Transient Heat Conduction in a Long Solid Rod Cooling Down the Rod

NEEDS REVISONS Experiment 2

Transient Heat Conduction in a long solid Rod -- Cooling down the Rod

Armfield Heat Conduction Module

APPM 4350/5350

Introduction

Perhaps the simplest phenomenon that can be modeled by the heat equation is heat conduction in a long uniform rod. In most instances heat conduction occurs in three dimensions --- a situation that is complicated to analyze. In the laboratory, we use an apparatus that exhibits one-dimensional heat flow to demonstrate the basic concepts associated with the heat equation.

To solve the heat equation for a long solid rod and compare your predictions with the actual temperature measurements made in the lab.

Experiment

The heat conduction apparatus consists of a cylindrical metal bar that is insulated. The metal bar is insulated on one end while the other end is exposed to cooling water. The cooling water is supplied when the tubes from the back of the apparatus and the electric cooler are attached. The cylinder is fitted with temperature sensors at evenly spaced locations along the rod. The experiment will best be modeled by the equation if the initial condition (temperature) is known precisely. The best way to do this is to start from a constant temperature. In other words, to do this experiment you should start with a room temperature rod, run the cooler until the water reaches 5C, and then attach it. (After making sure sensors are connected, etc.)

General Apparatus Guidelines

The instrumentation provided permits accurate measurement of temperature and power supply. Fast response temperature probes, with a resolution of 0.1°C, give direct digital readout. The power control provides a continuously variable electrical output of 0-100 Watts with direct readout. Figure 1 depicts the Heat Transfer Module with the necessary equipment (excluding cooler) to perform the experiment. Procedure Getting Started

The first thing you need to do is to obtain access to the Heat Conduction Module. Look for a sign-up sheet on the ground floor of the ITLL in the southeast corner. If there is a sheet posted for this module, then you need to sign up for this lab ahead of time. To actually get the equipment when it's time to do the experiment, you need to page a lab assistant. There is a phone right next to the sign-up sheet along with extensive directions on how to check out labs. You will also need to get the recirculating cooler, which comes separate from the module. The lab module and the cooler you will need to perform the lab will probably be located on level 2B. If possible, use labstation 28 on level 2B, because it has a drain to catch drips from the cooler.

NOTES:

 Since two other experiments use the same apparatus as this one, you will want to be sure to perform the lab portion of this experiment before December. In addition to this other classes will also be using these labs and waiting until the end will make it very difficult to check out the equipment.

General Operating Procedures

Setting-up the Apparatus: This module consists of five basic elements: a control box, power regulator, selector box, a linear conduction apparatus with various samples, and a radial conduction apparatus. You will also need to checkout the water chiller that will provide the cooling for the apparatus.

1) Make sure the Control Box (Figure 1A) and the Power Regulator (Figure 1C) are turned OFF. 2) Check that the Control Box is plugged into the Power Regulator. 3) Connect the P-1 Military Plug to the appropriate jack on the labstation. 4) Connect the Heater Power Cable (Figure 1E) from the desired conduction apparatus to the front of the Control Box. Heater Knob OFF

Figure 1: Heat Conduction Controls A: Control Box B: Selector Box C: Power Regulator D: Heater Knob (counterclockwise is OFF) E: Heater Power Cable (from either conduction apparatus)

5) If using the Linear Apparatus (Figure 2A), select and install the desired sample. The samples for the Radial Conduction Apparatus (Figure 2B) cannot be varied. 6) Determine which thermistors (Figure 2C) should be read by the computer. Connect these thermistor cables (Figure 2D) from the Conduction Apparatus to the connectors on the back of the Control Box labeled one through seven. The computer will read these thermistors if desired. 7) Connect thermistors 8 and 9 to the Control Box. thermistors 8 and 9 can only be read manually on the front panel of the Control Box. 8)

Figure 2: Heat Conduction Apparatuses A: Linear Conduction Apparatus B: Radial Conduction Apparatus C: Thermistors D: Thermistor cables E: Tubing with quick disconnect fittings

9) Plug the Power Regulator into one of the outlets (either circuit #7 or #8) located next to the computer hard drives on the labstation. 10) Plug the Water Chiller into the remaining outlet located next to the computer hard drives on the labstation. You may want to begin cooling the water before you connect the Water Chiller to the Conduction Apparatus, in order to get the water at a steady state (this takes about 10 minutes). Instructions for the Water Chiller are indicated on the top of the unit. After the bucket is in place, make sure the cooler tubing is connected to itself with the valve open, plug in the cooler equipment to the lab station, and turn it on. There are four 120 V outlets down low on the end of each lab station (Sides A and B). Set the cooler to 5°C-10°C (record this value) and let it run for 10-20 minutes until the water temperature has stabilized at that temperature. (If the cooler makes unhappy noises, it may be low on water; seek help.)

IMPORTANT: Do not plug both the Power Regulator and the Water Chiller into the same outlet. Use two different outlets that run off of separate circuit breakers.

Preparing to run an experiment: 11) Select the mode on the Selector Box (Figure 1B) to computer or manual. Remember that all thermistors can be read manually but the computer can only read thermistors 1-7. 12) Turn the heater knob (Figure 1D) on the Control Box fully counterclockwise (this is the OFF position). 13) When the Water Chiller temperature has reached steady state, turn it OFF and connect it to the Heat Conduction Apparatus using the quick disconnect fittings in the tubing (Figure 2J). Make sure that you are over a drain or bucket to avoid spilling water on the floor. 14) The middle section of the rod is removable so you can change samples. Make sure the sample that's in there is brass and its diameter matches that in the rest of the rod. IMPORTANT: Smear a modest amount of heat conduction compound on both sides of the removable section of the rod; this will help heat conduct along the rod. After you have done this replace the sample and be sure to match the edges on the sample with the edges along the rod. Make sure the connection is tight. 15) Turn ON the Power Regulator and Control Box but leave the Water Chiller OFF. 16) If you intend to use the computer for data acquisition follow steps 17-20, “Using the Heat Conduction Apparatus.vi,” at the end of this procedure. 17) Hit the play button on the VI so it starts taking data. Let it go a minute or two to make sure everything looks alright. Turn off the power on the the cooler, connect the cooler tubes to the insulated rod tubes, and then turn the cooler back on. Note when you turned the cooler on, because this is when the experiment really started.

WARNING: If the heater temperature reaches 100º C the Control Box will shut down. Monitor your temperature readings carefully.

18) The computer will take measurements of the temperature at each of the 7 probe locations every minute. Continue to take measurements until the experiment reaches steady state. You will do this for 10-20 minutes and should have data for each of the probes for the entire time. 19) When finished with the experiment disconnect everything and return the module to checkout.

Using the “Heat Conduction Apparatus.vi”

20) Open the “Heat Conduction Apparatus.vi” using the following path: H:\ITLL Documentation\ITLL Modules\Armfield Heat Conduction\Heat Conduction Apparatus.llb 21) When the VI opens, enter the following information into the “User Inputs” dialogue box: a. Indicate the temperature units desired b. Specify the time interval between samples in minutes c. Enter the watts applied for the experiment. (This is the same wattage that will be dialed in on the Control Box when running the experiment.) When you run LabView (using the white arrow in the upper left-hand corner) the program will double check to see that the watts applied is entered by telling you to fill it in before pushing stop. When you press OK, LabView will begin taking data. 22) When you are ready to take data, apply power to the heater using the heater knob, turn ON the Water Chiller, and press OK on Labview. 23) When you are finished taking data, hit “STOP” to quit and save the data to a file. The file will record the watts applied, the temperature units, and each data point. It is recommended to save with extension “.xls” so that Excel can open the file.

Program Behavior  While the program is running, it will tell you how many samples it has taken, how long it has been running, and how long until the next sample.  The plot shows the various temperatures of each thermistor with a different color in a temperature versus time format. The graph will remain blank until the second data point is taken because two data points are needed to create a line. Analysis

1. Describe the boundary conditions for this experiment. Explain your choice. Based on the data you have collected, where are the ends of the rod? 2. Derive the solution to the heat equation for this scenario 3. Run the experiment and compare the theoretical solution with the experimental results. Discuss the discrepancies, if any. 4. An important parameter in the problem in the thermal diffusivity of the material being tested. You are using a brass rod in this experiment and the thermal diffusivity of the brass can changes (sometimes by a factor of two) depending on its detailed chemical composition. Use your experiment to determine the thermal diffusivity of this particular specimen of brass. Determining the chemical composition of the rod is not necessary for this experiment. Calculate this value from your measurements and compare it to the value for brass quoted in a handbook. 5. Predict the global maximum temperature from your calculations. When and where does it occur? Does it occur at steady state or before?

NOTE: Reference for materials information can be found in the following books located in the Engineering Library.

 ASM Handbook, Volume 18, TA 459 A5 V.18, 1992  Standards Handbook; Copper, TA 480 C7C655  Engineering Formulas 4th Edition, TA151.G4713, 1983

Figures Figure A) Equipment set-up & core

The following list identifies the various parts of the heat conduction apparatus

1. Test module platform 2. Brass sample: 25 mm diameter, 30 mm length 3. Brass sample: 13 mm diameter, 30 mm length 4. Stainless steel sample: 25 m diameter, 30 mm length 5. Connection wires (9) 6. Control box 7. Main power cord 8. Heat conduction compound

You will not need each one of these items, but at least now you know what they are. The temperature probes on the specimen are connected to the jacks on the back of the control box with the connection wires [(part 5)].

Dimensions of the brass cylinder

 Diameter: 25 mm  Length: 80 mm  Distance between probes: 10 mm Per Steve Stone with Armfield 12/11/02

The composition of the Brass specimen: 60 to 65% Copper 35 to 40% Zinc K value of 117 W/m2

The composition of the Stainless Steel specimen: .08% Carbon 2% Manganese 1% Silicon 16 to 18% Chromium 10 to 14% Nickel 2 to 3% Molybdenum K value of 25 W/m2