Page 440 - Modelling in Transport Phenomena A Conceptual Approach

420 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

a) Obtain the temperature distribution as

b) Show that the Nusselt number for the upper and lower plates are the same and
equal to
2B(h) 35
Nu=-=-
k 2
in which the term 2B represents the hydraulic equivalent diameter.

9.12 Consider Couette flow of a Newtonian liquid between two large parallel
plates as shown in the figure below. As a result of the viscous dissipation, liquid
temperature varies in the x-direction. Although the thermal conductivity and
density of the liquid are assumed to be independent of temperature, the variation
of the liquid viscosity with temperature is given as

1

B

a) Show that the equations of motion and energy reduce to

d

dLT
k-+p(%) 2 =O
dx2
b) Integrate Eq. (1) and obtain the velocity distribution in the form
1' e

v=E
vz 0 P (4)
-

c) Substitute J3q. (4) into J3q. (3) to get
#e
-+Aee=O (5)
e2