I am trying to evaluate integral (-1/rho)*del (p)/del (x) dy within the limits y=0 to y=delta (x). For that I first evaluated (-1/rho)*del (p)/del (x) and stored it in res2. Then I tried to integrate it w.r.t dy within limits 0 to delta (x). I wrote the following Maple lines for the purpose:

Te := proc (x, y) options operator, arrow; T[inf]+(T[w]-T[inf])*(1-y/delta[t](x))^2/(1+2*A*H/delta[t](x)) end proc

PDE := diff(P(x, y), y)-rho*g*beta*(Te(x, y)-T[inf]) = 0

restart

u := proc (x, y) options operator, arrow; u[x](x)*(y/delta(x)-2*y^2/delta(x)^2+y^3/delta(x)^3+B*H*(1-3*y^2/delta(x)^2+2*y^3/delta(x)^3)/delta(x))/(3*B*H/delta(x)+2) end proc

int(u(x, y)^2, y = 0 .. delta(x))

I tried the following partial integration in MAPLE. But Maple says:

Error, (in u[x]) too many levels of recursion.

Analytically it is possible to evaluate the integral in the above lomits. Where lies the problem?

I wrote the following MAPLE lines to determine the three constants a, b and c from three boundary conditions. Whatever a, b and c I get as result are correct. Now I want to substitute back the values of obtained a, b and c in the expression for Te to obtain the resulting temperature distribution. I used both algsubs(a, b, c, Te) and subs(a, b, c, Te) one by one to substitute a, b and c in the expression for Te and get the result. But both way it is showing...

I wrote the following Maple lines:

I wrote the following lines in MAPLE: