School of Engineering
ME304 Mechanical Measurements II
Experiment 5: Radial Heat Conduction
To measure temperature distribution for transient and steady-state 1-D heat conduction in a
cylindrical wall and to determine the thermal conductivity k of the disk material.
When the inner and outer surfaces of a thick walled cylinder are each at a different uniform
temperature, heat flows radially through the cylinder wall. The heat conduction in this case is
governed by Fourier’s law for one-dimensional radial flow:
Q = −kA(dT dR) = −2Rhk (dT dR) (here h is the cylinder height, or thickness)
The disk can be considered to be constructed as a series of successive layers in the wall. The heat
conducted across each layer must be constant if the flow is steady. But since the area to the
successive layers increases with radius, the temperature gradient must decrease with radius. This
leads to the following logarithmic temperature distribution along the radial direction:
Q ln (Ra Rb ) = −2hk (Ta − Tb )
where Ta is the temperature at any radius Ra and Tb is the temperature at any radius Rb. Note that the
equation is valid for any pair of radii within the radial domain. Thus, if two temperatures at two known
radial positions are measured, the thermal conductivity k of the material can be found as:
Q ln (Rb Ra ) − Q ln Rb − ln Ra
2h(Ta − Tb ) 2h
Tb − Ta
The radial specimen in the HT12 apparatus consists
of a disk with the inside radius R1 = 5 mm, the
outside radius R0 = 55 mm and thickness h = 3.2
mm. Six thermocouples are located at R1 = 5.7 mm,
R2 = 9.9 mm, R3 = 20.3 mm, R4 = 30.1 mm, R5 =
40.1 mm and R6 = 50.5 mm. The outer diameter of
the disk is cooled with water while electric heater is
located at the disc center.
The heat power
generated can be determined from:
Q = VI
where V is heater voltage, I is heater current.
HT10X Heat Transfer service Unit
HT12 Radial Heat Conduction Accessory
IFD3 interface device
Confirm that the six thermocouples on the HT12 unit are connected to the appropriate sockets
of the service unit, with the labels on the thermocouple leads (T1-T6) matching the labels on
Ensure that the cold water supply is connected to the inlet of the pressure regulating valve on
HT12 and that the flexible cooling water outlet tube is directed to a suitable drain.
Switch on the main power switch.
Turn on the cooling water and adjust the flow to 1.5 liters/min +/- 0.2 liters/min
Start the computer and bring the HT12 program on
Start data acquisition, recording all temperatures every 10 seconds
Set the heating power to 50% and record data for about 10 minutes
Record all temperatures by hand
Turn the heating power off and continue recording data for about 15 minutes
Stop data acquisition and save the data file
Re-start the software and repeat steps 4-8 for the heating power of 100%
Calculations and Results
Calculate the average heat power Q added by the
heater to the disc (use only data points when the heater
was on) for 50% and 100% power.
For each power setting, graph six curves: T1 through T6
as a function of time (two graphs, 6 curves each).
For each power setting, estimate the steady-state
temperature values T1 through T6 from the two graphs
of point 2 (total of 12 values).
Create a single log/linear plot of steady-state
temperature (deg C) on the linear vertical axis as a
function of radius (mm) on the logarithmic horizontal
axis. Plot data for each power setting and draw two
linear trend lines. The plot should be similar to the one
shown. Estimate uncertainties on temperatures and
radial positions and add them as error bars.
Using the trend line equations, estimate temperature To at the outer periphery of the disk (Ro =
55 mm) for 50% and 100% power setting.
Using the trend line equations (slopes, in particular) and manipulating the equations presented
in the Theory section, calculate the thermal conductivity of the disk material for 50% and 100%
power setting. Compare the two values with each other. Note: An alternative (not as good)
way to calculate k is to use temperature values at any two selected positions. Do not use two
Based on thermal conductivity values available in the literature, list most likely materials the
disk is made of.
1. Heat transfer unit HT10X manual, Armfiled Inc. Jackson, NJ 08527
2. Radial heat conduction HT12 manual, Armfiled Inc. Jackson, NJ 08527
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