MATLAB Output
Part A Answers:
Case A: ε_f = 32.39, η_f = 0.7711.
Case B: ε_f = 25.96, η_f = 0.8652.
Part B Answers:
Case A: q_total = 114.22W, η_o = 79.64%.
Case B: q_total = 168.01W, η_o = 90.30%.
>>
MATLAB Code
clc;
%% Global Variables
w_a = 3e-3; w_b = 1e-3; L_a = 30e-3; L_b = 7e-3; H = 57e-3; W = 53e-3;
% physical dimensions
h_a = 125; h_b = 375; k = 175; Tb = 75; Tf = 25; % thermal properties
Nf_a = 54; Nf_b = 238; % # of fins
%% Design A
theta_b_a = Tb-Tf;
P_a = 4*w_a;
Ac_a = w_a^2;
Lc_a = L_a+w_a/2;
Af_a = P_a*Lc_a;
m_a = sqrt(h_a*P_a/(k*Ac_a));
qf_a = sqrt(h_a*P_a*k*Ac_a)*theta_b_a*tanh(m_a*Lc_a); % for single fin
theta_f_a = qf_a/(h_a*Ac_a*theta_b_a);
eta_f_a = qf_a/(h_a*Af_a*theta_b_a);
Ab_a = W*H-Ac_a*Nf_a;
A_total_a = Nf_a*P_a*Lc_a+Ab_a;
q_total_a = Nf_a*qf_a+h_a*Ab_a*theta_b_a;
eta_o_a = q_total_a/(h_a*A_total_a*theta_b_a);
eta_o_a = eta_o_a*100;
%% Design B
theta_b_b = theta_b_a;
P_b = 4*w_b;
Ac_b = w_b^2;
Lc_b = L_b+w_b/2;
Af_b = P_b*Lc_b;
m_b = sqrt(h_b*P_b/(k*Ac_b));
qf_b = sqrt(h_b*P_b*k*Ac_b)*theta_b_b*tanh(m_b*Lc_b); % for single fin
theta_f_b = qf_b/(h_b*Ac_b*theta_b_b);
eta_f_b = qf_b/(h_b*Af_b*theta_b_b);
Ab_b = W*H-Ac_b*Nf_b;
A_total_b = Nf_b*P_b*Lc_b+Ab_b;
q_total_b = Nf_b*qf_b+h_b*Ab_b*theta_b_b;
eta_o_b = q_total_b/(h_b*A_total_b*theta_b_b);
eta_o_b = eta_o_b*100;
%% Answers (Part A)
fprintf('Part A Answers: \n\n');
format_A = '\t Case A: \x03b5_f = %.2f, \x03b7_f = %.4f. \n \t Case B:
\x03b5_f = %.2f, \x03b7_f = %.4f. \n';
fprintf(format_A,theta_f_a,eta_f_a,theta_f_b,eta_f_b)
%% Answers (Part B)
fprintf('Part B Answers: \n\n');
format_B = '\t Case A: q_total = %.2fW, \x03b7_o = %.2f%%. \n \t Case
B: q_total = %.2fW, \x03b7_o = %.2f%%. \n';
fprintf(format_B,q_total_a,eta_o_a,q_total_b,eta_o_b);