Laboratory Experiment 5: Thermocouple Calibrations and Heat Transfer Coefficients Presented to the University of California, San Diego Department of Mechanical and Aerospace Engineering MAE 170 Prepared by Kimberly Nguyen, A05 Grace Victorine, A05 4/30/15
Abstract The objective of this experiment was to calibrate a type K thermocouple to observe the Seebeck Effect and calculate the Biot numbers and heat transfer coefficients of aluminum and copper spheres during both free and forced convection modes of cooling. The offset of the type K thermocouple was determined to be 3.0 ± 0.5. The Biot numbers under free convection were determined to be 0.0752 for aluminum and 0.0637 for copper. Under forced convection, they were determined to be 0.6315 for aluminum and 0.3518 for copper. The heat transfer coefficients for free convection were determined to be 604.0W/(m 2 K) for aluminum and 1005.7 W/(m 2 K) for copper. Finally, the heat transfer coefficients for forced convection were determined to be 5071.9 W/(m 2 K) for aluminum and 5554.0 W/(m 2 K) copper. The rate of heat loss was noticeably faster for forced convection than for free convection. The rate of heat loss was also faster for aluminum than for copper in both convection modes. 1
I. Introduction Thermocouples have a copious useful applications, including temperature sensors for control purposes, and the transduction of temperature differences into voltages. This experiment examines a type K thermocouple and the theory behind its operation as well as the rate of heat loss of metal spheres under both free and forced convection. The first portion of this experiment explored the ability of a type K thermocouple to transduce a temperature differential into a potential difference. The cold junction was created by submerging one wire in a temperature bath held at a constant 0. The hot junction was submerged in heated water to produce increasing temperatures so that the difference could be transduced into a measurable voltage. The voltage was displayed digitally while the temperature measurements were calculated via a mercury thermometer. The values produced were then graphed and compared to a given standard to assess both accuracy and precision. The second portion of the experiment was designed to allow determination of the Biot number and heat transfer coefficients of an aluminum and copper sphere under both free and forced convection modes. Each sphere was submerged in hot water until its temperature stabilized at 90. Then it was plunged into the ice bath at 0 so that the rate of cooling could be recorded and graphed. The cooling curves were then examined to determine the Biot numbers and heat transfer coefficients. It was then determined which metal exhibited better heat transfer properties and whether free or forced convection transferred heat more quickly. II. Theory The governing rule behind the operation of a thermocouple was explained to be the Seebeck Effect, according to which, two different metals or semiconductors were necessary to produce a voltage difference in a circuit due to the internal material properties that gave rise to different electron mobilities. In the presence of a temperature gradient, the more mobile electrons were be transferred to the metal with the lower electron mobility. This produced a measurable potential difference. Additionally, Newton s Law of Cooling was examined. It demonstrated that the heat loss rate, Q conv, of a body was directly proportional to the difference in temperature between the system in question and its surroundings. Necessary assumptions made were that temperature gradients inside the sphere were small such that conduction dominated over convection, yielding a Biot number less than 1, and that the heat transfer coefficient was not variable with time. Q conv = ha (T hot T cold ) (1) 2 The Biot number was introduced as a dimensionless number representing the ratio of convection to conduction. When the Biot number was small, conduction was the more prominent means of heat transfer, which was ideal in part II of the experiment as it meant that conductive forces dominated, which met one assumption of Equation (1). R B i = h k (2) 2 Fourier s Law, yielded a relationship from which the heat transfer coefficient was able to be calculated from with knowledge of the temperature difference as well, density, surface area, volume, heat capacity, and time: T s T T o T = e ha [ ]t ρv C (3) 2 2
III. Experimental Procedures Part I: Thermocouple Calibration The first part of the experiment sought to calibrate and analyze a type K thermocouple in terms of its voltage produced relative to the change in temperature. One wire was designated the cold junction and submerged in an ice bath in the form of a cooler filled with ice and water to be ideally held at a constant 0. The other wire was made the hot junction and placed in a pan filled to about ⅔ full of room-temperature water. The thermocouple was then connected to the bench multimeter with the BNC adapter, cable, and clips and monitored on the DC setting. The TC junctions were immersed together and stirred to determine the offset. Both junctions were then set in the place so that the multimeter reading increased with in the positive direction with heat added to the hot junction. A thermometer was then suspended in the water pan to record the initial temperature of the hot junction and corresponding voltage difference. The hot plate was then turned to the maximum setting and 12 data points were taken at increasing temperatures stopping at 90. At the last data point, the heat was lowered to avoid overheating the water. The recorded temperatures were then graphed and compared to a standard so that the accuracy and precision as well as the reliability of the type K thermocouple could be assessed. Part II: Determination of Biot number and convective heat transfer coefficients. In the second part of the experiment, after the thermocouples in the metal spheres were determined to be functional, the temperatures of the water in the cooler and the pan were checked for need of adjustment. Then the yellow connector on the sphere was plugged into the thermocouple extension cable, which was in turn connected to the DAS terminal AI0+. The red wire was attached to AI0-, and the ground wire from the stainless steel tube was placed to AI-Gnd. The sphere was fully submerged in the hot water by attachment to a ring clamp so that it did not touch the bottom of the pan as shown in Figure 1. Figure 1: Setup of sphere in hot pan 1 The Thermocouple CJC vi was then used to monitor the temperature change with time. The thermometer was used to read the temperature of the hot water and make note of the offset from the vi s reading. Once a constant hot temperature was observed, the sphere was quickly submerged in the cold water bath and its cooling curve was recorded. The same process was repeated for the second sphere. Then, the process was repeated for both spheres only with the addition of a stirring pump to implement forced convection. 3
IV. Data and Results The offset of the thermocouple wires was determined to be 0.00 ± 0.05mV DC. The Seebeck Effect was observed through a voltage produced by the circuit composed of two different metals. The recorded data, and standard data in Figures 2 and 3, respectively show a very close linear relationship. The slope of the best fit line for the recorded data was determined to be 25.03 /mv while the slope for the standard data was determined to be 24.44 /mv. Figure 2: Measured Voltage vs Temperature Plot Figure 3: Standard Voltage vs Temperature Plot In part II of the experiment, the Biot numbers and heat transfer coefficients were as displayed in Table 1. Table 1: Heat transfer coefficients and Biot numbers of Al and Cu spheres under free & forced convection Aluminum Free Aluminum Forced Copper Free Copper Forced h (W/(m 2 K)) 604.0 5071.9 1005.7 5554.0 Biot number 0.0752 0.6315 0.0637 0.3518 Figure 4: Aluminum Free Convection Figure 5: Copper Free Convection Figure 6: Aluminum Forced Convection Figure 6: Copper Forced Convection 4
IV. Data and Results (Continued) The Biot numbers and heat transfer coefficients were calculated from their corresponding best fit lines in Figures 4-7. The discrepancy between the thermometer and the LabVIEW vi was found to be 3.0 ± 0.5. The temperature of the ice bath remained at 3.0 ± 0.5 throughout part II of experiment. Figure (7) Aluminum & Copper Free Convection Cooling Figure (8) Aluminum & Copper Forced Convection Cooling 5
V. Discussion and Error Analysis In part I, the k thermocouple made of two different metals in a circuit did succeed in producing a voltage in the presence of a temperature differential, thus confirming the Seebeck Effect. Additionally, data recorded for the thermocouple corresponded closely with the standard values. When graphed, the best fit line of the recorded data appeared nearly identical to the graph of the standard data. The slope of the best fit line for the recorded data was determined to be 25.03 /mv while the slope for the standard data was determined to be 24.44 /mv. The error between the two was a mere 2.4%, which indicated that the values agreed closely and that the recorded values were therefore most likely reasonably accurate. In part II of the experiment, the Biot number of the spheres in forced convection were higher than of those in free convection, indicating that the increase in convection caused the Biot number to increase. It can be seen in Figures 4-8 how the forced convection curves had steeper curves and higher Biot numbers, indicating higher rates of heat transfer. This substantiates the idea that convection was more efficient at heat transfer than conduction. Additionally, the curve for Copper under free and forced convection is noticeably steeper than that of Aluminum, indicating higher thermal conductivity and heat transfer coefficient. This indicated that the copper sphere more readily transferred heat as compared to the aluminum sphere. Therefore, the copper sphere cooled faster than the aluminum sphere. Copper was therefore at least a slightly better conductor of heat than aluminum. The Biot number remained less than 1, indicating that in all examined cases, conduction forces dominated. It is when the Biot number approached 1 that the convective forces were higher and heat transfer rates were also higher. For Figures 4-7, the values of the best fit lines generally coincided well with the plotted data. It could be observed that the R 2 values were rather close to 1 for each of the graphs, indicating that the best fit line was generally an accurate representation of the trend of the data without large enough error to raise concern. The data collected during the free convection mode of the aluminum sphere had the most poorly fitted line. While it still represented the data well, there was noticeably more deviation in the data. This could have been because it was the first trial conducted. While heating the water, it was noted that there was an odd veneer of film inside the container.this could have presented a source of impurities that may have affected the boiling rate of the water and perhaps the heat transfer rate to a small extent. It was unclear whether or not this was the case, but the existence of subsequent trials with noticeably less error seemed to support that there was more deviation in the first trial than could be attributed to simply random error. That the Biot numbers in the case of forced convection were higher than 0.1 (a 1 to 10 ratio), brought into question their validity. While the best fit lines may have been good fits for the recorded data, whether or not they managed to accurately represent the Biot numbers and heat transfer coefficients of aluminum and copper is questionable. Ideally, it would have been preferable to compare the values with standards or average data of the lab session in an effort to quantify accuracy. Especially since any error in the Biot numbers was propagated to and magnified in the heat transfer coefficients, as they were calculated from the Biot numbers. That there were discernible offsets in parts I and II of the experiment indicated that noise was most likely constantly present, and minute fluctuations in it could have given rise to deviations in recorded and analyzed values. Most likely the trends remain the same, but the precision might have been marred, as random errors such as noise do not affect accuracy, but do impact precision. Concerning the assumptions of Newton s Law of Cooling, it idealized that the temperature gradient inside the sphere was small so that conduction dominated and the heat transfer coefficient did not vary with time. While these were good approximations, they were idealizations and had the heat transfer coefficient varied even slightly with time, then the value obtained would be an average at best. Such assumptions were important to take into consideration as, had they been found not to hold, the laws used would not have yielded accurate calculations. 6
VI. Conclusions This experiment successfully demonstrates the validity of the Seebeck Effect in which a two different metals in a circuit subject to a temperature differential will produce a voltage difference. However, the power source and exposed wiring of the thermocouple make it vulnerable to random error such as noise. Additionally, this experiment demonstrates that forced convection significantly increases the rate of heat transfer as opposed to free convection. Finally, it shows that copper is a better conductor than aluminum since copper has a lower Biot number and does not dissipate heat as quickly as aluminum does. Copper s lower heat transfer coefficient, lower Biot number, and ability to retain heat longer than aluminum make it a better conductor. 7
VII. References 1. Nicholas Busan, Steve Roberts, and Rahul Kapadia. Experiment 5A: Thermocouple Calibration and Determination of Heat Transfer Coefficients. (2014). UCSD MAE 170. Web. 29 Apr. 2015. < http://mae170.eng.ucsd.edu/lab-procedures > 2. Chapter VI. Heat Transfer Coefficients. (2014). UCSD MAE 170. Web. 29 Apr. 2015. < http://mae170.eng.ucsd.edu/additional-lab-manual > VIII. Appendix I: Raw Data Table A2: Temperature and Voltage GV Temperature (C) Voltage (mv) Uncertainty (mv) 31 1.233 0.001 37 1.38 0.01 44 1.68 0.01 48 1.88 0.05 54 2.093 0.005 60 2.36 0.02 68 2.68 0.05 72 2.86 0.005 77 3.06 0.05 82 3.26 0.05 86 3.41 0.01 90 3.59 0.05 Table A3: Temperature and Voltage KN Temperature (C) Voltage (mv) Uncertainty (mv) 31 1.2315 0.0005 38 1.38 0.05 44 1.65 0.05 48 1.84 0.05 53 2.05 0.10 58 2.27 0.010 63 2.465 0.020 69 2.69 0.05 76 2.993 0.002 81 3.225 0.050 86 3.410 0.050 90 3.6 0.05 8