% Conduction of heat in a semiinfinite slab with the x=0 surface varying
% sinusiodally in time with amplitude T0 and radian frequency omega.
% The diffusivity is kappa=k/(rho*c)
% This m-file was written at the University of Wyoming in the Electrical
% and Computer Engineering Department and is to be distributed without
% cost.
clear all
set(0,'DefaultAxesFontSize',12);
set(0,'DefaultTextFontSize',12);
figure(1);clf
figure(2);clf
figure(3);clf
figure(4);clf
omegat=linspace(0,20,201);
betax=linspace(0,10,101);
Tdata=[];
for i=1:201
    T=exp(-betax).*sin(omegat(1,i)*ones(1,101)-betax);
    Tdata=[Tdata;T];
end

figure(1);% Plot T(x,t) vs x for various t
xlabel('Dimensionless Distance, \betax')
hold on
ylabel('Dimensionless Temperature, T(x,t)/T_0')
for k=1:4:49
    plot(betax,Tdata(k,:),'k')
    hold on
    axis([0 10 -1.2 1.2]);
    hold on
    %pause
end
text(6,-.8,'\beta = sqrt(\omega/2*\kappa)')
text(1.2, -.3,'\omegat = 0')
text(6,-1 ,'\Delta(\omegat) = 0.4')
set(gca,'Box','on')
text(6,.8,'Press Enter to Continue')
pause

figure(2)%Plot T(x,t) vs t for various x
for j=1:4:101
    plot(omegat, Tdata(:,j));
    hold on
    axis([0 10 -1.2 1.2]);
    hold on
end
text(6,-1,'\Delta(\betax) = 0.4')
text(2.5,.8,'\betax = 0')
xlabel('Dimensionless Time, \omegat')
ylabel('Dimensionless Temperature, T(x,t)/T_0')
text(6,-.8,'\beta = sqrt(\omega/2*\kappa)')
text(12,.8,'Press Enter to Continue')
pause

figure(3)%now do animation
axis([0 10 -1.2 1.2])
hold on
box on
xlabel('Dimensionless Distance, \betax')
hold on
ylabel('Dimensionless Temperature, T(x,t)/T_0')
hold on
L=plot(betax, Tdata(1,:),'k','EraseMode','xor');
hold on
texthandl=text(6, .8,'Press Enter to Animate');
pause
set(texthandl,'String','                       ');
for i=1:201
    set(L,'Ydata',Tdata(i,:))
    pause(.04)
end
hold on
set(texthandl,'String','Press Enter to Continue');
pause
    
figure(4)%3-D Plot of T(x,t) vs x and t
Tdata2=[];
for i=1:2:201
    Tdata2=[Tdata2;Tdata(i,:)];
end
axis([0 20 0 10 -1.2 1.2])
omegat2=linspace(1,20,101);
[X,Y]=meshgrid(omegat2,betax);
mesh(X,Y,Tdata2')
colormap([0 0 0])%cool)
text(0, 1, -2.,'Time,\omegat','Rotation',-30)
text(20, 4, -1.7,'Distance, \betax','Rotation',13)
zlabel('Dimensionless Temperature, T(x,t)/T_0')
text(0,6,.7,'Press Enter to Continue')
view(60,30)
axis([0 20 0 10 -1.2 1.2])