AERO 214 Thermal Properties of Materials

Transcription

1 AERO 214 Thermal Properties of Materials The purpose of this experiment is to measure the coefficient of thermal expansion and heat transfer conductivity of materials. Coefficient of Thermal Expansion Introduction Materials change shape under a change in temperature. Objective To determine the coefficient of thermal expansion (CTE) Theory where L is the total heated length of the rod. L=L 1 +L 2 +L 3 It is assumed that heat flows in one direction from one end of the rod to the other and convection to the environment from the surface is ignored. The total strain in the material is assumed to be decomposed into elastic and thermal portions. el th The Hook s law is given as a linear relationship between the stress and the elastic strain. However el th E E th ref T T T Where α is the coefficient of thermal expansion and T ref is the reference temperature at which thermal strains are considered zero. Hence the change of length at the free tip of the rod, considering the fact that the rod is load free, can be calculated via ref ref ref L L T T L T T L T T Every experiment has controlled inputs, measured outputs, and parameters that must be known. In this bending experiment, we have Controlled Input: T, Temperatures of different sections of the rod. Measured Output: Tip deformation

2 Parameters: L i, Lengths of different sections and, D, diameter of the rod Materials The experiment contains a rod of material with circular cross section. Test Procedure 1) Find the thermal expansion setup for your team. 2) Measure the dimensions necessary for analysis 3) Secure the dial properly at the free tip of the rod and zero the reading. 4) Set the heater to a desired level. a) Measure the temperatures at various sections of the rod with corresponding thermocouples and the hand held digital thermometer. b) Make sure that the type of the thermocouple (K or J) matches the setting on the thermometer. c) Wait until the experiment goes into a steady state condition. 5) Record the temperature readings and measure the deformation at the tip. 6) Repeat the experiment for another level for the heater. Reporting Requirements 1. Use the format given at the end. 2. The purpose is to measure the coefficient of thermal expansion for the rod and identify the material based on the values in the book or literature. 3. Uncertainty analysis and propagation of uncertainty. 2

3 Thermal Conductivity Introduction Fourier s law relates the heat per are, or heat flux, transferred in a material through conduction to the spatial gradient in temperature. This relationship is linear and its coefficient, thermal conductivity, varies in different materials. Objective To determine the heat transfer conductivity. Theory Q dt q k A where k is the thermal conductivity and q is the heat flux. It is assumed that heat flows in one direction from one end of the rod to the other and convection to the environment from the surface is ignored. Also it is assumed that the cross sectional areas of the three segments are similar. Therefore, after reaching the steady state condition Or q qi q qi dt dt dt k k k I I I I For example dt T T L 4 3 Controlled Input: T, Temperatures of different sections of the rod. Parameters: L i, Lengths of different sections and, D, diameter of the rod. Note: The top and bottom segments are made from Al 6061, therefore K I and K I are known. Output: find K Test Procedure 7) Find the thermal conductivity setup for your team. 8) Measure the dimensions necessary for analysis 9) Set the PID controller to a desired level. This controls the temperature of the bottom plate. a) Measure the temperatures at various sections of the rod with corresponding thermocouples and the hand held digital thermometer. 3

4 b) Make sure that the type of the thermocouple (K or J) matches the setting on the thermometer. c) Wait until the experiment goes into a steady state condition. 10) Record the temperature readings. 11) Repeat the experiment for another level for the heater. Reporting Requirements 4. Use the format given at the end. 5. The purpose is to measure the thermal conductivity for the rod and identify the material based on the values in the book or literature. 6. Uncertainty analysis and propagation of uncertainty. Note: Those who miss the lab or do not contribute to the lab report will not get credit. 4

5 AERO 214 Technical Laboratory Report Format Each group submits one report. The following sections must be included in each Technical Laboratory Report. 1. TITLE PAGE This is the cover page and should present the report in a professional manner. The following should be included: a. Title of Report b. Authors (Team #, Team Leader(s) for this report, other Team Members) c. Date 2. TABLE OF CONTENTS This page should include all sections of the report, figures, tables, and appendices and their corresponding page numbers. 3. ABSTRACT This is a brief summary (6-10 sentences) of what was done, what was found, and why it is important. 4. INTRODUCTION This section provides motivation and a general summary of the experiment. definitions, theory, and background literature are included in this section. Any 5. EXPERIMENTAL PROCEDURE This section describes step-by-step the procedures used to conduct the experiment(s). If an ASTM standard test method was used, only the standard test number needs to be cited along with any deviations from this standard method. 6. RESULTS This section includes summary data in tables and figures used in the analysis (next section) and text to describe these tables and figures. Each table and figure must have a number and be cited in the text. This section does not include raw data. 7. DISCUSSION In this section, results presented in the previous section are analyzed and discussed in response to the reporting requirements. Additional figures may also be added. Any problems encountered in the experiment should also be highlighted as well as the effects of these problems on the results and analysis and methods by which to avoid these problems in the future. 8. CONCLUSIONS AND RECOMMENDATIONS This section contains summary conclusions based on the analysis, positive aspects of the experiment in terms of learning, and recommendations for improving and/or expanding the experiment. 9. APPENDICES This section (if necessary) contains specific calculations and raw data. 5