Page 255 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 235

0 The surrounding fluid temperature varies periodically with time, i.e.,

Take A = 1°C and w = 87rh-l.

e) Now assume that the liquid temperature within the pump is uniform but dif-
ferent from the surrounding fluid temperature as a result of a finite rate of heat
transfer. If the temperature of the surrounding fluid changes as

where T, is the asymptotic temperature and I- is the time constant, show that the
fractional error in mass flow rate is given by

The terms f and (b are defined as

UA
(b=-
PVCP
where A is the surface area of the liquid being pumped, U is the overall heat
transfer coefficient, and Cp is the heat capacity of the pump liquid.
f) Show that the time, t*, at which the fractional error function f achieves its
maximum absolute value is given by
t* = -
ln(#/r>
4-7
This problem is studied in detail by Eubank et al. (1985).

7.24 A spherical salt, 5 cm in diameter, is suspended in a large, well-mixed tank
containing a pure solvent at 25 "C. If the percent decrease in the mass of the sphere
is found to be 5% in 12 minutes, calculate the average mass transfer coefficient.
The solubility of salt in the solvent is 180kg/m3 and the density of the salt is
2500 kg/ m3.
(Answer: 8.2 x m/ s)

7.25 The phosphorous content of lakes not only depends on the external loading
rate but also on the interactions between the sediments and the overlying waters.
The model shown in Figure 7.6 is proposed by Chapra and Canale (1991) in which