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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)
 
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