Page 87 - Modelling in Transport Phenomena A Conceptual Approach

68 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

transition takes place at x,, where 0 < x, < L, then the average friction factor is
given by
1
L
-k
(f) = $ [~zc(fz)tamd~ 1 (fz)turbdx (4.2-2)
zc
Change of variable from x to Re, reduces Eq. (4.2-2) to

where Re,, the Reynolds number at the point of transition, and ReL, the Reynolds
number based on the length of the plate, are defined by
Re, = - (4.2-4)
2, vC.2
U

L vC.2
hL=- (4.2-5)
U
Substitution of Eqs. (A) and (D) in Table 4.1 into Eq. (4.2-3) gives
0.074 1.328 - 0.074b2/5
(f) = 1/5 + (4.2-6)
Re, ReL
Taking Re, = 500,000 resdts in
0.074
1743
(f) = - - (4.2-7)
-
ReL
L
The average values of the friction factor, the Nusselt number and the Sherwood
number can be calculated in a similar way for a variety of flow conditions. The
results are given in Table 4.2. In these correlations all physical properties must be
evaluated at the film temperature.
Note that once the average values of the Nusselt and Sherwood numbers are
determined, the average values of the heat and mass transfer coefficients are cal-
culated from

(4.2-8)

(4.2-9)

On the other hand, the rate of momentum transfer, i.e., the drag force, the rate
of heat transfer and the rate of mass transfer of species A from one side of the
plate are calculated as
(4.2-10)