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Heat Transfer In this project, you will perform analysis on a two-dimensional fin. The fin is made of aluminum (k = 200 W/mK, ρ = 2700 kg/m3 , cp = 890 J/kgK, α = 8.4x10-5 m2 /s and is 5 cm long and 1 cm thick. The fin is initially at a uniform temperature of 250 deg C, when it is exposed to a convective environment with an ambient temperature of 25 deg C and an arbitrary heat transfer coefficient. The base temperature remains at 250 deg C. 1. Create a program that will solve the two-dimensional temperature distribution of the fin for elapsed times of 3, 30, and 300 s, and h = 400, 4000 and 40000 W/m2K (a total of 9 configurations). Also find the steady state temperature distribution for all 3 h values and the amount of time it takes to reach that state (in seconds). Use a grid size of 0.25 cm. Present your temperature data using contour plots and line graphs. a. Compare your centerline steady state data to the temperature profiles created using the fin theory in chapter 3. For each h value case, what type of fin best models your data? Explain why. b. Use your program to calculate the amount of heat lost (NOT the rate) by the fin in each transient and steady state case, and present that data in a table. c. Use your program to calculate the steady state heat transfer rate of the fin in each case. Compare these values to the predicted values using fin theory Present all of your findings in a simple report. The report should begin with a cover page, including your name, the date, and the UOSA Academic Integrity Pledge: “On my honor I affirm that I have neither given nor received inappropriate aid in the completion of this exercise” along with your signature (your report will not be accepted without a signature). While an introduction and theory section is not necessary, you should include enough explanation throughout the report so that your findings are understood. Include your program codes, fully commented, in text within your report. You will also submit your codes electronically for verification. You are free to use any programming package to complete the assignment except for modeling packages such as ANSYS or FLUENT (you MUST program using the principles demonstrated in class). The project will be graded as follows:

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Tb = 250;
Tair = 25;
L=0.05;
W=0.01;
t = 0.01;
k=200;
%% h = 400
h1=400;

Ac=W*t; %% consider unit cross section
p=2*(W+t); %% perimeter
M=sqrt(h1*p*k*Ac)*(Tb-Tair);
m=sqrt((h1*p)/(k*Ac));
U=M*tanh(m*L);

qf1=M*(sinh(m*L)+h1*cosh(m*L)/(m*k))/(cosh(m*L)+h1*sinh(m*L)/(m*k))
Ttip1=(Tb-Tair)*(1/(cosh(m*L)+h1*sinh(m*L)/(m*k)))+Tair%% h = 400
h1=400;

Ac=W*t; %% consider unit cross section
p=2*(W+t); %% perimeter
M=sqrt(h1*p*k*Ac)*(Tb-Tair);
m=sqrt((h1*p)/(k*Ac));
U=M*tanh(m*L);

qf1=M*(sinh(m*L)+h1*cosh(m*L)/(m*k))/(cosh(m*L)+h1*sinh(m*L)/(m*k))
Ttip1=(Tb-Tair)*(1/(cosh(m*L)+h1*sinh(m*L)/(m*k)))+Tair;

%% h = 4000
h2=4000;

Ac=W*t; %% consider unit cross section
p=2*(W+t); %% perimeter
M=sqrt(h2*p*k*Ac)*(Tb-Tair);
m=sqrt((h2*p)/(k*Ac));
U=M*tanh(m*L);

qf2=M*(sinh(m*L)+h2*cosh(m*L)/(m*k))/(cosh(m*L)+h2*sinh(m*L)/(m*k))
Ttip2=(Tb-Tair)*(1/(cosh(m*L)+h2*sinh(m*L)/(m*k)))+Tair

%% h = 400
h3=40000;

Ac=W*t; %% consider unit cross section
p=2*(W+t); %% perimeter
M=sqrt(h3*p*k*Ac)*(Tb-Tair);
m=sqrt((h3*p)/(k*Ac));
U=M*tanh(m*L...

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