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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:

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

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...