Page 396 - Modelling in Transport Phenomena A Conceptual Approach

376 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

Note that the term 2B in the definition of the Nusselt number represents the
hydraulic equivalent diameter for parallel plates. In dimensionless form Eq. (9.3-
93) becomes
2 (de/w€=o
Nu, = (9.3-94)
6b - 1
The use of Eq. (9.3-87) in Eq. (9.3-94) gives

(9.3-95)

Note that Nu, takes the following values depending on the value of Br :

0 Br=2
<O 2<Br<4 (9.3-96)
00 Br=4

When Br = 2, the temperature gradient at the lower plate is zero, i.e., adiabatic
surface. When 2 < Br < 4, as can be seen from Figure 9.13, temperature reaches a
maximum within the flow field. For example, for Br = 3, 0 reaches the maximum
value of 1.042 at [ = 0.167 and heat transfer takes place from the fluid to the lower
plate. When Br = 4, = 1 from Eq. (9.3-91) and, as a result of very high viscous
dissipation, Tb becomes uniform at the value of To. Since the driving force, Le.,
To - Tb, is zero, Nu, is undefined under these circumstances.

Calculation of the Nusselt number for the upper plate

The heat flux at the upper plate is

(9.3-97)

Therefore, the Nusselt number becomes

-_ 2 (de/dt),=l (9.3-98)
-
ob
Substitution of Eq. (9.3-87) into Eq. (9.3-98) gives

(9.3-99)