Page 342 - Modelling in Transport Phenomena A Conceptual Approach

322 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

8.3 A spherical tank containing liquid nitrogen at latm pressure is insulated
with a material having a thermal conductivity of 1.73 x W/ m. K. The inside
diameter of the tank is 60 cm, and the insulation thickness is 2.5 cm. Estimate the
kilograms of nitrogen vaporized per day if the outside surface of the insulation is
at 21 "C. The normal boiling point of nitrogen is -196 "C and its latent heat of
vaporization is 200 kJ/ kg.
(Answer: 7.95 kg/day)

8.4 For a rectangular fin of Section 8.2.4 the parameters are given as: T, =
175OC, T, = 260"C, k = 105W/m. K, L = 4cm, W = 30cm, B = 5mm.
a) Calculate the average heat transfer coefficient and the rate of heat loss through
the fin surface for A = 0.3,0.6,0.8,1.0,3.0,6.0, and 8.0.
b) One of your friends claims that as the fin efficiency increases, the process
becomes more reversible. Do you agree?

8.5 Show that the mass average velocity for the Stefan diffusion tube experiment,
Example 8.16, is given by
v, = MA ML DAB In (&)

where M is the molecular weight of the mixture. Note that this result leads to the
following interesting conclusions:
i) The mass average velocity is determined on the basis of a solution to a diffusion
problem rather than a conservation of momentum.
ii) No-slip boundary condition at the wall of the tube is violated.
For a more thorough analysis of the Stefan diffusion tube problem, see Whitaker
(1991).
8.6 Repeat the analysis given in Section 8.4.4 for a zero-order reaction in the
following way:
a) Show that the concentration distribution is given by

where