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University of Arkansas

MEEG3212 April 6, 2014, Fort Smith, Arkansas, USA

010675548

PIN FIN CONVECTIVE HEAT TRANSFER

Brad Daniel Student - University of Arkansas

Fort Smith, Arkansas, United States

ABSTRACT Fins are useful in increasing the amount of heat transferred

from a body to its surroundings. Fins are commonly used in

electronics, heating/cooling systems, and various machines.

In this lab, the convective heat transfer coefficient of an

aluminum pin fin was to be determined experimentally. The pin

fin was heated at the base until steady state conditions could be

assumed. A computer model was generated based on the

temperature gradient of the pin.

The temperature gradient was determined by

experimentation. Changes in temperature along the length of

the pin fin were observed and noted by measuring the

temperature at various locations. The collected data was to be

used in the computer model to determine the value of the

convective heat transfer coefficient.

NOMENCLATURE h Convective heat transfer coefficient

p Perimeter

k Thermal conductivity

Ac Area of the cross section

L Length

Rate of heat transfer

INTRODUCTION In this experiment, we will determine the convective heat

transfer coefficient of the pin fin. The temperature of the

aluminum rod is a function of length assuming steady state

conditions. By making these assumptions, we can estimate the

value of h with a computer model based on temperatures taken

at increments of 1 inch along the rod.

This lab is based on the following objectives:

Measure the dimensions of the aluminum rod to be tested.

Generate a computer model using SolidWorks

Use a thermal analysis for the computer model to determine value of h.

Compare the model data with the theoretical concepts.

As a general statement, the heat transfer of a system is

determined by:

= ( ) (4.1)

(Cengel/Ghajar, 1)

It is assumed that the system is at steady state. Because this

concept is assumed, it can be said that , A, and are constant. Therefore, we must assume that T is a function of the

convective heat transfer coefficient, h.

Based on this assumption, we can determine the value of h

by collecting experimental values for T. Then, by modeling the

pin fin in the computer, we can vary the value of h to get close

to the experimental temperature profile.

When the approximate value of h is found, the temperature

profile can be graphed as a function of position on the fin. The

function generated by the computer data can be compared to

that of the actual experimental data.

EQUIPMENT

Calipers - To measure the test specimen

3D Modeling Software (SolidWorks) - To model

the pin fin and simulate a thermal analysis

Base Block - Aluminum block which the pin is

inserted.

Hot Plate - To supply the base block with heat

Water in glass beaker - To reduce the thermal

resistance from the hot plate to the base block

Lab Jack - Data acquisition device

Thermocouple - For temperature readings

Operation Amplifier - To amplify the voltage

signal from the thermocouple

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10k Resistor - For use with the Op-Amp

PROCEDURE To set up the experiment, the dimensions of the aluminum

bar and base block must be measured. The beaker is filled with

water and the base block is inserted into the beaker (Be sure to

begin with the water level as high as possible to ensure low

thermal resistance). The hot plate must be turned to the highest

setting. Allow the water to boil. While the pin fin is warming,

insert the pin fin into the furthest hole from the base block and

observe the temperature. When the temperature seems to level

off, we will assume steady state conditions. A sketch of the

setup can be seen in appendix 1.

Now that a steady state has been achieved, record the

temperature in each hole along the pin fin (Be sure to record the

temperature of the base block as well. This data will be used to

compare to the computer model.

The computer model is generated from the measured

dimensions and mass properties of the pin fin. 2024 aluminum

alloy was used as the model material. (note: the material was

determined according to the closest mass properties). Only the

length of the fin that extended from the base block was

modeled. The outer and end surfaces of the cylinder were

selected to model convective heat transfer. The other end was

set with a constant temperature to model a steady state from the

base block.

With the model correctly configured, run the thermal

simulation and guess the value of h. Use the probe tool to view

the temperature along the fin and compare the model to the

experimental data. When the model closely represents the

thermal profile of the experimental pin fin, export the

temperature data as an excel file using the probe tool and record

the value of h that was found.

Create graphs of the computer data and experimental data

to compare the results.

RESULTS Table 1 Pin Fin Temperature Profile displays the

temperature profile of the experimental data.

Table 1 Lab Data Temp(Kelvin) Distance(Inches)

324.2

1 324.6

2

325.7

3 327

4

328.4

5 331.1

6

333.8

7 336.9

8

340.9

9 345.3

10

349.8 11

The data was plotted in excel and compared to the data

collected from the thermal analysis as seen in Figure 2

Temperature Profile.

Trendlines were created to compare the results of the two tests

where temperature (in Kelvin) is a function of distance from the

base block (in inches).

For the experimental data:

() = 0.00123 + 0.26452 5.5844 + 355.24 (4.2) For the thermal analysis:

() = 0.00933 + 0.49142 7.8347 + 362.87 (4.3)

The convective heat transfer coefficient was determined by

evaluating the temperature of the location of the last hole in the

pin fin and was found to be 10.25 W/m*K. The value of h was

said to be determined when the temperature at 11 inches in the

computer model was the same as the experimental temperature

at 11 inches.

As the data in Figure 2 displays, the experimental and

computer functions converge toward the end.

The uncertainty in the recorded vs the theoretical values in

temperature can be observed by evaluating the two trendlines.

In this case, the uncertainty can be evaluated as a percent error

from the theoretical value. Assuming that the computer model

is completely correct, we find the following:

% =()()

() (4.4)

The functions are from the graph in figure 2. This gives the

error as a percent of the theoretical temperature determined in

SolidWorks at any given point on the pin fin.

DISCUSSION The convective heat transfer coefficient was hard to

determine because it required a guess and check method. Compared to the Temperatures in the computer model, the test

data was fairly accurate. It should be noted that although some

losses may not have been accounted for, the temperature

trendlines did converge toward the end of the pin fin.

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Some losses may be due to the base losing more heat than

expected because the water in the beaker evaporated during the

duration of the experiment. Another factor of error could result

from the air conditioner vents being above the desks in the lab

creating some forced external convection on the fin. It should

however be noted that the temperature at each hole was better

measured when a small drop of water was inserted before using

the thermocouple to collect data.

The experiment could be improved by increasing the

length of the fin as well as decreasing the diameter so that it

could be assumed that the end temperature of the fin is equal to

T. By making this assumption, the fin could be modeled as an

infinitely long pin fin. This would allow the heat transfer coefficient to be calculated truly theoretically with relative

ease. The temperature of the pin fin at any point could then be

determined theoretically and compared to the expiramental

data.

REFERENCES

1. Yunus A. Cengel and Afshin J. Ghajar

Heat and Mass Transfer Fundamentals

and Applications. P.163, 3-6 Heat

Transfer From Finned Surfaces

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APENDIX 1

LAB DATA

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