Environmental Engineering Reference
In-Depth Information
and
D
M
0
At
0
Fig. 5.8
D
0
ε
Step 2.
Apply a constant initial temperature
K
on
D
O
ε
and start to record time. Math-
ematically, we consider
⎧
⎨
u
t
τ
0
+
A
2
R
2
u
tt
=
Δ
u
,
×
(
0
+
∞
)
,
K
D
O
,
(
,
)
∈
ε
,
x
y
⎩
u
(
x
,
y
,
0
)=
ϕ
(
x
,
y
)=
u
t
(
x
,
y
,
0
)=
0
.
D
O
0
,
(
x
,
y
)
∈
ε
,
Its solution reads
1
1
2
0
+
∂
t
e
−
u
(
x
,
y
,
t
)=
2
τ
0
A
(
t
)
K
(
ϕ
)
d
ξ
d
η
.
2
π
τ
∂
D
At
Step 3.
Observe the variation of temperature at point
M
0
and record the time instant
t
0
when there is a reading of temperature at point
M
0
(
u
(
0
,
y
0
,
t
0
)
=
0, no matter how
small).
)
t
0
by using
known
y
0
,
y
1
and
t
0
Th
is
comes from the fact that the characteristic cone surface
=(
−
Step 4.
Calculate the wave speed
A
y
0
y
1
(
x
−
x
0
)
2
+(
y
−
y
0
)
2
=
A
(
t
0
must cross the
y
-axis at point
M
1
(Fig. 5.8).
Once
A
is available, we can obtain
−
t
)
a
2
A
2
.
τ
0
by the definition of
A
as
τ
0
=
Search WWH ::
Custom Search