164
R i \ Mathur and N.S. Grewal
For the range of flow within the Darcy's range, which is so in the present case, the
molecular diffusion constant could be neglected and equation (i) could be written as:
3t
3z
3z
2
°
2 [ r
3 r
( r 3 r
) + r 3r J
From the best fit data of C V
x w e h a v e t h e relation of the form
s
C - C 0 = a 0 + a 1
t + a 2 t
2 +a 3 t
3 +a 4 t
4
where a 0 , ai, a 2 , a 3 and a 4 have been obtained from the analysis. From the above
equation we can obtain the value of |°— as Z and r are constants.
dt
Similarly, from the best fit data of C v Z
C - C 0 = b 0 + b 1 Z + b 2 Z
2 +b 3 Z
3 +b 4 Z
4
3c
we can determine ä^~f°
r t and r as constants
3c 1
3Γ]
Γ = Ι
3c_
3z
3
2 c
:
: const., Z const. = f (t) say
Similarly,
[ t const, r const. = f(Z)
t const, r const. = f'(Z)
By substituting the values we get
r [ f ( t ) + w f ( z ) + D I f ( z ) ] = D 2 [ | Γ ( 3 Γ )
+
| Γ ]
by integrating partially with respect to r we get
£ [ f ( t ) + w f ( z ) - D , f ' ( z ) ]
= D 2 [ g - + c J + L
where L is the constant of integration.
Integrating the above equation again with respect to r we have
f [f(t) + w f ( z ) - D 1 f ' ( z ) l
= D 2 f " c + C r l + L r + m
where m is another constant of integration
when
r
=
0 )
z
=
0 [
C = C 0
and
t
=
0 )
or
m
=
— C 0 D 2
Also when
r
=
°° )
Z
=
X |
C = 0
or
t
=
t' i
L = 0