solve thFile: Copy_of_heattransfer.m Line: 18 Column: 13 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for misme error

k_steel = 50; %w/m-k conductivity

k_copper = 500;

[xs,ts,u_steel,flux_s] = FDM(k_steel); % Temperature distribution in steel rode

[xc,tc,u_copper,flux_c] = FDM(k_copper); % Temperature distribution in copper rode

figure()

plot(ts,u_steel(:,6),tc,u_copper(:,6),'LineWidth',3)% Maximum temperature

title('Maximum Temperature Distribution')

xlabel('Time (s)')

ylabel('Maximum Temperature (Degree C)')

legend('Steel','Copper')

figure ()

plot(ts,flux_s,tc,flux_c,'LineWidth',3)% Maximum temperature

title('Heat Flux')

xlabel('Time (s)')

ylabel('Heat Flux (W/m^2)')

legend('Steel','Copper')

function[x,t;u;flux]= FDM(k) % Explicit finite difference methode

rho = 8000; %kg/m3 densityk_steel

cp = 400; %J/kg-k specific heat

q = 5000; %W/m3 Heat generation rate

dx = 0.1; %m step size

alpha = k/(rho*cp);

dt = 25;

%dt = 0.5*dx^2/alpha;

if k == 50

tle = 'Steel';

else

tle = 'Copper';

end

x = 0:dx:1;

t = 0:dt:2000;

u0 = -q/(2*k)*x.^2+q/(2*k)*x+30;

u = zeros(length(t),length(x));

u(1,:) = u0;

u(:,1) = 30;

u(:,end) = 30;

for i = 1:(length(t)-1)

for j = 2:length(x)-1

u(i+1,j) = u(i,j)+dt*alpha/dx^2*(u(i,j-1)-2*u(i,j)+u(i,j+1));

end

end

flux = -k*(u(:,2)-u(:,1))/dx;

[X,T] = meshgrid(x,t);

figure()

surf(X,T,u)

xlabel('Length (m)')

ylabel('Time (s)')

title(tle)

figure()

plot(x,u(find(t==500),:),x,u(find(t==1000),:),x,u(find(t==1500),:),x;u(find(t==2000,:);'LineWidth';3)

legend('t= 500 s','t= 1000 s','t= 1500 s','t= 2000 s')

xlabel('Length (m)')

ylabel('Temperature (Degree C)')

title(tle)

end

Answer 1

[VBBV]

k_steel = 50; %w/m-k conductivity
k_copper = 500;
[xs,ts,u_steel,flux_s] = FDM(k_steel); % Temperature distribution in steel rode

[xc,tc,u_copper,flux_c] = FDM(k_copper); % Temperature distribution in copper rode

figure(1)
plot(ts,u_steel(:,6),tc,u_copper(:,6),'LineWidth',3)% Maximum temperature
title('Maximum Temperature Distribution')
xlabel('Time (s)')
ylabel('Maximum Temperature (Degree C)')
legend('Steel','Copper')

figure(2)
plot(ts,flux_s,tc,flux_c,'LineWidth',3)% Maximum temperature
title('Heat Flux')
xlabel('Time (s)')
ylabel('Heat Flux (W/m^2)')
legend('Steel','Copper')

function[x,t,u,flux]= FDM(k) % Explicit finite difference methode
    rho = 8000; %kg/m3 densityk_steel
    cp = 400; %J/kg-k specific heat
    q = 5000; %W/m3 Heat generation rate
    dx = 0.1; %m step size
    alpha = k/(rho*cp);
    dt = 25;
    %dt = 0.5*dx^2/alpha;
    if k == 50
        tle = 'Steel';
    else
        tle = 'Copper';
    end
    x = 0:dx:1;
    t = 0:dt:2000;
    u0 = -q/(2*k)*x.^2+q/(2*k)*x+30;
    
    u = zeros(length(t),length(x));
    
    u(1,:) = u0;
    u(:,1) = 30;
    u(:,end) = 30;
    for i = 1:(length(t)-1)
        for j = 2:length(x)-1
            u(i+1,j) = u(i,j)+dt*alpha/dx^2*(u(i,j-1)-2*u(i,j)+u(i,j+1));
        end
        
    end
flux = -k*(u(:,2)-u(:,1))/dx;
[X,T] = meshgrid(x,t);
figure()
surf(X,T,u)
xlabel('Length (m)')
ylabel('Time (s)')
title(tle)
figure()
plot(x,u(find(t==500),:),x,u(find(t==1000),:),x,u(find(t==1500),:),x,u(find(t==2000),:),'LineWidth',3)
legend('t= 500 s','t= 1000 s','t= 1500 s','t= 2000 s')
xlabel('Length (m)')
ylabel('Temperature (Degree C)')
title(tle)
end

[VBBV]

In the below lines, there are misplaced parenthesis used for plot function and also for vector u at different times

plot(x,u(find(t==500),:),x,u(find(t==1000),:),x,u(find(t==1500),:),x,u(find(t==2000),:),'LineWidth',3)

There are also ; being used as separaters for plotting multiple data sets in plot function. Matlab recommends to use comma , instead