Page 390 - Modelling in Transport Phenomena A Conceptual Approach

370 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

The use of Eq. (9.3-55) in Eq. (9.3-53) yields
dT 4h(Tw-T)
-- - (9.3-56)
aZ D(VZ)PCP
Substitution of Eq. (9.3-56) into Eq. (9.3-39) gives

In terms of the dimensionless variables defined by Eqs. (9.3-44) and (9.3-45), Eq.
(9.3-57) becomes

(9.3-58)
The boundary conditions associated with Eq. (9.3-58) are

(9.3-59)

at <=1 8=1 (9.3-60)
Note that the use of the substitution
u=i-e (9.3-61)
reduces Eqs. (9.3-58)-(9.3-61) to

<4 z
-2N~(l--<~)u=-- (IdU) (9.3-62)
d< -'
du
at 5=0 -- (9.3-63)
at <=1 u=O (9.3-64)
Equation (9.3-62) can be solved for Nu by the method of Stodola and Vianello as
explained in Section B.3.4.1 in Appendix B.
A reasonable first guess for u which satisfies the boundary conditions is

u1=l-E 2
(9.3-65)
Substitution of Eq. (9.3-65) into the left-side of Eq. (9.3-62) gives

f 62) =-2Nu(E-2t3+t5) (9.3-66)

The solution of Eq. (9.3-66) is

(11 - 18t2 +9J4 - 2E6
U=NU (9.3-67)
36
f 1 (E)