Iterative of Nonlinear Functions
Someone please help, whenever i run my code I keep getting the same errors. My code and a screenshoot of the error page is attached.
% Given Values
k = 120;
alpha = 3.91e-6;
Ti=1073.15;
Tw=288.15;
Ta=288.15;
hw=100;
ha=10;
dt=10;
n_steps=60;
l=0.1;
tau=0.00391;
T1=zeros(n_steps,1);
T1(1,1)=Ti;
T2=zeros(n_steps,1);
T2(1,1)=Ti;
T3=zeros(n_steps,1);
T3(1,1)=Ti;
T4=zeros(n_steps,1);
T4(1,1)=Ti;
T5=zeros(n_steps,1);
T5(1,1)=Ti;
T6=zeros(n_steps,1);
T6(1,1)=Ti;
T7=zeros(n_steps,1);
T7(1,1)=Ti;
T8=zeros(n_steps,1);
T8(1,1)=Ti;
T9=zeros(n_steps,1);
T9(1,1)=Ti;
T10=zeros(n_steps,1);
T10(1,1)=Ti;
T11=zeros(n_steps,1);
T11(1,1)=Ti;
T12=zeros(n_steps,1);
T12(1,1)=Ti;
T13=zeros(n_steps,1);
T13(1,1)=Ti;
T14=zeros(n_steps,1);
T14(1,1)=Ti;
T15=zeros(n_steps,1);
T15(1,1)=Ti;
for i=1:(n_steps-1)
syms t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15
eqn1 = l*k*(ha+hw)*(Ta-T1(i))+(T6-T1(i))+(T2(i)-T1(i))==(t1-T1(i))/tau;
eqn2 = ha*l*(Ta-T2(i)+((T7(i)-T2(i))+(T3(i)-T2(i))+(T1(i)-T2(i))))==(t2-T2(i))/tau;
eqn3 = ha*l/k*(Ta-T3(i))+((T4(i)-T3(i))+(T8(i)-T3(i)+(T2(i)-T3(i))))==(t3-T1(i))/tau;
eqn4 = ha*l*(Ta-T4(i)+((T9(i)-T4(i))+(T3(i)-T4(i))+(T5(i)-T4(i))))==(t4-T4(i))/tau;
eqn5 = l*k*(ha+hw)*(Ta-T5(i))+(T10-T5(i))+(T4(i)-T5(i))==(t5-T5(i))/tau;
eqn6 = hw*l/k*(Ta-T6(i))+((T1(i)-T6(i))+(T7(i)-T6(i))+(T11(i)-T6(i)))==(t6-T6(i))/tau;
eqn7 = (T6(i)-T7(i))+(T8(i)-T7(i))+(T2(i)-T7(i))+(T12(i)-T7(i))==(t7-T7(i))/tau;
eqn8 = (T7(i)-T8(i))+(T9(i)-T8(i))+(T3(i)-T8(i))+(T13(i)-T8(i))==(t8-T8(i))/tau;
eqn9 = (T8(i)-T9(i))+(T10(i)-T9(i))+(T4(i)-T9(i))+(T14(i)-T9(i))==(t9-T9(i))/tau;
eqn10 = hw*l/k*(Ta-T10(i))+((T5(i)-T10(i))+(T9(i)-T10(i))+(T15(i)-T10(i)))==(t10-T10(i))/tau;
eqn11 = hw*l/k*(Ta-T11(i))+((T6(i)-T11(i))+(T12(i)-T11(i)))==(t11-T11(i))/tau;
eqn12 = hw*l/k*(Ta-T12(i))+((T13(i)-T12(i)+(T7(i)-T12(i))+(T11(i)-T12(i))))==(t12-T12(i))/tau;
eqn13 = hw*l/k*(Ta-T13(i))+((T12(i)-T13(i)+(T8(i)-T13(i))+(T14(i)-T13(i))))==(t13-T13(i))/tau;
eqn14 = hw*l/k*(Ta-T14(i))+((T13(i)-T14(i)+(T5(i)-T14(i))+(T9(i)-T14(i))))==(t14-T14(i))/tau;
eqn15 = hw*l/k*(Ta-T15(i))+((T14(i)-T15(i))+(T10(i)-T15(i)))==(t15-T15(i))/tau;
s = solve([eqn1 eqn2 eqn3 eqn4 eqn5 eqn6 eqn7 eqn8 eqn9 eqn10 eqn11 eqn12 eqn13 eqn14 eqn15],…
[t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15]);
nodal_temperatures = double(struct2array(s));
T1(i+1,1) = s(1);
T2(i+1,1) = s(2);
T3(i+1,1) = s(3);
T4(i+1,1) = s(4);
T5(i+1,1) = s(5);
T6(i+1,1) = s(6);
T7(i+1,1) = s(7);
T8(i+1,1) = s(8);
T9(i+1,1) = s(9);
T10(i+1,1) = s(10);
T11(i+1,1) = s(11);
T12(i+1,1) = s(12);
T13(i+1,1) = s(13);
T14(i+1,1) = s(14);
T15(i+1,1) = s(15);
end
% Display the results for the final temperatures
disp(‘Final Temperatures at Step 60:’);
disp([T1(60,1), T2(60,1), T3(60,1), T4(60,1), T5(60,1), T6(60,1), …
T7(60,1), T8(60,1), T9(60,1), T10(60,1), T11(60,1), T12(60,1),…
T13(60,1), T14(60,1), T15(60,1)]);Someone please help, whenever i run my code I keep getting the same errors. My code and a screenshoot of the error page is attached.
% Given Values
k = 120;
alpha = 3.91e-6;
Ti=1073.15;
Tw=288.15;
Ta=288.15;
hw=100;
ha=10;
dt=10;
n_steps=60;
l=0.1;
tau=0.00391;
T1=zeros(n_steps,1);
T1(1,1)=Ti;
T2=zeros(n_steps,1);
T2(1,1)=Ti;
T3=zeros(n_steps,1);
T3(1,1)=Ti;
T4=zeros(n_steps,1);
T4(1,1)=Ti;
T5=zeros(n_steps,1);
T5(1,1)=Ti;
T6=zeros(n_steps,1);
T6(1,1)=Ti;
T7=zeros(n_steps,1);
T7(1,1)=Ti;
T8=zeros(n_steps,1);
T8(1,1)=Ti;
T9=zeros(n_steps,1);
T9(1,1)=Ti;
T10=zeros(n_steps,1);
T10(1,1)=Ti;
T11=zeros(n_steps,1);
T11(1,1)=Ti;
T12=zeros(n_steps,1);
T12(1,1)=Ti;
T13=zeros(n_steps,1);
T13(1,1)=Ti;
T14=zeros(n_steps,1);
T14(1,1)=Ti;
T15=zeros(n_steps,1);
T15(1,1)=Ti;
for i=1:(n_steps-1)
syms t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15
eqn1 = l*k*(ha+hw)*(Ta-T1(i))+(T6-T1(i))+(T2(i)-T1(i))==(t1-T1(i))/tau;
eqn2 = ha*l*(Ta-T2(i)+((T7(i)-T2(i))+(T3(i)-T2(i))+(T1(i)-T2(i))))==(t2-T2(i))/tau;
eqn3 = ha*l/k*(Ta-T3(i))+((T4(i)-T3(i))+(T8(i)-T3(i)+(T2(i)-T3(i))))==(t3-T1(i))/tau;
eqn4 = ha*l*(Ta-T4(i)+((T9(i)-T4(i))+(T3(i)-T4(i))+(T5(i)-T4(i))))==(t4-T4(i))/tau;
eqn5 = l*k*(ha+hw)*(Ta-T5(i))+(T10-T5(i))+(T4(i)-T5(i))==(t5-T5(i))/tau;
eqn6 = hw*l/k*(Ta-T6(i))+((T1(i)-T6(i))+(T7(i)-T6(i))+(T11(i)-T6(i)))==(t6-T6(i))/tau;
eqn7 = (T6(i)-T7(i))+(T8(i)-T7(i))+(T2(i)-T7(i))+(T12(i)-T7(i))==(t7-T7(i))/tau;
eqn8 = (T7(i)-T8(i))+(T9(i)-T8(i))+(T3(i)-T8(i))+(T13(i)-T8(i))==(t8-T8(i))/tau;
eqn9 = (T8(i)-T9(i))+(T10(i)-T9(i))+(T4(i)-T9(i))+(T14(i)-T9(i))==(t9-T9(i))/tau;
eqn10 = hw*l/k*(Ta-T10(i))+((T5(i)-T10(i))+(T9(i)-T10(i))+(T15(i)-T10(i)))==(t10-T10(i))/tau;
eqn11 = hw*l/k*(Ta-T11(i))+((T6(i)-T11(i))+(T12(i)-T11(i)))==(t11-T11(i))/tau;
eqn12 = hw*l/k*(Ta-T12(i))+((T13(i)-T12(i)+(T7(i)-T12(i))+(T11(i)-T12(i))))==(t12-T12(i))/tau;
eqn13 = hw*l/k*(Ta-T13(i))+((T12(i)-T13(i)+(T8(i)-T13(i))+(T14(i)-T13(i))))==(t13-T13(i))/tau;
eqn14 = hw*l/k*(Ta-T14(i))+((T13(i)-T14(i)+(T5(i)-T14(i))+(T9(i)-T14(i))))==(t14-T14(i))/tau;
eqn15 = hw*l/k*(Ta-T15(i))+((T14(i)-T15(i))+(T10(i)-T15(i)))==(t15-T15(i))/tau;
s = solve([eqn1 eqn2 eqn3 eqn4 eqn5 eqn6 eqn7 eqn8 eqn9 eqn10 eqn11 eqn12 eqn13 eqn14 eqn15],…
[t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15]);
nodal_temperatures = double(struct2array(s));
T1(i+1,1) = s(1);
T2(i+1,1) = s(2);
T3(i+1,1) = s(3);
T4(i+1,1) = s(4);
T5(i+1,1) = s(5);
T6(i+1,1) = s(6);
T7(i+1,1) = s(7);
T8(i+1,1) = s(8);
T9(i+1,1) = s(9);
T10(i+1,1) = s(10);
T11(i+1,1) = s(11);
T12(i+1,1) = s(12);
T13(i+1,1) = s(13);
T14(i+1,1) = s(14);
T15(i+1,1) = s(15);
end
% Display the results for the final temperatures
disp(‘Final Temperatures at Step 60:’);
disp([T1(60,1), T2(60,1), T3(60,1), T4(60,1), T5(60,1), T6(60,1), …
T7(60,1), T8(60,1), T9(60,1), T10(60,1), T11(60,1), T12(60,1),…
T13(60,1), T14(60,1), T15(60,1)]); Someone please help, whenever i run my code I keep getting the same errors. My code and a screenshoot of the error page is attached.
% Given Values
k = 120;
alpha = 3.91e-6;
Ti=1073.15;
Tw=288.15;
Ta=288.15;
hw=100;
ha=10;
dt=10;
n_steps=60;
l=0.1;
tau=0.00391;
T1=zeros(n_steps,1);
T1(1,1)=Ti;
T2=zeros(n_steps,1);
T2(1,1)=Ti;
T3=zeros(n_steps,1);
T3(1,1)=Ti;
T4=zeros(n_steps,1);
T4(1,1)=Ti;
T5=zeros(n_steps,1);
T5(1,1)=Ti;
T6=zeros(n_steps,1);
T6(1,1)=Ti;
T7=zeros(n_steps,1);
T7(1,1)=Ti;
T8=zeros(n_steps,1);
T8(1,1)=Ti;
T9=zeros(n_steps,1);
T9(1,1)=Ti;
T10=zeros(n_steps,1);
T10(1,1)=Ti;
T11=zeros(n_steps,1);
T11(1,1)=Ti;
T12=zeros(n_steps,1);
T12(1,1)=Ti;
T13=zeros(n_steps,1);
T13(1,1)=Ti;
T14=zeros(n_steps,1);
T14(1,1)=Ti;
T15=zeros(n_steps,1);
T15(1,1)=Ti;
for i=1:(n_steps-1)
syms t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15
eqn1 = l*k*(ha+hw)*(Ta-T1(i))+(T6-T1(i))+(T2(i)-T1(i))==(t1-T1(i))/tau;
eqn2 = ha*l*(Ta-T2(i)+((T7(i)-T2(i))+(T3(i)-T2(i))+(T1(i)-T2(i))))==(t2-T2(i))/tau;
eqn3 = ha*l/k*(Ta-T3(i))+((T4(i)-T3(i))+(T8(i)-T3(i)+(T2(i)-T3(i))))==(t3-T1(i))/tau;
eqn4 = ha*l*(Ta-T4(i)+((T9(i)-T4(i))+(T3(i)-T4(i))+(T5(i)-T4(i))))==(t4-T4(i))/tau;
eqn5 = l*k*(ha+hw)*(Ta-T5(i))+(T10-T5(i))+(T4(i)-T5(i))==(t5-T5(i))/tau;
eqn6 = hw*l/k*(Ta-T6(i))+((T1(i)-T6(i))+(T7(i)-T6(i))+(T11(i)-T6(i)))==(t6-T6(i))/tau;
eqn7 = (T6(i)-T7(i))+(T8(i)-T7(i))+(T2(i)-T7(i))+(T12(i)-T7(i))==(t7-T7(i))/tau;
eqn8 = (T7(i)-T8(i))+(T9(i)-T8(i))+(T3(i)-T8(i))+(T13(i)-T8(i))==(t8-T8(i))/tau;
eqn9 = (T8(i)-T9(i))+(T10(i)-T9(i))+(T4(i)-T9(i))+(T14(i)-T9(i))==(t9-T9(i))/tau;
eqn10 = hw*l/k*(Ta-T10(i))+((T5(i)-T10(i))+(T9(i)-T10(i))+(T15(i)-T10(i)))==(t10-T10(i))/tau;
eqn11 = hw*l/k*(Ta-T11(i))+((T6(i)-T11(i))+(T12(i)-T11(i)))==(t11-T11(i))/tau;
eqn12 = hw*l/k*(Ta-T12(i))+((T13(i)-T12(i)+(T7(i)-T12(i))+(T11(i)-T12(i))))==(t12-T12(i))/tau;
eqn13 = hw*l/k*(Ta-T13(i))+((T12(i)-T13(i)+(T8(i)-T13(i))+(T14(i)-T13(i))))==(t13-T13(i))/tau;
eqn14 = hw*l/k*(Ta-T14(i))+((T13(i)-T14(i)+(T5(i)-T14(i))+(T9(i)-T14(i))))==(t14-T14(i))/tau;
eqn15 = hw*l/k*(Ta-T15(i))+((T14(i)-T15(i))+(T10(i)-T15(i)))==(t15-T15(i))/tau;
s = solve([eqn1 eqn2 eqn3 eqn4 eqn5 eqn6 eqn7 eqn8 eqn9 eqn10 eqn11 eqn12 eqn13 eqn14 eqn15],…
[t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15]);
nodal_temperatures = double(struct2array(s));
T1(i+1,1) = s(1);
T2(i+1,1) = s(2);
T3(i+1,1) = s(3);
T4(i+1,1) = s(4);
T5(i+1,1) = s(5);
T6(i+1,1) = s(6);
T7(i+1,1) = s(7);
T8(i+1,1) = s(8);
T9(i+1,1) = s(9);
T10(i+1,1) = s(10);
T11(i+1,1) = s(11);
T12(i+1,1) = s(12);
T13(i+1,1) = s(13);
T14(i+1,1) = s(14);
T15(i+1,1) = s(15);
end
% Display the results for the final temperatures
disp(‘Final Temperatures at Step 60:’);
disp([T1(60,1), T2(60,1), T3(60,1), T4(60,1), T5(60,1), T6(60,1), …
T7(60,1), T8(60,1), T9(60,1), T10(60,1), T11(60,1), T12(60,1),…
T13(60,1), T14(60,1), T15(60,1)]); for loop, iteration, nonlinear, multiple, iteration equation, simulation, mathematics MATLAB Answers — New Questions









