Page 490 - Modelling in Transport Phenomena A Conceptual Approach

470 CHAPTER IO. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.

Deen, W.M., 1998, Analysis of Transport Phenomena, Oxford University Press,
New York.

Middleman, S., 1998, An Introduction to Mass and Heat Transfer - Principles of
Analysis and Design, Wiley, New York.

Slattery, J.C., 1999, Advanced Transport Phenomena, Cambridge University Press,
Cambridge.

PROBLEMS

10.1 A spherical material of 15 cm in radius is initially at a uniform temperature
of 60°C. It is placed in a room where the temperature is 23°C. Estimate the
average heat transfer coefficient if it takes 42min for the center temperature to
reach 3OOC. Take k = 0.12 W/ m. K and a = 2.7 x m2/s.
(Answer: 6.5 W/ m2. K)

10.2 The fuel oil pipe that supplies the heating system of a house is laid 1 m below
the ground. Around a temperature of 2°C the viscosity of the fuel oil increases
to a point that pumping becomes almost impossible. When the air temperature
drops to -15"C, how long does it take to have problems in the heating system?
Assume that the initial ground temperature is 10°C and the physical properties
are: IC = 0.38W/m.K and Q =4 x 10-'m2/s
(Answer: 351.3 h)
10.3 Two semi-idinite solids A and B, initially at TA, and TB, with TA, > TB,,
are suddenly brought into contact at t = 0. The contact resistance between the
metals is negligible.
a) Equating the heat fluxes at the interface, show that the interface temperature,
Ti, is given by
Ti -TB, - &i kA
-
TA, - TB, &Z~A + &k~
b) Consider two slabs made of copper and wood which are at a temperature of
80°C. You want to check if they are hot by touching them with your finger.
Explain why you think the copper slab feels hotter. The physical properties are
given as follows:

k a
W/m.K m2/ s

Skin 0.3 1.5 x 10-7
Copper 401 117 x
Wood 0.15 1.2 x 10-7