% Author: Housam Binous
% Free Convection Past a Vertical Flat Plate
% National Institute of Applied Sciences and Technology, Tunis, TUNISIA
% Email: binoushousam@yahoo.com
global Pr
% Prandtl number is Pr
% figure 1 gives velocity profile
% figure 2 gives temperature profile
% we find the boundary conditions at the surface using
% the outer fluid conditions thanks to fsolve
% a, the solution of fsolve, gives these surface boundary conditions
Pr=1
options=optimset('TolFun',1e-6,'TolX',1e-6);
a=fsolve(@derivation,[0.5 -0.6],options);
a
x0=[0 0 a(1) 1 a(2)];
[t,Y]=ode15s(@freeconv,[0 5],x0);
figure(1);
plot(t,Y(:,2),'r')
hold on
figure(2);
plot(t,Y(:,4),'r')
hold on
Pr=100
options=optimset('TolFun',1e-6,'TolX',1e-6);
a=fsolve(@derivation,[0.25 -2.0],options);
a
x0=[0 0 a(1) 1 a(2)];
[t,Y]=ode15s(@freeconv,[0 5],x0);
figure(1);
plot(t,Y(:,2),'b')
figure(2);
plot(t,Y(:,4),'b')
Pr=10
options=optimset('TolFun',1e-6,'TolX',1e-6);
a=fsolve(@derivation,[1 -1],options);
a
x0=[0 0 a(1) 1 a(2)];
[t,Y]=ode15s(@freeconv,[0 5],x0);
figure(1);
plot(t,Y(:,2),'g')
figure(2);
plot(t,Y(:,4),'g')
Pr=0.01
options=optimset('TolFun',1e-6,'TolX',1e-6);
a=fsolve(@derivation1,[1 -0.05],options);
a
x0=[0 0 a(1) 1 a(2)];
[t,Y]=ode15s(@freeconv,[0 5],x0);
figure(1);
plot(t,Y(:,2),'y')
figure(2);
plot(t,Y(:,4),'y')
