Download CONDUCTION HEAT TRANSFER EXPERIMENT The purpose of

CONDUCTION HEAT TRANSFER EXPERIMENT
The purpose of this experiment is to determine the thermal conductivity of low k materials
through direct measurement.
INTRODUCTION AND BACKGROUND
The basis for analysis of conduction heat transfer situations is known as Fourier's Law Of Heat
Conduction. The “Law” which is so glibly pronounced as an obvious truth was submitted as part
of a 234 page paper by Joseph Fourier in 1807. The work was controversial, and it remained
unpublished until 1822. Compare this publication rate with that of any assistant professor today!
No tenure for Joseph. The empirical law that he stated is “The heat flux resulting from thermal
conduction is proportional to the magnitude of the temperature gradient and opposite to it in
sign”. Note that he did not state that heat flux is directly proportional to the first power of the
gradient: it is just proportional. This experiment is designed to measure the value of the
proportionality factor through knowledge of the heat flux, temperature difference, and the distance
of conduction.
APPARATUS
The apparatus is very straightforward and simple (Fig. 1). An electric heater, which is potted in
silicone, is used to heat an aluminum plate which has thermocouples set into it. A sample of
ordinary Balsa wood or a stack of paper, subsequently referred to as the Low Conductivity Material
(LCM), is placed on the plate and the LCM itself is covered with a second aluminum plate with
thermocouples. The following figures are for Balsa wood but are identical for paper. The
conductivity of the aluminum is high compared to the LCM, and thermal gradients should be
negligible. A thermocouple is also located in the geometric center of the sample. The LCM is
insulated on the 4 sides with microquartz insulation and on the bottom with Temperlite 1200.
Heater current and voltage are measured with digital multimeters, and power can be determined
by multiplication. A single thermocouple is used for ambient temperature. The following figures
show Balsa wood as the LCM.
Fig. 1 - Experimental Apparatus
Thermocouple placements are shown below in Figures 2 and 3.
Fig. 2 - Thermocouple locations as viewed from above. TC 8 is located in the geometric center of the wood block
Fig. 3 - Thermocouples located between the 2 layers of soft insulation as seen from above. Thermocouples are at the
same height as the center of the wood block.
Thermocouples are Type K chromel-alumel, 60 gauge. Typical variation in an isothermal
environment at room temperature is ±0.5°F. The heater is “Flexible Silicone Rubber Fiberglass
2
Insulated” from OMEGA Engineering. Model number SRFG-206 rated at 10 watts/in , but the
power limitation is due to the maximum temperature for silicone which is 450°F.
The insulation surrounding the sample and plates on the sides is microquartz and has a nominal
conductivity of 0.05 W/m°C. The insulation below the heater is Temperlite 1200° with a nominal
conductivity of 0.06 W/m°C at room temperature. It is a rigid, high temperature, water resistant
molded perlite thermal insulation available in many forms. It contains no asbestos. The top
aluminum plate is open to the ambient air except for a small ceramic disk which takes the 10 lb
compressive load.
Overall Dimensions
The apparatus is a square 12 x 12 inches and 6 inches high with ½ inch thick pressboard sides
and bottom giving outside dimensions of 13 x 13 x 6 1/2.. The Temperlite below the heater is 4
¼ inches thick. The aluminum plates are ¼ inch thick and the top plate is recessed ¼ inch (i.e.,
the microquartz insulation top surface is ¼ inch above that of the top aluminum plate). The
heater is of negligible thickness.
WHAT’S THE PROBLEM?
In this experiment we are estimating the thermal conductivity of the LCM. Balsa wood is used in
model building and as insulation for cryogenic systems. When the LCM is paper there is a
contact resistance between each layer that is a strong function of the pressure applied.
CONDITIONS
The apparatus will be set up and running with such that heat is conducted in the vertical
direction. For Balsa wood it is transverse to the grain. All you need to do is to record the data (20
temperatures and power). Each group should have at least 10 sets of data.
WHAT TO OBSERVE
 Each aluminum plate has 7 thermocouples. How uniform is the temperature of each
plate?
 Use the center thermocouple to determine the temperature gradient in the lower half and
the upper half. What can you say?
ANALYSIS AND DISCUSSION
In analyzing the system, you can assume that the microquartz top surface is even with the
top aluminum plate, i.e., ignore the ¼ inch recess.
A. Simple Analyses
1.
2.
3.
Assuming that the mid-plane thermocouple is exactly centered between the aluminum
plates, explain why this mid-plane temperature is not exactly the average of the
aluminum plate temperatures. Describe an experiment(s) that could be conducted to
justify your reasoning.
Calculate the thermal conductivity of the LCM. State what assumptions you have made in
computing the heat loss.
Compare the measured values of thermal conductivity for the LCM with values published
in the open literature (at least three cited sources. Sources can be found in the engineering
library). Do the values seem reasonable?
If the measured thermal conductivity values are higher than the average of the published
values, then perhaps heat loss effects in the experiment were underestimated.
If the thermal conductivity values are less than the average of the published values, then
perhaps contact resistance may have had an influence on your results. If your results
exhibit this behavior, assume that the actual thermal conductivity of the LCM is the
average of the three published values. Then for Balsa wood evaluate the contact
resistance between the wood and the aluminum plates. For paper, evaluate the contact
resistance between the paper layers. In both cases use the actual heat transfer rate through
the LCM. Do your results seen reasonable when compared to typical contact resistance
values tabulated in Table 3.2?
The experiment was conducted with insulation (ki = 0.05 W/m K) surrounding the
aluminum plate/LCM, except for the outer surface of the top plate which was exposed to
atmospheric air (ka = 0.03 W/m K). Even though as air is a better insulator than the
blanket insulation used (air has a lower thermal conductivity), why weren’t the four side
walls of the LCM exposed to atmospheric air during the experiment to lower the heat loss
through these walls? Justify your answer with back-up calculations.
4.
5.
6.
B. Finite Element Analysis
1.
Open the instructions for using the COMSOL multiphysics program from the home page.
2.
Using the COMSOL multiphysics program choose different values of h for the top of
the conductivity experiment, the top of the pressure plate and the bottom of the
experiment and the conductivity of the LCM until the predicted temperatures match the
measured temperatures. Note that it is unlikely that you can match every temperature so
you will need to exercise some judgment and consider matching spatial averages. Does
the conductivity of the LCM match the results obtained from the simple analyses above.
3. You can get details of the Comsol model by asking for a report when executing the
Comsol program.