# Physics

NORTHEASTERN UNIVERSITY

DEPARTMENT OF MECHANICAL ENGINEERING TECHNOLOGY

MET3601 – HEAT TRANSFER ENGINEERING

Lab 2: Fin Analysis

1 GOALS

The primary goals of this experiment are:

1. To measure the temperature distribution along the length of a fin 2. To compare the temperature distribution with the distribution calculated using the equations developed for

differing boundary conditions

2 OVERVIEW OF EXPERIMENT

In this experiment, you will be exploring the steady-state temperature distribution along fins of different lengths. As

shown in Figure 1, the setup consists of a flat heater with a fin clamped to it, sensors to measure temperature, and

power for the heater. You will supply power to the heater, allow the system to reach steady-state, and then record the

temperatures along the length of the fin. This will be repeated for fins of different length. The data will allow you see the

differences between the different boundary condition assumptions, compared to actual data.

Figure 1: Experimental setup

3 RELEVANT THEORY

In analyzing fins, we make several simplifying assumptions. We assume that the thermal conductivity, k, of the fin

material is a constant. We also assume that the convection heat transfer coefficient, h, is constant and uniform over the

entire surface of the fin. An energy balance on the fin results in a second-order differential equation. In order to obtain

the specific solution to this equation, two boundary conditions are needed. One boundary condition, at the base of the

fin, is obtained by specifying the temperature at the base, Tb. The boundary condition at the other end of the fin, the

tip, can be set several ways. Each of these tip boundary conditions, has an assumption associated with it.

If we assume that the fin is long enough that the fin tip remains at the temperature of the surrounding environment

(L = β T(L) = Tβ), the solution to the energy balance equation yields the following equations for the temperature

distribution along the fin (1) and the rate of heat transfer to (or from) the fin (2):

(1)

(2)

Where Tb is the temperature at the base of the fin, Tβ is the temperature of the environment around the fin, h is the

convection heat transfer coefficient, p is the perimeter of the fin, k is the thermal conductivity of the fin, and AC is the

cross-sectional area of the fin.

A second approach is to assume that there is no heat transfer from the end of the fin. In this case, we have:

(3)

(4) where ππ = οΏ½βππ πππ΄π΄πΆπΆοΏ½ .

A third possibility, is that the heat transfer from the end of the fin is not negligible, and that we need to consider the

heat transfer from the end of the fin. With this boundary condition assumption, we get:

(5)

(6)

A fourth possible boundary condition, that of having the temperature at the tip of the fin known, and held constant,

would not apply to this situation.

It will be up to you to determine whether equation 1, 3, or 5 best reflects the temperature distribution data that you collect, and to justify your conclusions.

4 SENSORS

Temperature measurement will be accomplished using the SensorDAQ and five or more K-type thermocouples. These

thermocouples will be wire type thermocouples, and can be taped onto the surface of the fins. Power to the heater will

be both provided and measured by the combination of a power meter and power supply, as shown in Figure 2, below.

Figure 2: Power supply for heater

The specs for the heater are found here: http://www.chromalox.com/catalog/resources/MOD-SN-WS.pdf .

5 LAB PROCEDURE

Safety Notes: Please note that the heater gets very hot, very quickly. Take care not to bump into the heater during your experiment, and make sure the thermocouples are securely fixed in place and the heater is secure on the stand before

starting.

1. Check to confirm that all of the thermocouples are connected and reading correctly. 2. Tape the thermocouple wires to the fin at the locations marked. It is important to make sure each

thermocouple is securely in contact with the fin. The other end of the thermocouple should be connected to

the SensorDAQ.

3. The heater should be plugged into the power meter, and that should be plugged into one of the 240V outlets on the power supply (see Figure x). Verify all connections.

4. Turn on the power supply. Start recording the temperature in LabView, watching for when the temperatures stabilize.

5. Record ambient air temperature, all final fin temperatures, and the heater power reading. 6. Disconnect the heater, and wait until the temperature at the base is below 100 oF. 7. Attached the other fin to the heater, and repeat steps 3 and 4.

6 RESULTS

1. In a well labeled table, present the data gathered for the power input, fin temperatures, and ambient temperature, and any constants you used. Be sure to state units. In your write up, explain what equations you

used and define all variables and constants clearly.

2. Plot temperature vs. location for each temperature measured. 3. Plot the temperature vs. location as calculated using the various boundary condition approximations discussed

in the Relevant Theory section, above.

7 ANALYSIS

1. Compare the approximation relationships to your experimental data. Did you see a similar relationship among them?

2. Does equation 1, 3, or 5 best fit with your data? What differences exist, and how do you explain them? 3. Are there any modifications that could be made to the experimental setup that you think would improve your

data? If so, describe the modifications and what their impact would be.

8 DELIVERABLES

The results for this lab should be written up in the standard lab report format. All the questions above must be

addressed (as a minimum) to get full credit. Please refer to the Lab Report Format document on Blackboard for the

correct report format and other details. The report is due at the beginning of the following lab period. Note that this is a group lab report, so only one person in the group needs to submit the report along with the cover sheet with the percent contribution from each group member.

- 1 Goals
- 2 Overview of Experiment
- 3 Relevant Theory
- 4 Sensors
- 5 Lab Procedure
- 6 Results
- 7 Analysis
- 8 Deliverables