Page 441 - Modelling in Transport Phenomena A Conceptual Approach
P. 441
PROBLEMS 421
where the dimensionless quantities are defined by
E=- 2
B
P0V2
Br = -
TO
d) Multiply Eq. (5) by 2(dO/d<) and integrate the resulting equation to get
E=*mdm
4
where C is an integration constant.
e) Note that 6 reaches a maximum value at lnC. Therefore, the plus sign must be
used in Eq. (10) when 0 5 8 5 1nC. On the other hand, the negative sign must
be used when 1nC 5 0 5 1. Show that the integration of Eq. (10) leads to
Solve Eq. (11) to obtain
8 = In { C sech2
- I)]}
C = cosh2 (E)
where C is the solution of
f) Substitute Eq. (12) into Eq. (4) and show that the velocity distribution is given
bv
For more detailed information on this problem, see Gavis and Laurence (1968).
