Page 148 - Modelling in Transport Phenomena A Conceptual Approach

128 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

in which N and R are defined as

N=

T'
To -
R=
2 sinh NL
a) Show that there is indeed no internal generation of energy within the fin.
b) Determine the location and the value of the minimum temperature within the
fin.
(Answer: z = 0.1 cm, T = 30.14"C)

4.7 Rework Example 4.8 by using the RamiMarshall correlation, Eq. (4.3-33),
the Frossling correlation, &. (4.3-34), and the modified F'rossling correlation, Eq.
(4.3-35). Why are the resulting Sherwood numbers differ significantly from the
value of 541?

4.8 In an experiment carried out at 20°C, a glass sphere of density 2620 kg/m3
falls through carbon tetrachloride (p = 1590 kg/ m3 and p = 9.58 x lod4 kg/ m. s)
with a terminal velocity of 65 cm/ s. Determine the diameter of the sphere.
(Answer: 21 mm)

4.9 A CO2 bubble is rising in a glass of beer 20cm tall. Estimate the time
required for a bubble of 5 mm in diameter to reach the top if the properties of C02
and beer can be taken as equal to that of air and water, respectively.
(Answer: 0.54 s)

4.10 Show that the use of the Dittus-Boelter correlation, Eq. (4.5-26), together
with the Chilton-Colburn analogy, Eq. (3.512), yields

f N 0.046
which is a good power-law approximation for the friction factor in smooth circular
pipes. Calculate f for Re = lo5, lo6 and lo7 using this approximate equation
and compare the values with the ones obtained by using the Chen correlation, Eq.
(4.516).
4.11 For laminar flow of an incompressible Newtonian fluid in a circular pipe,
Eq. (4.512) indicates that the pressure drop is proportional to the volumetric flow
rate. For fully turbulent flow show that the pressure drop in a pipe is proportional
to the square of the volumetric flow rate.

4.12 The purpose of the blood pressure in a human body is to push blood to
the tissues of the organism so that they can perform their function. Each time