Cross Sectional Integration

Dear Fellows,

I've got this problem since long time, and despite searching everywhere, I couldn't find the answer.
The problem is a heat transfer with fluid flow coupled.
I need to integrate over the xy plane at every z to get the function: Tmean(z)=integrate(T*u,dx,dy) /integrate(u,dx,dy)

u and T are the velocity and temperature fields.

Does anyone know how to do this?

Thanks in advance

Jorge Concepción