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ASEN 3113 Lab 2 Heat ConductionAssigned: 18 October 2013

Prelab #1-3: 1 & 4 Nov. 2013Prelab #4-6, Analysis 1-2: 8 & 11 Nov. 2013

Lab Due: 21 November 2013

OBJECTIVES

Completely understand transient and steady state heat conduction. Understand the fundamentals of heat conduction through constant mediums. Appreciate how partial differential equations and boundary value problems have real engineering use. Continue to improve lab report technical writing skills.

EXPERIMENTAL BACKGROUND AND DESCRIPTION

In this experiment you will analyze the steady state, and transient heat conduction through solid metalrods. In the experiment there are 3 different material rodsBrass, Aluminum and Stainless Steel. Eachrod is individually housed in an insulated casing, with one side heated and the other, chilled. You willknow the voltage in at the heater side, and the temperature of the water chilling on the other side. Inaddition, you will use the National Instruments USB Data Acquisition (DAQ) hardware and LabVIEW toview and record temperature data from evenly spaced type K thermocouples along one of the material rod

types.

REQUIRED HARDWARE / EXPERIMENTAL APPARATUS

You will use the experimental apparatus shown below (Fig. 1), and a water chiller (Fig. 2). Inside theapparatus is a solid metal rod, containing one of the three metals mentioned above. The metal rod isaffixed at one end to chilled water, held at a constant temperature (displayed on the water chiller). Inside

the insulation, the other end has a band heater, which wraps around the circumference of the rod (Fig. 3).

Figure 1.Experimental Apparatus

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Figure 2.Water Chiller

Figure 3Experimental Apparatus Diagram

NOTE: The heater has an internal resistance of 110 and draws a current of 0.28 A at 30 V.

Table 1 Properties of the materials used in the experiment

Material Properties

Thermal conductivity

(k) in W/(m*K)

Density () in kg/m3 Specific heat capacity

(C) in J/(kg*K)

Stainless Steel T-303

Annealed

16.2 8000 500

Aluminum Alloy 7075-T651 130 2810 960

Brass 360 H02 115 8500 380

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EXPERIMENTAL PROCEDURE

1. Log in to a LabStation.2.

Check that the USB thermocouple box is plugged into a USB port on the computer you are using.

3. Check that all 8 thermocouples are plugged into the thermocouple box receptacles.4. Open Heat Conduction Rods EEF.vi5. Before running the VI, set the desired sample time and select Celsiusor Fahrenheit from the User

inputs dialog box. (These cannot be changed while the VI is running.)

6. Check that water entrance and return lines are plugged into the experimental apparatus provided.7. Check that the water chiller is plugged in and turned on.8. Set for desired water temperature of T0. (Refer to water chiller instructions.) Make sure you record

what T0 you used, it is not recorded by the VI.

9. The entire rod is now being cooled to the initial temperature T0. Allow some time for the rod toconduct to this initial temperature. You can run the VI to monitor the temperature, but you will not

use this data.

10.Verify the power supply is set to 30V.11.When the apparatus has reached a rather uniform initial temperature T0 according to the VI, restart

the VI and turn on the power supply. You are now taking experimental data.

12.Monitor the data until the rod attains a steady state (All temperature lines become horizontal).13.While waiting for the rod to reach steady state, investigate the hardware using the stainless steel rod

experiment. Remove the PVC casing and insulation to expose the thermocouple connections, bandheater and cooling lines. Make notes of how these attachments are made and how these might affect

the assumptions that were made in the analytical solution.

14.Save data, and clean up.

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DATA ANALYSIS AND REPORT / LAB WRITEUP (90 points)

You will have taken data from one material type rod, either aluminum or brass. You must report onresults from all three types of materials (aluminum, brass, steel). Use data that you collected, along withthree data files provided in the ASEN 3113 class folder, for a total of five data files you need to analyze.

Discuss in a formal lab report the following questions (question 1 is revisited from the prelab):

1. Assuming that x=0 where the temperature is equal to T0 (chiller temperature), determine thedistance to the first thermocouple for the data file you collected. Also, determine H and plot theexperimental and analytical results of all five datasets for this steady state solution. Compare

results.

2. Note that in question 1 we assumed that the initial temperature of the entire rod was constant andequal to the chiller temperature T0. Is this assumption valid? Justify your answer withexperimental data. If the assumption is not valid, determine how the temperature profile will

affect the transient solution - do this without solving any formulas. Can the transient solution besolved analytically given an initial temperature distribution?

3. Recall from the lab discussion that the general solution for T(x, t) involves taking the summationof n from 0 to , and that the solution converges and can be approximated very accurately by

the summation of n over a finite range. Plot the analytical temperature T(x, t) versus time foreach thermocouple location for the material types of all five datasets and compare with the

experimental results.

4. Recall, that the thermal diffusivity can vary quite a bit within materials and what happens to thetransient model if the thermal diffusivity increases or decreases. What value for gives the

best correlation between analytical and experimental results? Is this value of consistent with the

values found in the property table? What assumptions made about the hardware could contributeto any discrepancies?

5. What determines the time to steady state? In all five datasets, what is the approximate value of thetime required to reach steady state? Compare the values of t/L2 for all five datasets. What do

those values represent and how does changing them change your results?

Note: Use Table 1 as a reference for obtaining the required parameters for the different materials.

Use diameter of 1 inch for all rods. Also, make assumptions about the spacing distance between two

thermocouples.

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Your group lab reports should include at minimum the following sections and address each topic

within each section

Points Section

5 Abstract / Nomenclature

20 Introduction & Theory Qualitatively describe the theory of heat conduction in a metal rod. Discuss the methods used in order to analyze the metal rod in this experiment (heat equation

and its initial and boundary conditions). Make sure to include your assumptions.

5 Procedure

Write a step-by-step procedure with enough detail so that a person reading your lab would beable to go through the experiment and reproduce similar results.

Include a diagram of the system setup.15 Results

Include all plots and tables of results from the lab questions.35 Analysis & Discussion

Discuss how you answered the lab questionsapproach methods and assumptions. Discuss results for each question. Discuss errors.

5 Conclusion

Summary of the entire experiment What you learned How to improve this for next year

5 References (including MATLAB code)

You will need to make sure that you reference are in the correct AIAA format. Look it up ifyou do not know.

90 TOTAL

Finally, this report is to be completed in the AIAA format as you will need to be familiar with this

format for senior year. Please visit the AIAA homepage1for FAQs regarding this format.

1AIAA Authors Toolkit; http://www.aiaa.org/content.cfm?pageid=899