
Computer Simulations and Thermal Design 371
for the x -component of velocity and is shown in Figure 14.6. The integration of the
continuity over this control volume gives
()(),UUyV Vx
E
n
P
n
ne
n
se
n++ ++
−+−=
11 11
0∆∆
(14.66)
where
is given above and
UU
y
a
PP
E
n
E
n
EE
eee
++
=+ −
11*
(),
∆
ρ
′′
(14.67)
VV
x
a
PP
ne
n
ne
n
ne ne
e nne
++
=+ −
11*
(),
∆
ρ
′′
(14.68)
VV
x
a
PP
se
n
se
n
se se
sse e
++
=+ −
11*
().
∆
ρ
′′
(14.69)
Substituting these in the nite-difference form of the continuity equation, Equation
14.66, gives
(
**
)(
**
)
()
UUyV Vx
y
E
n
P
n
ne
n
se
n++ ++
−+−+
11 11
2
∆∆
∆
ρρ
ρρ
EE
eee
PP
we
ne
a
PP
y
a
PP
x
()
()
()
()
′′
′′
−
−−+
∆∆
22
aa
PP
x
a
PP
ne
e nne
se se
sse e
()
()
().′′ ′′−− −=
∆
2
0
ρ
(14.70)