Solve multiple equations dependent on each other, knowing how one variable changes

This is what I had first but I'm stuck. An error pops up (Error using / Matrix dimensions must agree) in line 10 where I have s = (w+2)/N. So I tried the loop, I think I did something wrong with the loop because the answers are wrong compared to the actual. Final answers I'm trying to get are for q_c, q_f, T_b, T_tip, and volume of aluminum chip. I'm not sure how to resolve this. Thank you

w = 0.02;                                                % with of aluminum chip
k = 180;                                                 % W/(m*K)
Lb = 0.003;                                              % Base thickness, in meters
Lf = 0.012;                                              % Fin length, in meters
T_infinity = 20;                                         % degree C
T_chip = 85;                                             % degree C
A_b = w^2;                                               % Area of Base
Rt_cont = 0.00002/(A_b);                                 % Contact Resistance (K/W)

N = [3,4,5,6,7,8,9,10];                                  % Number of fins from 3 to 10 intervals of 1 
s = (w + 2)/N;                                           % Spacing between Fins
t = s - 2;                                               % Thickeness of Fins
P = 2*w + 2*t;                                           % Perimeter of Fin, in meters
A_f = 2*w*Lf;                                            % Area of Fin, in meters
A_t = N*A_f + (w^2) - (N*w*t);                           % Total Area
A_c = w*t;                                               % Cross sectional Area
Rt_cond = Lb/(k*A_b);                                    % Conduction Resistance (K/W)
m = sqrt((h*P)/(k*A_c))
n_f = tanh(m*Lf)/(m*Lf);                                 % Fin Efficiency
n_o = 1-((N*A_f)*(1-n_f))/(A_t);                         % Overrall Efficiency 
Rt_f = 1/(n_o*h*A_t);                                    % Fin Resistance
Req = Rt_cont + Rt_cond + Rt_f;                          % Total Resistance
q_c = (T_chip - T_infinity)/Req;                         % Changes depending on Req because req depends on Rt_f which changes depending on N
T_b = T_infinity + (q_c*Rt_f);
T_tip = T_infinity + ((T_b - T_infinity)*(1/(cosh(m*Lf))));
M = sqrt(h*P*k*A_c)*(T_b*T_infinity)*tanh(m*Lf);
q_f = M*tanh(m*Lf);

[Stephan]

h is not defined

Answer 1

[Stephan]

Hi,

due to N is a vector you have to use '.*' and './' to perform elementwise operations and avoid this error. Since h is not defined, i setted it equal to 1. It appears to work mow:

h = 1;
w = 0.02;                                                % with of aluminum chip
k = 180;                                                 % W/(m*K)
Lb = 0.003;                                              % Base thickness, in meters
Lf = 0.012;                                              % Fin length, in meters
T_infinity = 20;                                         % degree C
T_chip = 85;                                             % degree C
A_b = w^2;                                               % Area of Base
Rt_cont = 0.00002/(A_b);                                 % Contact Resistance (K/W)
N = [3,4,5,6,7,8,9,10];                                  % Number of fins from 3 to 10 intervals of 1 
s = (w + 2)./N;                                           % Spacing between Fins
t = s - 2;                                               % Thickeness of Fins
P = 2*w + 2*t;                                           % Perimeter of Fin, in meters
A_f = 2*w*Lf;                                            % Area of Fin, in meters
A_t = N.*A_f + (w^2) - (N.*w.*t);                           % Total Area
A_c = w*t;                                               % Cross sectional Area
Rt_cond = Lb/(k*A_b);                                    % Conduction Resistance (K/W)
m = sqrt((h*P)/(k*A_c));
n_f = tanh(m*Lf)/(m*Lf);                                 % Fin Efficiency
n_o = 1-((N*A_f)*(1-n_f))/(A_t);                         % Overrall Efficiency 
Rt_f = 1./(n_o.*h*A_t);                                    % Fin Resistance
Req = Rt_cont + Rt_cond + Rt_f;                          % Total Resistance
q_c = (T_chip - T_infinity)./Req;                         % Changes depending on Req because req depends on Rt_f which changes depending on N
T_b = T_infinity + (q_c.*Rt_f);
T_tip = T_infinity + ((T_b - T_infinity)*(1/(cosh(m*Lf))));
M = sqrt(h.*P*k.*A_c).*(T_b*T_infinity)*tanh(m*Lf);
q_f = M*tanh(m*Lf);

Best regards

Stephan