... nonwetting phase can be larger than unity when
µ
r
> 1 (lubrication
effects). However, for gas and liquid two -phase flows,
µ
r
<< 1 and, consequently, the
second term in the right-hand-side ... because the geometry of the interfaces between
the fluids is unknown and one of the phases may be discontinuous. Fourar and
Lenormand [1998] assumed that the complexity of the real flow can be modeled, ... is accompanied by phase transformation effects. The interfacial mass flux enables
molecules in one phase to be transported to the other phase or to pass through the other
phase without forming...
... and Tadtmuller, 1987; Ulmer and Barnes,
1987; Byrappa and Yoshimura, 2001; Hefter and Tomkins,
2003). The purpose of this review is to summarize existing
experimental methods for studing phase ... obtaining informa-
tion on phase equilibria and on coexisting phase composi-
tions at high temperatures and pressures. These groups
comprise:
1. methods of visual observation of phase equilibria (‘Vis.
obs.’ ... ubiquitous, in the deep ocean and in the earth’s
crust, and of major importance in geology, geochemistry,
mining, and in industrial practices such as metallurgy and
the synthesis and growth of crystals.
The...
...
In Phase Equilibria and Fluid Properties in the Chemical Industry; Storvick, T., et al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1977.
12
PHASE
EQUILIBRIA
AND
... th e
In Phase Equilibria and Fluid Properties in the Chemical Industry; Storvick, T., et al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1977.
PHASE
EQUILIBRIA AND FLUID ... 1974)
In Phase Equilibria and Fluid Properties in the Chemical Industry; Storvick, T., et al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1977.
22
PHASE
EQUILIBRIA AND FLUID...
... applicable to
grain boundaries andphase interfaces.
The three new chapters are the results of long and intensive discussions and collabora-
tion withProfessorJohn Ågren andcould not have beenwritten ... like T, −P and −D.Itwas first introduced by Gibbs [3]
and is called chemical potential. Its close relation to G
m
will be explained in Section 4.1.
µ
i
and N
i
are conjugate variables and theterms ... C
P
is defined with T and
P as independent variables and we should thus use G,which has T and P as its natural
variables. The fundamental equation G = G(T,P)givesS =−(∂G/∂T )
P
and thus
H(T ,P) =...
... laser deposition and micromachining. Phase
explosion induced by laser heating will be briefly
described. The nucleation process and its time lag
in a superheated liquid leading to phase explosion ... than the threshold of
phase explosion shows that the time lag of nucleation
has prevented phase explosion to occur at an earlier
time when the laser fluence is increased; and this time
lag, according ... [11,12],
and phase explosion was explained as the ablation
mechanisms [13]. However, given the time lag much
longer than the pulsewidth, detailed studies are needed
to gain a thorough understanding...
... radiation and convection. The
TWO PHASE FLOW,
PHASE CHANGE AND
NUMERICAL MODELING
Edited by Amimul Ahsan
X Preface
ACKNOWLEDGEMENTS
All praise be to Almighty Allah, the Creator and ... gradient and the surface
movement speed in this (normal) direction:
Two Phase Flow, Phase Change and Numerical Modeling
6
()
oo
TM,t T(M), M D=∈
(8)
In time, successions the phases ... top a
uT/T,= and
1top
u(x,
y
,)τ is the heat
equation solution in according to phase 1.
If
top vap
[, )τ∈ τ τ both solid and liquid phases coexist in material, occupying
s
D()τ and
l
D( )τ...
... 703/15.01.2009, code 2291:
Two Phase Flow, Phase Change and Numerical Modeling
34
()
() ( )
rr r
in b
ou
PP P=−Δ (2b)
For single phase, subcooled liquid and superheated vapour, the Darcy-Weisbach ... 1 to 4 and corresponding heat transfer coefficients, internal pressure
drop and saturation temperature variations were obtained. Despite a substantial
Two Phase Flow, Phase Change and Numerical ... two tubes; the
coordinates I and K indicate the direction of flow: incoming and destination, respectively.
The values of J(I,K) are:
Two Phase Flow, Phase Change and Numerical Modeling
42
being...
...
and d
o
are, respectively, the inside and outside diameters of tubes
Two Phase Flow, Phase Change and Numerical Modeling
52
increasingly cold air flowing across the coil. In (Fig.19) and ... preliminary comparison of the simulated
and the experimental results are shown in Figure 6a and Figure 6b.
Two Phase Flow, Phase Change and Numerical Modeling
62
and refrigerant sides, in order ... data, defined as follows:
Two Phase Flow, Phase Change and Numerical Modeling
68
[m], k
m
is the thermal conductivity [W/mK], R
fi
and R
fo
are the tube-side and shell-side
fouling resistances...
... condensing and evaporating thin
films. The velocity, pressure, and temperature distributions in the vapor and liquid phases
are calculated. Various boundary conditions fixed to the FMHP evaporator and ... capillary limit and the evaporator boiling limit.
An improved model is suggested and it is compared with the simulation and experimental
Theoretical and Experimental Analysis of Flows and Heat Transfer ... a) T
sf
= 10 °C, b) T
sf
=20 °C, and c) T
sf
=
40 °C, and copper plate axial temperature profile for T
sf
= 40 °C (d)
Two Phase Flow, Phase Change and Numerical Modeling
102
system...
... and a temperature dependent term and can be related to
correspond to the latent heat of phase change. Furthermore, T is the temperature, and ρ, C
p
,
and k are the density, heat capacity, and ... axis and illustrated by straight line 4) throughout the caster.
Two Phase Flow, Phase Change and Numerical Modeling
124
what makes this purely computational study more intriguing and specific ... lines (1) and (2)
illustrate the centreline and surface temperatures of a 130 x 390 mm x mm Sovel slab; lines
(3) and (4) depict the shell thickness and the distance between the solidus and liquidus...
... lines (1) and (2)
illustrate the centreline and surface temperatures of a 130 x 390 mm x mm Sovel slab; lines
(3) and (4) depict the shell thickness and the distance between the solidus and liquidus ... this hinders the
attainment and maintenance of the plasma density and temperature on a required level and
forces to develop sophisticated and expansive methods to feed and heat up the plasma
components. ... selected in normal
Two Phase Flow, Phase Change and Numerical Modeling
168
In the limit cases,
τ
<<
τ
c
and
τ
c
<<
τ
we have
τ
0
≈
τ
c
and
τ
0
≈
τ
/ln(
τ
/
τ
c
),...
... azimuthal, (a) and ( b), and axial, (c) and (d), velocity profiles for S2
configuration. Q
≈ 100 l/h for (a) and (c); and Q ≈ 270 l/h for (b) and (d). The circles
indicate mean velocity values and the ... Γ
k
and Γ
ω
aretheeffectivediffusivityofk and ω, respectively; G
k
and G
ω
are the
generation of k and ω, respectively, due to mean velocity gradients; and Y
k
and Y
ω
are the
dissipation of k and ... et al., 2010, for recent results
184
Two Phase Flow, Phase Change and Numerical Modeling
Two Phase Flow, Phase Change and Numerical Modeling
194
and
zo
w(r) = w . (3)
Whereas there are...
... 10
13
K.s
−1
and τ = 1 ns.This
224
Two Phase Flow, Phase Change and Numerical Modeling
Two Phase Flow, Phase Change and Numerical Modeling
214
9. References
Aboelkassem, Y., Vatistas, G. H., and ... mechanisms
218
Two Phase Flow, Phase Change and Numerical Modeling
Recent Advances in Modeling Axisymmetric Swirl
and Applications for Enhanced Heat Transfer and Flow Mixing
203
Fig. 12. Impact of Re and ... it can be observed
228
Two Phase Flow, Phase Change and Numerical Modeling
Recent Advances in Modeling Axisymmetric Swirl
and Applications for Enhanced Heat Transfer and Flow Mixing
199
4....
... of KDP crystals, J. Crystal Growth 204, 4: 512.
238
Two Phase Flow, Phase Change and Numerical Modeling
Two Phase Flow, Phase Change and Numerical Modeling
254
Chen J.; Tzou D.& Beraun ...
Two Phase Flow
Two Phase Flow, Phase Change and Numerical Modeling
240
For pulsed laser ablation of metals, the ultrafast heating mechanisms perform great
disparity for femtosecond and ... to 400K and
350K at front surface and rear surface, respectively. With time, the electron and phonon
subsystems also would get the thermal equilibrium state, and if the united electron and
phonon...
...
Two Phase Flow, Phase Change and Numerical Modeling
272
All these delayed effects combine in single -phase pressure drop term and two -phase
pressure drop term acquiring 180° out-of -phase ...
Modelling equations are derived by the continuity of mass and energy for a single -phase
fluid and a two -phase fluid, respectively.
Single -phase flow equations read:
0
G
tz
ρ
∂∂
+=
∂∂
(6)
... single -phase region. The propagation of this perturbation in the
two -phase zone (via quality and void fraction perturbations) causes further lags in terms of
two -phase average velocity and exit...