ENME 471 Linear Conduction

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University of Calgary *

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471

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Mechanical Engineering

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Apr 3, 2024

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ENME 471 Heat Transfer Laboratory Experiment 1: Linear Heat Conduction Objectives and Purpose: i) To develop an understanding of temperature measurement fundamentals and uncertainty by taking quantitative measurements using thermocouples. ii) To show how heat conducts linearly along a solid bar of uniform dimensions and material. iii) To demonstrate how experimental work can be used to determine the material of a solid by applying the principals of one-dimensional conduction in a solid (Chapter 3 of Incropera and DeWitt). Introduction: One-dimensional heat transfer is used extensively for the analysis of many different types of heat transfer problems. The experiment performed here involves what can be approximated as one- dimensional conduction through a rod of unknown material, with a constant temperature on one side set by water heated by a heater. The heat is conducted through the rod, and seven thermocouples are used to determine the temperature distribution axially along the rod, as seen in Figure 1. The experimentalist must apply the fundamentals of one-dimension conduction in a solid to perform a linear regression of the temperature profile along the solid material. From this, tables of typical thermal conductivities of various solids will be referenced, and the material will be determined. Apparatus: K-type Thermocouple A thermocouple is a thermoelectric device for measuring temperatures. Thermocouples consist of two wires of different materials, connected at two points called junctions . Due to the difference in the thermal conductivity of the two materials, a small voltage differential is developed at the junction that is proportional to the temperature difference. This voltage is normally in the mV range, and a signal conditioner (read amplifier ) is used to boost this voltage to the voltage range, generally 0-5V. In understanding how the voltage changes with respect to temperature, accurate temperature measurements are made. 1 ENME 471 #1: Linear Heat Conduction

Figure 1: K-type thermocouple This experiment utilizes K-type thermocouples to measure temperatures axially along the solid cylinder. K-type thermocouple refers to a thermocouple containing Chromel and Alumel conductors, and are the most widely used thermocouples due to their robust nature and wide temperature profile. As with all sensors, there is an associated error with the measurement. For a K-type thermocouple, the error is ±0.75% OR ±2.2C, whichever is greater. Thermocouple error must be considered in experimental analysis. Thermocouples have a natural drift in their measurement. Drift occurs due to the changes in the thermoelements during the operation of a thermocouple. The offset associated with the drift of each thermocouple will be provided as a part of analysis under the lab heading in D2L. TD1002A Mkll This experiment is mounted onto the TD1002 Base Unit, and is called TD1002a Mkllm, seen in Figure 3. The experiment consists of a rod surrounded by insulation, heated on one side by an electric heater, and cooled on the hotter by a Thermo Fosher cooling unit, holding the water at 6C. The display is used to set the heating value of the electric heater from 30-100W, as well as read out the temperature data in Celsius. The cross-sectional area of each test article is 0.000707m 2 . Figure 2: TD1002a Mkll Experimental Set Up 2 ENME 471 #1: Linear Heat Conduction

The unit has a interchangeable middle section material that can be one of four materials. There are seven K-type thermocouple probes that are evenly spaced out at a distance of 15mm from one another, sketched in Figure 3. The entire tube section of the experiment is isolated using insulation to reduce heat loss by radiation and convection, reducing error relative to theoretical calculations. Figure 3: Schematic of heated block The experimental set-up has inherent heat loss associated with it due to the spacing between the interchangeable section and the ends. This heat loss is somewhat mitigated using thermal paste, however TecQuipment Ltd provides a heat loss approximation based on the ambient temperature of the experiment. The estimated percent heat loss for the temperature difference measured by the first thermocouple and the ambient temperature is given in Figure 4. Figure 1: Heat Loss Percentage of TD1002a Experiment 3 ENME 471 #1: Linear Heat Conduction

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Table 1 provides thermal conductivities for various materials at 298K. Use this table to determine the material in the interchangeable section. Table 1: Thermal Conductivity of Common Metals at 298K Material (at 298K) Thermal Conductivity (k) [W/(mK)] Aluminum (pure) 205-237 Aluminum (grade 6082) 170 Brass (CZ121) 123 Brass (63% Copper) 125 Brass (70% Copper) 109-121 Copper (Pure) 353-386 Copper (type c101) 388 Mild Steel 50 Stainless Steel 16 Background Exercises: Review the concepts behind energy conservation and the surface energy balance by watching Heat Transfer L3 p1 and p2 on the course YouTube channel. Procedure: 1. Record the room temperature and atmospheric pressure. 2. Go to the station initially appointed by the TA and record the station number. 3. Start a timer and record the temperatures and power supplied by the electric heater in the TD1002A Mkll set up using the thermocouples installed in the system once every 15 seconds, over 2 minutes, for a total of 8 measurements. 4. Switch to the next station sequentially according to the station number. 5. Repeat for each station in the lab, for a total of 5 datasets. 6. Save each data set so that every individual that participated in the lab has the data sets saved locally. Analysis: 1. When under isothermal conditions, thermocouple channels do not always measure the same temperature. The source of this is attributed to slight differences in the electronic signal conditioning for each channel. We need to “correct” the data that we collect for these slight differences. The appendix of this report contains thermal drift data. This is the value that you have to add (or subtract) from each measured channel. 2. Correct the raw temperature data using the aforementioned values. 3. Find the mean and standard deviation of each collected data set. These values should be included in the data section, and the raw data in the appendix. 4. Perform a 1-d first law analysis to determine the thermal conductivity of the material as a function of the heat supplied, cross sectional area, and temperature gradient along the material. 5. Draw a resistive circuit of the energy transfer from the electric heater to the cooling water. 6. Correct the heat supplied to the system by applying the approximate heat loss percentage from Figure 4. 7. Perform a line of best fit for the temperature gradient axially along the material. 4 ENME 471 #1: Linear Heat Conduction

8. From your first law analysis and resistive diagram, determine the overall thermal conductivity of the system. 9. Repeat the above analysis, however this time perform 3 individual fits on the dataset: the hot side, the interchangeable material, and the cold side. 10. Compare the thermal conductivities found in steps 7 and 9. How does including all the temperature measurements affect the thermal conductivity of the system. 11. Refer to Table 1 of the lab manual to determine the material contained in each of the respective stations. Which of the two stations have the same material? 12. Comment on the thermal conductivity of a material and the effects it has on thermal gradient. 13. Comment on the weighting of the statistical and experimental error of a thermocouple. How would increasing the number of measurements change your error? 14. Why is it that the thermal gradient of the brass CZ121 on the hot side is consistently higher than the cold side in step 9? 15. Table 1 holds values for a fixed temperature. How does thermal conductivity change with temperature? How would this change your results? Appendix: Table 2: Thermocouple drift corrections. Station Number T1 [K] T2 [K] T3 [K] T4 [K] T5 [K] T6 [K] T7 [K] 1 0 0 0.1 0 0 0 0.1 2 -0.1 0 0.1 -0.1 0 0 0.1 3 0 0 -0.1 -0.1 -0.1 0 0.1 4 -0.1 0 0.1 -0.1 0 0 0.2 5 -0.1 0 0.1 -0.2 -0.1 0 0 5 ENME 471 #1: Linear Heat Conduction