given the equation

Tm(x) = Tm(i) + (q"*P*x)/(mdot*Cp)

If I know my mdot can I make the equation into a local temperature for a finite difference scheme? For example, if I have 25 nodes perpindicular to the flow, can I take the mdot and divide it by 25 and assume the each node gets 1/25 of the total mdot and then calculate the Temp at that node? My problem is that I have boundary conditions at each of the 4 walls that contain no reference to the flow velocity. So, when I change velocities my temperature profile does not change. I can get the temperature at each of the boundaries, but I am having trouble getting the temperature within the grid. I wanted to take the above equation and use it for the temperature above the heated wall and then go from there.

thanks

what is your problem i just do not understand what the meaning of mdot ! since you have know the temerature at the boundary, why you have problem within grid.

mdot is mass flow rate - sorry

I have a problem inside the grid because I have velocities. My boundary conditions do not involve velocity, so when I change velocities my temperatures don't change.

thanks

for the fully developed channel flow, the dimensionless temperature is constant, it has no relation with velocity

yes, I know that. But, if I change my velocity for an entirely new problem my temperatures do not change. For example, if I want to compare the heat transfer characteristics at a Re of 10 and an Re of 1000. In my current set-up I get the same answer regardless.