Example 3.2.10 Blasius Equation - Infinite Domains

The Blasius problem is defined by:[22][12]

f

with the boundary conditions

f(0)=0 (3.3.25)

and

This boundary value problem is different from other boundary value problems discussed in this chapter because equation (3.2.24) is a third order ODE with three boundary conditions. In addition, the domain is semi-infinite. This boundary value problem is solved in Maple below by replacing ∞ in equation (3.2.27) by 10.

> | restart:

> | with(plots):

> | eq:=f(eta)*diff(f(eta),eta$2)+2*diff(f(eta),eta$3);

| (1)

> | BCs:=(f(0),D(f)(0),D(f)(10)-1);

| (2)

> | sol:=dsolve({eq,BCs},{f(eta)},type=numeric);

| (3)

The solution for η = 0 and η = 10 are obtained as:

> | sol(0);

| (4)

> | sol(10);

| (5)

The solution obtained is plotted below:

> | odeplot(sol,[eta,f(eta)],0..10,thickness=4,color=red,title="Figure Exp. 3.2.19.",axes=boxed);

> | odeplot(sol,[eta,diff(f(eta),eta)],0..10,thickness=4,color=green,title="Figure Exp. 3.2.20.",axes=boxed);

> |