Transport Phenomena
Homework # 1
Magister Program in Chemical Engineering
Universitas Gadjah Mada
Due date: November 7, 2018
1.
An underground pipe transport refrigerated liquid at -20 oC. The pipe diameter is 3 ft
and made of steel. The ground physical properties is given in the table below:
Material bulk density ()
:
1500 kg/m3
Heat capacity (Cp)
:
800 J/(kg.oC)
Heat conductivity (k)
:
0.5 W/(m. oC)
Heat transfer coefficient (h) between the
refrigerated liquid and the pipe surface
:
8000 W/(m2. oC)
An expert suggested that we do not need to put insulation on the pipe. The pipe is
buried about 5 meters under the soil surface. The pipe stretch between two industrial
complexes with a distance of 500 m. Check this suggestion using a quantitative
calculation and state clearly your assumption
2
A huge volcanic material in the form of a 2 m diameter sphere is slowly cooled and solidified
due to the contact with the surrounding air which is at 20 oC. The molten rock is comprised
mostly of molten silica with a melting point (Tm) of 650 oC. As part of a disaster mitigation team,
you are asked to study the cooling process of the molten rock. Due to the slow heat transfer
between the surface of the sphere and the air, you may assume that the Nusselt number is 2.
Heat transfer within the solidified rock can be modeled with a quasi steady state approach. You
can start your work by applying equation of change on the solidified part between Rm and Ro by
neglecting the transient part. Solved the resulted differential equation using the applicable
boundary condition. We may assume the molten part has a uniform temperature of Tm. The
freezing zone is moving closer to the center of the sphere as the time passes
a. By writing a heat balance that equate the amount of heat
released by the freezing along the freezing front equal to
heat released to the air from the sphere surface, obtain a
differential equation that describe the change of Rm with
time.
b. Estimate the surface temperature after 30 days of cooling
(literally it means also 30 days after the volcanic eruption).
c. Estimate Rm 30 days of cooling.
Estimated physical and thermal properties of the rock:
Latent heat of freezing () = 400 J/g, thermal conductivity of the
solid rock : 3.5 W/(m.K), density of the molten rock (s) = 3
g/cm3
Thermal conductivity of air: 0.024 W/(m.K)
3.
Saturated steam in the amount of 600 ton/hr with a pressure of 100 bars is transported through
a 1 ft inside diameter pipe. The pipe is stretched along a distance of 100 m. The pipe is made of
steel with wall thickness of 2.5 cm. For the purpose of energy conservation as well as for safety
reason, the pipe is insulated with an insulation material which has thermal conductivity of 0.04
W/(m.K). The surrounding air has a temperature of 35 oC. Heat transfer coefficient between pipe
surface and the air is about 100 W/(m2.K). Since the heat transfer coefficient between saturated
steam and the pipe’s inner wall is very high, its heat resistance can be neglected.
a. Recommend the suitable thickness of the insulation for the pipe to minimize the steam
condensation no more than 0.01 % of the total steam load.
b. What is the surface temperature if the insulation thickness is according to your
recommendation in part a? Is it safe if by accident an employee touches the surface of
the insulation?
You may find additional necessary data from the literatures.
Melting rock
Solidified rock
Rm
Ro
