// example24.edp from chapter3/thermal.edp
verbosity = 0;
func u0 = 10 + 90*x/6;
func k = 1.8 * (y<0.5) + 0.2;

real ue = 25, alpha = 0.25, T = 5, dt = 0.1 ;

mesh Th=square(30,5,[6*x,y]);
fespace Vh(Th,P1);
Vh u=u0,v,uold;

// for the flat plate
problem thermic(u,v)= int2d(Th)(u*v/dt + k*(dx(u) * dx(v) + dy(u) * dy(v)))
                + int1d(Th,1,3)(alpha*u*v)
                - int1d(Th,1,3)(alpha*ue*v)
                - int2d(Th)(uold*v/dt) + on(2,4,u=u0);

// write a 2-column file
ofstream ff("example24.dat");
for(real t=0; t < T + dt/100.; t += dt){
    uold=u;
    thermic;
    ff << t << " " << u(3,0.5) << endl;
    plot(u);
}