Page 74 - Introduction to Computational Fluid Dynamics

P1: IWV/ICD
CB908/Date
0 521 85326 5
0521853265c02
EXERCISES
5 cm 10 cm 2 cm May 25, 2005 10:49 53

T = 600 C T = 50 C
8 8
1 2 3
2
h = 5 W/m -K
2
h = 50 W/m -K

Figure 2.14. Composite slab.

but the fully developed velocity profile is determined from Exercise 19.
Also, k in Equation 2.80 is replaced by (k + k t ), where k t = C p µ t /Pr t . Cal-
culate the Nusselt number Nu for different Reynolds numbers at Prandtl
numbers Pr = 1, 10, and 100. Take Pr t = 0.85 + 0.039(Pr + 1)/Pr. Com-
pare your result with following correlations: (a) Nu 1 = 0.023 Re 0.8 Pr 0.4
m
n
and (b) Nu 2 = 5 + 0.015 Re Pr , where m = 0.88 − 0.24(4 + Pr) −1 and
n = 0.333 + 0.5exp(−0.6 Pr).
28. Consider laminar fully developed flow and heat transfer in a circular tube under
constant wall heat flux conditions. The fluid is highly viscous. Therefore, Equa-
2
tion 2.80 must be augmented to account for viscous dissipation µ(∂u/∂r) .
Calculate Nu and compare your result with Nu = 192/(44 + 192Br), where
2
the Brinkman number Br = µu /(q w D). In this problem, Equation 2.81 must
be modified as follows:
2
∂T dT b 2(q w + 4µu /R)
= = .
∂z dz ρ Cp uR
Explain why.

29. Repeat Problem 1 from the text using ψ = 0.3 and ψ = 0.7. Choose N = 7.
Determine the largest allowable time step using constraints (2.36) and (2.37).
Compare your solution for the time required for adhesion with the exact solution
determined in Exercise 2.

30. Consider fully developed laminar flow of a non-Newtonian fluid between two
parallel plates 2b apart. For such a fluid, the shear stress is given by

n−1

∂u ∂u
τ yx = µ ,
∂y ∂y