NORTHERN ILLINOIS UNIVERSITY - Department of Mechanical Engineering
MEE 390 EXPERIMENTAL METHODS IN MECHANICAL ENGINEERING
©1990-1997 M. Kostic

Objective: To measure the thermal conductivity of two materials (steel and brass).

Theory:
We know from Heat Transfer, that if a plane wall of thickness (Dx) and a cross sectional area (A) is maintained at two different temperatures at both ends of (Dx) with a temperature difference of (DT), then the heat transfer per unit time (Q) will be proportional to the cross-sectional area (A) and the corresponding temperature gradient (dT/dx= DT/Dx), i.e.:

Q a A (DT/Dx).

The heat flow will be in the perpendicular-to-the-cross-section direction, i.e. one-dimensional. The coefficient of proportionality is (k) and is called the "coefficient of thermal conductivity" or simply "thermal conductivity." It may be easily determined if all the above quantities are known (measured), i.e.:

All quantities in the above equation have coherent units (SI units in this experiment): k [W/m/ K]; Q [W]; A [m²]; DT [K or °C], because this is temperatures difference, so [K] or [°C] will give the same result; and Dx [m].

1. Setup the apparatus as shown in the figure using the steel sample.
2. Measure the thickness and diameter of the sample and note down the values. Lubricate the contact surfaces with a good thermal-conducting lubricant or grease to minimize thermal contact resistance (it is better for any surface irregularities NOT to be filled with poorly conducting air). Switch on the instrument.
3. Before turning heating or cooling, check all temperature readings (at all points 1-8). If the apparatus is in equilibrium with the room air, all temperature sensors should indicate the same temperature except for the measurement errors. Record the readings and use any consistent discrepancy for corresponding correction later.
4. Connect the tube to the water supply, which connects the cooler end of the apparatus to be cooled. Make sure the outlet water goes to the drain. This may be already done for you.
5. Open the water supply so that enough water flows through the cooler.
6. Switch on the heater so that the power supplied is about 15 W. An optimum heating power should be found so that the relative lost to the surroundings by radiation and convection is minimized. Even though we have covered the apparatus with plastic insulation, it is not a perfect thermal insulator, so some fraction of the heat supplied will be lost and the error in the calculation will occur.
7. Hook the temperature sensor connector to any one of the temperature sensors on the hot side (number 1, 2, and 3 on the Figure) and wait until the system reaches a steady state. Steady state means the temperature does not change with respect to time. For example, if the temperature does not change by more than 0.1° C we may assume the steady state is reached.
8. Record the readings for all the six locations (1, 2, and 3 on the hot side and 6, 7, and 8 on the cold side, see the Figure).

NOTE: Your previous Lab assignment and Lab report are due before the demonstration of the next Lab. It is the best for you if you do your lab experiments right after the demonstration while TA is still in the Lab. Also, you have to perform the uncertainty analysis for every experimental lab and include it in your lab report.

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