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

2019 2 28
1 个回答
更新时间：2019 2 28
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0 个投票

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);

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回答（1 个）

Stephan
Stephan 2019-2-28

0 个投票

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

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