CONDUCTION THROUGH
THICK-WALLED CYLINDERS
(RADIAL CONDUCTION)
ENGR. JETHON C. VILLARIAS
PROBLEM 1
A cylindrical cement tube of radii 0.05 cm and 1.0 cm has a
wire embedded into it along its axis. To maintain a steady
temperature difference of 120°C between the inner and
outer surfaces, a current of 5 ampere is made to flow in the
wire. Make calculations for the amount of heat generated
per meter length and the thermal conductivity of cement.
Take resistance of wire equal to 0.1 ohm per cm of length.
PROBLEM 2
A stainless steel pipe with a length of 35ft has an inner
diameter of 0.92 ft and an outer diameter of 1.08 ft. The
temperature of the inner surface of the pipe is 122 °F and
the temperature of the outer surface is 118 °F. The thermal
conductivity of the stainless steel is 108 Btu/hr-ft-°F.
Calculate the heat transfer rate through the pipe. Calculate
the heat flux at the outer surface of the pipe.
PROBLEM 3
A 10ft length of pipe with an inner radius
of 1 in and an outer radius of 1.25. It has
and outer surface temperature of 250°F.
The heat transfer rate is 30,000 Btu/hr.
Find the interior surface temperature
assuming k = 25 Btu / hr-ft-°F.
PROBLEM 4
A thick-walled nuclear coolant pipe (k = 12.5 Btu/hr-ft-°F)
with 10 in. inside diameter (ID) and 12 in. outside diameter
(OD) is covered with a 3 in. layer of asbestos insulation (k =
0.14 Btu/hr-ft-°F). If the inside wall temperature of the pipe
is maintained at 550°F, calculate the heat loss per foot of
length. The outside temperature is 100°F.
PROBLEM 5
A steam pipe 10 cm outside diameter is covered with two
layers of insulation, each having a thickness of 2.5 cm. The
average thermal conductivity of one material is 3 times that
of other and the surface temperatures of the insulated
steam pipe are fixed. Examine the position of a better
insulating layer relative to the steam pipe if heat dissipation
from steam is to be minimum. What % age saving in heat
dissipation results from that arrangement?
PROBLEM 6
Water at 50°C is flowing through a pipe (1.3 cm ID, thermal
conductivity of 2.4 W/m °K) at a rate of 0.5 kg/s. The walls
of the pipe are 0.6 cm thick, the pipe is 30 m long, and it
has a layer of insulation wrapped around it that is 0.7 cm
thick and has a thermal conductivity of 0.22 W/m °K. If the
temperature outside the pipe is 23°C, what is the rate of
heat transfer from the inner pipe wall to the outside of the
insulation layer?
PROBLEM 7
A hot-water pipe with an inner radius of 3 cm and an outer radius of
3.5 cm is wrapped with an insulation layer that is 5 cm thick. The
pipe wall is made of steel with a thermal conductivity of 50 W/m·K,
while the insulation has a thermal conductivity of 0.12 W/m·K. The
temperature at the inner wall of the pipe is maintained at 160 °C,
and the temperature at the outer surface of the insulation is
measured at 40 °C. Assuming steady-state conditions and
neglecting any heat losses by convection or radiation, determine the
temperature at the interface between the steel wall and the
insulation and the heat loss per meter length of pipe.
PROBLEM 8
A steam pipe with an inner diameter of 6 inches and an outer
diameter of 6.5 inches is covered with multiple layers of insulation.
The first layer is asbestos with a thickness of 1 inch and a thermal
conductivity of 0.10 Btu/hr·ft·°F. The second layer consists of
fiberglass insulation with a thermal conductivity of 0.025 Btu/hr·ft·°F,
but its thickness is not yet determined. The temperature at the inner
wall of the pipe is maintained at 400 °F, while the temperature at the
outermost surface of the fiberglass is found to be 90 °F. If the
allowable heat loss through the insulated pipe must not exceed
1500 Btu/hr per foot of pipe length, calculate the required thickness
of the fiberglass insulation layer.
