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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 The work was controversial, and it remained unpublished until 1822.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.