mean pressure head gradient to the mean velocity, is given by a local linear relationship. As a result, the mean head and velocity satisfy the local flow equations in a fictitious homogeneous medium of effective conductivity. However, recent analysis has shown that for nonuniform flows the effective Darcy's law is determined by a nonlocal relationship of a convolution type. Hence, the average flow equations for the mean head are expressed as a linear integro-differential operator. Due to the linearity of the problem, it is useful to derive the mean head distribution for a flow by a source of unit discharge. This distribution represents a fundamental solution of the average flow equations and is called the mean Green function G
d (x). The mean head G
d(x) is derived here at first order in the logconductivity variance for an arbitrary correlation function (x) and for any dimensionality d of the flow. It is obtained as a product of the solution G
d
(0)(x) for source flow in unbounded domain of the mean conductivity K
A and the correction
d
(x) which depends on the medium heterogeneous structure. The correction
d
is evaluated for a few cases of interest.Simple one-quadrature expressions of
d
are derived for isotropic two- and three-dimensional media. The quadratures can be calculated analytically after specifying (x) and closed form expressions are derived for exponential and Gaussian correlations. The flow toward a source in a three-dimensional heterogeneous medium of axisymmetric anisotropy is studied in detail by deriving 3 as function of the distance from the source x and of the azimuthal angle . Its dependence on x, on the particular (x) and on the anisotropy ratio is illustrated in the plane of isotropy (=0) and along the anisotropy axis ( = /2).The head factor k
* is defined as a ratio of the head in the homogeneous medium to the mean head, k
*=G
d
(0)/G
d=
d
–1. It is shown that for isotropic conductivity and for any dimensionality of the flow the medium behaves as a one-dimensional and as an effective one close and far from the source, respectively, that is, lim
x0
k
*(x) = K
H/K
A and lim
x
k
*(x) = K
efu/K
A, where K
A and K
H are the arithmetic and harmonic conductivity means and K
efu is the effective conductivity for uniform flow. For axisymmetric heterogeneity the far-distance limit depends on the direction. Thus, in the coordinate system of (x) principal directions the limit values of k
* are obtained as
. These values differ from the corresponding components
of the effective conductivities tensor for uniform flow for = 0 and /2, respectively. The results of the study are applied to solving the problem of the dipole well flow. The dependence of the mean head drop between the injection and production chambers on the anisotropy of the conductivity and the distance between the chambers is analyzed. 相似文献
14.
Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r
0/r
c
= 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to
competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different
transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating
conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced.
To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe.
Experiments are carried out for the Reynolds numbers range 420 ≤ Rest ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U
max,osc/U
m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters
8.37 < (α = r
0(ω/ν)0.5) < 24.5, where α2 is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional
average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing.
The effects of each parameter (Rest, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ
P
|/|ζ
S
|) and dimensionless transverse strain rates (|ε
P
|/|ε
S
|) during a complete oscillation period. 相似文献
15.
In the present case, the conjugate heat transfer involving a turbulent plane offset jet is considered. The bottom wall of
the solid block is maintained at an isothermal temperature higher than the jet inlet temperature. The parameters considered
are the offset ratio (OR), the conductivity ratio (K), the solid slab thickness (S) and the Prandtl number (Pr). The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then it becomes independent of the
Reynolds number. The ranges of parameters considered are: OR = 3, 7 and 11, K = 1–1,000, S = 1–10 and Pr = 0.01–100. High Reynolds number two-equation model (k–ε) has been used for turbulence modeling. Results for the solid–fluid interface temperature, local Nusselt number, local
heat flux, average Nusselt number and average heat transfer have been presented and discussed. 相似文献
16.
A. Salhi 《Theoretical and Computational Fluid Dynamics》2002,15(6):339-358
Linear theory is applied to examine rotation and buoyancy effects on homogeneous turbulent shear flows with given vertical
velocity shear, S=d/dx
3. In the rotating shear case (where the rotation vector is perpendicular to the plane of the mean flow, Ω
i
=Ωδ
i
2), general solutions for the Fourier components of the fluctuating velocity are proposed. These solutions are compared with
those proposed in the literature for the Fourier components of the fluctuating velocity and density in the case of a homogeneous
stratified shear flow with vertical density gradient, S
ρ=d/dx
3. It is shown that from the normal mode stability stand point the Bradshaw parameter B=2Ω/S(1+2Ω/S) (in the rotating shear case) and the Richardson number R
i
(in the statified shear case) play similar roles in identifying the stability for all the wave components except in the case
where Ω·k=0, for which rotation has no effects on the flow.
Analysis of the long-time behavior of the non-dimensional spectral density of energy, e
g
, is carried out. In the stable case, e
g
has decaying oscillations or undergoes a power law decay in time. Analytical solutions for the streamwise two-dimensional
energy ℰ
ii
1/2 (i.e. the limit at k
1=0 of the one-dimensional energy spectra) are proposed. At large time, ℰ
ii
1(t)/ℰ
ii
1(0) oscillates around the value (3R
i
+1)/(4R
i
) except at R
i
=1 it stays constant in time. Similar behavior for ℰ
ii
1(t)/ℰ
ii
1(0) is also observed in the rotating shear case (ℰ
ii
1(t)/ℰ
ii
1(0) oscillates around the value (1+4B)/(4B)).
Due to the behavior of the dimensionless spectral density of energy in both flow cases, the turbulent kinetic energy, /2, the production rate, ?, and the rate due to the buoyancy forces, ℬ, are split into two parts, , ?=?1+?2, ℬ=ℬ1+ℬ2 (in the stratified shear case, both ?1 and ℬ1 vanish when R
i
>?, while in the rotating shear case one has ℬ=0). It is shown that when rotation is “cyclonic” (i.e. Ω/S>0), part reaches maximum magnitudes at St
≈2, independent of the B value, and the first time to a zero crossing of ?2 occurs at this particular value. When rotation is “anticyclonic” (i.e. Ω/S<0) one finds St
≈1.6 instead of St
≈2. In the stratified shear case, both ?2 and ℬ2 cross zero at Nt=St
≈2, and part reaches maximum magnitudes at this particular value. These results and in particular those for the turbulent kinetic energy
are compared with previous direct numerical simulation (DNS) results in homogeneous stratified shear flows.
Received 30 July 2001 and accepted 19 February 2002 相似文献
17.
A fully developed laminar Poiseuille flow subject to constant heat flux across the wall is analysed with respect to its stability
behavior by applying a weakly nonlinear stability theory. It is based on an expansion of the disturbance control equations
with respect to a perturbation parameter ε. This parameter is the small initial amplitude of the fundamental wave. This fundamental
wave which is the solution of the linear (Orr-Sommerfeld) first order equation triggers all higher order effects with respect
to ε. Heat transfer is accounted for asymptotically through an expansion with respect to a small heat transfer parameter ε
T
. Both perturbation parameters, ε and ε
T
, are linked by the assumption ε
T
=O(ε2) by which a certain distinguished limit is assumed. The results for a fluid with temperature dependent viscosity show that
heat transfer effects in the nonlinear range continue to act in the same way as in the initial linear range.
Received on 11 August 1997 相似文献
18.
The optimal dimensions of convective-radiating circular fins with variable profile, heat-transfer coefficient and thermal
conductivity, as well as internal heat generation are obtained. A profile of the form y=(w/2) [1+(r
o/r)
n
] is studied, while variation of thermal conductivity is of the form k=k
o[1+ɛ((T−T
∞)/ (T
b−T
∞))
m
]. The heat-transfer coefficient is assumed to vary according to a power law with distance from the bore, expressed as h=K[(r−r
o)/(r
e−r
o)]λ. The results for λ=0 to λ=1.9, and −0.4≤ɛ≤0.4, have been expressed by suitable dimensionless parameters. A correlation for
the optimal dimensions of a constant and variable profile fins is presented in terms of reduced heat-transfer rate. It is
found that a (quadratic) hyperbolic circular fin with n=2 gives an optimum performance. The effect of radiation on the fin performance is found to be considerable for fins operating
at higher base temperatures, whereas the effect of variable thermal conductivity on the optimal dimensions is negligible for
the variable profile fin. It is also observed, in general, that the optimal fin length and the optimal fin base thickness
are greater when compared to constant fin thickness.
Received on 22 February 1999 相似文献
19.
Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries 总被引:3,自引:0,他引:3
This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - cm mass concentration of microcapsules - cp specific heat, kJ kg–1 K–1 - hfs phase change material heat of fusion, kJ kg–1 - hm* modified convective heat transfer coefficient, W m–2 K–1 - k thermal conductivity, W m–1 K–1 - ke effective thermal conductivity of slurry, W m–1 K–1 - kb slurry bulk thermal conductivity, W m–1 K–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - qwn wall heat flux, Wm–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r0 duct radius, m - r1 dimensionless radial coordinate - Ste Stefan number - T temperature, K - T1 lower phase change temperature limit, K - T2 upper phase change temperature limit, K - Ti slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x1 dimensionless axial coordinate - thermal diffusivity, m2/s - dimensionless temperature - dynamic viscosity, N·s/m2 - kinematic viscosity, m2/s - t width of thermal boundary, m - degree of heat transfer enhancement, = hm*/(hm*)single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid 相似文献
20.
We consider the three-dimensional flow through an aperture in a plane either with a prescribed flux or pressure drop condition.
We discuss the existence and uniqueness of solutions for small data in weighted spaces and derive their complete asymptotic
behaviour at infinity. Moreover, we show that each solution with a bounded Dirichlet integral, which has a certain weak additional
decay, behaves like O(r
−2) as r=|x|→∞ and admits a wide jet region. These investigations are based on the solvability properties of the linear Stokes system
in a half space ℝ
+
3
. To investigate the Stokes problem in ℝ
+
3
, we apply the Mellin transform technique and reduce the Stokes problem to the determination of the spectrum of the corresponding
invariant Stokes-Beltrami operator on the hemisphere. 相似文献