Page 392 - Modelling in Transport Phenomena A Conceptual Approach

372 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

a) Since the wall temperature is constant, from Eq. (9.3-26)
L=- DRePr In ( ~ ~ ~ ~ t )
~
4 Nu
- (0.05)(758)(4.32) 100 - 20
-
4 (3.66) (100 - 60) = 7*8m
b) For a constant heat flux at the wall, the use of Eq. (9.3-33) gives

- (60 - 20)(632 x 10-3)(758)(4.32)
- = 13.8111
4 (1500)

9.3.2 Viscous Heating in a Couette Flow
Viscous heating becomes an important problem during flow of liquids in lubrica-
tion, viscometry and extrusion. Let us consider Couette flow of a Newtonian fluid
between two large parallel plates as shown in Figure 9.12. The surfaces at 2 = 0
and 2 = B are maintained at To and TI, respectively, with To > TI.

xL -V

Figure 9.12 Couette flow with heat transfer.

Rate of energy generation per unit volume as a result of viscous dissipation is
given by3
2
(9.3-70)

3The origin of this term comes from -(T : Vv), which represents the irreversible degradation of
mechanical energy into thermal energy in the equation of energy. For a more detailed discussion
on the subject, see Bird et. 41. (1960).