Recommended
More Related Content
Similar to IntroductionThis experiment uses the computer program Tracer.docx
Similar to IntroductionThis experiment uses the computer program Tracer.docx (20)
More from normanibarber20063
More from normanibarber20063 (20)
Recently uploaded
Recently uploaded (20)
IntroductionThis experiment uses the computer program Tracer.docx
- 1. Introduction This experiment uses the computer program TracerDAQ to determine heat loss and record temperature over a period of time. Higher surface areas would result in a high cooling temperatures according to convective cooling. However, standard calculations don’t account for other factors such as gravity. One focus is to determine whether or not changing the surface area subject to gravity affects the cooling rate of the object. Another focus is comparing heat loss rates with different materials. The program uses the same thermocouple to acquire results for the experiments. Information then goes through an amplifier and A / D board to constantly record the temperature. Theory The purpose of the experiment was to determine whether or not the orientation or position of an object in respect to gravity will affect the rate of cooling. In a Control Volume system, the formula for heat loss is: Qdot = m * Cp * DT/dt In relation, the formula for convective cooling is: Qdot = -h * A * (T - Ta) Where h is the heat transfer coefficient. If both equations were to equal together, the resulting equation will be: dT / (T−T∞) = − dt / τ
- 2. Where τ = mCp / hA. The equation can then be integrated and rewritten as: (T−T∞ ) / (Ti − T∞) = e ^ (-t / τ) Where Ti is the initial temperature at t = 0. Furthermore, we can declare that an object has a uniform heat distribution if Bi (Biot Number) is less than .1. The equation for the Bi is: Bi = - hL∗ / k Because our objects is spheres and cubes, L∗ = D / 6. Once h is determined, we can calculate the Biot number value and verify the uniform heat distribution throughout the objects. Experimental Procedure Header Size: 8 Version: 2 Sampling Interval: 4
- 3. Sampling Rate: 0.25 Sample Count: 675 Device Serial Number: 0 Culture Info: en-US Sample Number Date/Time CHANNEL0 CHANNEL1 CHANNEL2
- 154. 34.41415 DAQ Stop LOG Stop Biot Numbers Data Set h ( Bi Copper Sphere 291.121 0.00309 Stainless Steel Sphere 265.350 0.00282 Copper cube connected at the corner 783.299 0.00833 Copper cube connected at the center 275.168 0.00292 Copper Sphere 0.0596
- 155. 6.347E-6 Stainless Steel Sphere 0.0557 5.926E-6 Copper cube connected at the corner 0.247 2.632E-6 Copper cube connected at the center 0.6406 6.813E-6 Discussion 1) 2) 3) 4) Uncertainty The thermocouples used in this experiment are of Copper- Constantan composition (Type T). According to Measurement Computing USB -Temp and TC Series user’s manual, the Type T thermocouple has a temperature range of -200 to 400 degrees Celsius. At -200 degrees, the maximum error is 2.082 degrees, while the average error is 0.744 degrees. At 0 degrees, the maximum error is 0.870, while the average is 0.290 degrees. At the maximum temperature of 400 degrees, the maximum is 0.568 degrees and the average is 0.208 degrees. The amount of digital bits (maximum resolution) of the USB measuring device is 24. MCE 313 – LAB # 2
- 156. Combined Convective and Radiative Cooling of Objects in the Environment February 8, 2017 1 Purpose of Experiment In this experiment is an introduction to heat transfer phenomena and to the use of a data acquisition software (TracerDAQ). The experiment consists of two major sections, which are variations of a single theme and result in the investigation of slightly different effects. 1.1 Geometric effects In this section, the investigation focuses on the coupled natural convective and radiative cooling of two copper cubes suspended in air (see Fig. 1). The data obtained is to be used to find the effective heat transfer coefficients of the cubes and to determine whether orientation with respect to the direction of gravity has a significant influence on the heat transfer processes. Figure 1: Copper cubes hung from corner (left) and from mid- face (right). 1.2 Material effects In this section, the investigation focuses on the cooling of two spheres. One sphere is made of copper and the other is made from 316 stainless steel (see Fig. 2). They will be suspended in air and the cooling process will be monitored. The effective heat transfer coefficients of the two spheres will be determined and the data
- 157. will be used to quantify the effect of using different metals on the cooling process. All four objects have Type T (coper-constantan) thermocouples embedded within them, and are posi- tioned at the respective specimens’ geometric centers. These thermocouples are connected to an amplifier (Fig. 3), which, in turn, is attached to an A/D board. Using TracerDAQ, the time history of the temperature of the cubes and spheres can be measured as they cool. 1 Figure 2: Copper (left) and stainless steel (right) spheres. Figure 3: USB-based 8-channel thermocouple input. 2 Theoretical Background Consider an object surrounded by a control volume taken to coincide with the object’s surface. Applying the first law of thermodynamics to this control volume gives: q = mCp dT dt , (1) where m is the mass of the specimen; Cp is the specific heat of the material; q is the heat transfer rate; T denotes temperature; and t represents time.
- 158. The right hand side of the equation represents the time rate of change of the energy inside the control volume and the left hand side, known as the rate of heat transfer, is the total energy transferred into the control volume, per unit time, across its surface. In writing this equation, two assumptions are made. The first is that the specific heat is a constant. The second is that the entire object, consisting of its surface and interior, can be taken to have a single temperature. The latter assumption depends upon the object having a very high internal ability to conduct energy from point to point when compared to the rate at which energy is transported across the surface. This condition can be quantified and the validity of this assumption can be verified after determining the effective heat transfer coefficient. Newton suggested that the rate of energy transported across the surface could be related to the differ- ence between the surface temperature, taken to be T because of the above assumption, and the ambient temperature of the surroundings T∞ = Ta. Thus, q = −h̄ A(T − Ta), (2) where h̄ is the assumed constant surface averaged film coefficient or heat transfer coefficient; and A is the surface area of the object. The equation also assumes that the objects temperature is greater than the surroundings so that energy will flow out of the control volume. Equating 1 and 2 gives a simple differential equation in terms of temperature: 2
- 159. mCp dT dt = −h̄ A(T − T∞). (3) Separating the variable, this equation can be rewritten as: dT T − T∞ = − dt τ , (4) where τ = mCp h̄ A . (5) Note that in this form, the left side of the equation in non- dimensional. Therefore, the right side must also be unitless. Thus τ must have units of time. To solve for temperature, note that Eq. 4 can be directly integrated, the left side from To to T and the right side, from 0 to t, yielding:
- 160. ln T − T∞ Ti − T∞ = − t τ , (6) where Ti is the temperature at t = 0. The equation can also be rewritten by taking the exponent of both sides: T − T∞ Ti − T∞ = exp ( − t τ ) . (7) So, given the assumptions made, i.e. the object can be characterized by a single temperature and the average heat transfer coefficient is constant, the temperature of the object decreases exponentially from its initial value Ti to its final value T∞, which is reached only as time tends toward infinity. The rate of the exponential decay is controlled by the time constant τ.
- 161. Research has shown that the assumption of a uniform internal temperature is justified if a certain non- dimensional parameter called the Biot number is small. If the Biot number is less than 0.1, then assuming a constant internal temperature results in an error that is less than 5%. The Biot number is the ratio of the average surface heat transfer coefficient to the internal unit heat conductance. This is expressed as: Bi = h̄ L∗ k , (8) where k is the coefficient of heat conduction ; L∗ is a characteristic length corresponding to the ratio of volume to surface area. For a cube, L∗ = S 6 . For a sphere, L∗ = D 6 . S is the length of one side of the cube, and D is the diameter of the sphere. Since both S and D are have a numerical value of 1 inch, L∗ = 0.1667in = 0.4233cm for both cube and sphere. In these experiments, once the heat conduction coefficient has been determined, the value of the Biot number can be calculated and the uniform temperature assumption can be verified. The physical properties of copper relevant to this experiment are given in Tbl 1.
- 162. 3 Procedure 1. Record the ambient temperature, T∞, in the lab. This can be done by verifying the temperature of any of the specimens, through TracerDAQ. 3 Table 1: Physical properties of copper and 316 stainless steel at 20oC Material k (W/m oK) ρ (kg/m3) Cp (J/kg oK) Copper 398 8954 384 SS 13.8 8000 400 2. Turn on the hot plate, fill the container with water, and heat it to boiling. 3. Open and setup TracerDAQ. On the basic setup window • Channel 0 is connected to the copper sphere. • Channel 1 is connected to the stainless steel sphere. • Channel 2 is connected to the corner of the copper cube. • Channel 3 is connected to the center of the copper cube. Set the frequency of acquisition.
- 163. Using a sample frequency of 10 Hz, for instance, means that 10 data values will be collected every 1 sec- ond. This is a negligible time on the order of the total time to cool these objects to room temperature. Experience has shown that the total time to observe significant cooling hovers in the vicinity of 30 to 45 minutes. Therefore, set the frequency such as to collect approximately one (1) data point per minute. The data output should be in terms of oC for each channel. 4. While in the process of setting up the TracerDAQ software, place the four specimens into the boiling water. Allow them to heat up until they attain constant, uniform temperature. This should take several minutes. When TracerDAQ is fully ready to begin sampling, swiftly remove the objects and suspend them from the horizontal rods held by the provided stands. Place each object at one end of the rod, making sure they hang vertically. Partitions screens will be present and are meant to shield the cooling objects from random disturbances (air streams) coming from the surroundings. They also prevent the radiation emanating from the objects from cross- influencing each other. As soon as this is done, activate the computer software to initiate data collection. 5. New data will appear on the computer screen every (1) minute for the next forty-five minutes. The computer software will desist its task of data collection at this point. Save the data as a text (.txt) file, which can then be read by a spreadsheet. Plan your time efficiently during the waiting period, monitoring the data collection, and discussing the meaning of the various tasks required for the report.
- 164. This may seem trivial but in effect requires much thought. A sample screen shot from TracerDAQ is show in Fig. 4 4 Figure 4: Screen shot of TracerDAQ software. 4 Data reduction 1. Plot the data for each object against time. Write a small code to generate these initial plots, repre- senting data values with symbols. View the results and decide whether it is necessary to remove the first few data points because they do not appear consistent with the rest of the data set. The first few points may have been subjected to unwanted transient effects such as swinging back and forth after being hung or the surface water film evaporating. If this is not necessary just continue; or else edit the unreliable data values from the data arrays. Remove both the suspect temperatures and their corresponding times. If this is done, be sure to readjust the time values so that the first temperature retained corresponds to time equal zero. 2. Next, perform a linear least squares fit with the remainder of the data on semi-ln scales with a curve- fitting program or software. The variables used are to be x = t and y = ln T−T∞ Ti−T∞ , as in Eq. 6. Note
- 165. that when this is done, the first point is T = Ti. From the slope of this fit, which will be the value of (− 1 τ ), calculate the average heat transfer coefficient for each data set and the associated Biot numbers. 3. Make eight (8) plots, two for each data set. One is a semi-ln plot representing the fitting process with the fit curve and the data (using a curve-fitting program or software). The second plot for each data set is to be the data compared to Eq. 7 on rectangular coordinates showing the exponential behavior (or lack of it) for each data set. Generate these plots by modifying the code written for section 1 above. 5 5 Contents of the report Each team is to produce a formal report, as described in the syllabus. The presentation of “results” that must contain at a minimum: 1. The eight plots indicated in the above section (50 points) 2. A presentation of the Biot numbers calculated for the experiment (20 points) 3. Other considerations and text (30 points) The “discussion” section should address each section of the
- 166. results listed above. Present your discussion quantitatively rather than qualitatively. Specifically address the following questions, among others 1. Does the data demonstrate that the assumption of a constant heat transfer coefficient is reasonable, i.e., are the semi-ln plots straight lines? Quantify this answer using some uncertainties analysis. 2. Does the data demonstrate that the assumption of a constant internal temperature for the objects in the experiment is valid? 3. For Part 1 of the lab, is there an effect of orientation shown in the results? Orientation relates to the geometry of suspension, either being face centered or diagonal down. 4. For Part 2 of the lab, is there any association between heat transfer and material property? For purposes of “uncertainty” at the minimum the following should be considered: 1. The thermocouples are Type T (coper-constantan). (Please refer to the user manuals associated with this experiment to obtain the accuracies associated with the equipment.) (25% of section mark). 2. The number of digital bits associated with the equipment. (Again refer to use manual). (25% of section mark). In the “equipment” section, the following will be discussed, amongst others:
- 167. 1. Discussion of voltages associated with the temperatures of the thermocouples being used. (25% of section mark). 2. Discussion of the fact that Type T thermocouples have a sensitivity of about 43 µV/oC. (25% of section mark). 6 PLEASE CHECK PAGE 32-37 IN DOCX FILE FOR DATA NEEDED TO ANSWER QUESTIONS The “discussion” section should address each section of the results listed above. Present your discussion quantitatively rather than qualitatively. Specifically address the following questions, among others 1. Does the data demonstrate that the assumption of a constant heat transfer coe cient is reasonable, i.e., are the semi-ln plots straight lines? Quantify this answer using some uncertainties analysis. 2. Does the data demonstrate that the assumption of a constant internal temperature for the objects in the experiment is valid? 3. For Part 1 of the lab, is there an e?ect of orientation shown in the results? Orientation relates to the geometry of suspension, either being face centered or diagonal down. 4. For Part 2 of the lab, is there any association between heat transfer and material property?