Example 12.4-1 Heat Transfer in Forced Convection Laminar Flow along a heated Flat Plate.   
We start with the equations we checked in sec124.mws. 
First eq. 12.4-4 leaving out the gravitational term.
>  restart;
>  Ibook1:=mu*D[2](vx)(x,0);
>  Ibook2:=-rho*diff(int(vx(x,y)*(ve(x)-vx(x,y)),y=0...b),x);
>  Ibook3:=-rho*D(ve)(x)*int(ve(x)-vx(x,y),y=0..b);
>  Ibmot:=Ibook1+Ibook2+Ibook3;
>  ve:=x->vinf;
>  Ibmot;
Now using 12.4-6,7 for the assumed velocity profile in the boundary layer.
>  vx:=(x,y)->vinf*(2*y/delta(x)-2*(y/delta(x))^3+(y/delta(x))^4);
>  Ibmot;
>  b:=delta(x);Ibmot; The integration should go only to delta(x)
>  s:=dsolve({Ibmot,delta(0)=0},delta(x));
>  assign(s[1]);delta:=unapply(delta(x),x);
Now looking at the energy equation: 12.4-5
>  Ieb1:=k*D[2](T)(x,0);
>  Ieb2:=-rho*Cphat*diff(int(vx(x,y)*(Tinf(x)-T(x,y)),y=0...be),x);
>  T:=(x,y)->T0-(T0-Tinf0)*(2*y/deltaT(x)-2*(y/deltaT(x))^3+(y/deltaT(x))^4);

>  Tinf:=x->Tinf0;
>  deltaT:=x->Delta*delta(x);
>  Ieb2;
>  be:=Delta*delta(x); If Delta<1, the integrand will be zero for y>deltaT

>  Ieb:=simplify(Ieb1+Ieb2);
>  Cphat:=Pr*k/mu;
>  simplify(Ieb);

>  eq12414:=2*Delta^3/15-3*Delta^5/140+Delta^6/180-37/Pr/315; Eq. 12.4-14
>  simplify(7*180*eq12414*Pr); Obviously Ieb will be zero if eq. 12.4-14 is satisfied.
>  Pr1:=solve(Ieb,Pr);
>  Pr1:=unapply(Pr1,Delta);
>  Pr1(1);
>  Pr1(0.5);
>  with(plots):
>  loglogplot(Pr1(x),x=.2...1,color=blue);