Geoscience Reference
In-Depth Information
where
r
1
a
2
r
2
D.r/
D
1
(3.202)
The
q
-profile found from Eq.
3.194
is then
1
C
T
T
1
1
D.r/
˛
2
q.r/
D
q
1
(3.203)
The density profile can also be found:
1
1
D.r/
˛
2
T
T
n.r/
D
n
1
(3.204)
It is important to notice that n.a/ found from Eq.
3.204
coincides with n
from
Eq.
3.195
.
The temperature at
r
D
a
differs from T
:
s
T
T
1
"
1
C
1
!#
˛
2
n
T.a/
D
n
1
T
1
(3.205)
The temperature jump at the particle surface is then
s
T
T
1
"
1
1
!#
T
T.a/
D
T
p
T
T
1
˛
2
(3.206)
3.7.3
Limiting Sphere
Now let the temperature at
r
D
R
be fixed. Then, to satisfy the boundary condition
of Eq.
3.20
, we should modify the distribution by introducing the multiplier C.R/
and replacing q
1
!
q
R
:
q.r/
D
q
R
C.R/
"
1
C
s
T
T
R
1
!
1
!#
r
1
˛
2
a
2
r
2
(3.207)
This step is possible because of the linearity and homogeneity of the boundary
conditions for
f
. From the condition q.R/
D
q
R
we have
s
T
"
1
C
T
R
1
!
1
!#
1
r
1
˛
2
a
2
R
2
C.R/
D
(3.208)