Pipe flow heat transfer
 

Hello,

For calculating heat transfer in laminar, incompressible pipe flow, I am using PISO with NS and energy equation. As a solution to energy equation, I see heat is transferred due to diffusion only. There is no convection (though convection term is included in the energy equation) observed in the flow. I tried increasing Reynolds number and Prandtl number still no effect.
The boundary conditions for temperature are: T = 20C at the Inlet, T = 0 at the output and Neumann BC for temperature on the walls. The graph I got is a linear drop in temperature.

Any one can help ?

The outlet boundary condition for your case is wrong but the convection scheme is taking care of it.

As there is no transversal difference in temperature (Neumann at the walls), the axial propagation is the only one that matters, but only the diffusion can sense the outlet bc.

Also, flow is probably fully developed and laminar, so the convection effects at the interior (which are nonetheless present) are negligible, even in the developing zone.

Thank you so much for your reply. What should be the outlet condition then? Neuman at the outlet too?

Typically yes, but with Neumann at walls you are not going to see anything. So, the question is, what do you want to study in the first place?

I want to analyze the heat transfer due to convection/diffusion in a channel(cartesian coordinates) and in a tube (axisymmetric coordinates). As there is no heat generation and removal, therefore insulated walls are considered.
With the same boundary conditions, Neumann at the walls, Dirichlet at the inlet/Outlet, Fluent gives correct profile and considers heat transfer due to convection but in Fortran only diffusion is observed.

Correct here is really a misnomer because the outlet bc is not exactly well posed.

However, let's put things in order.

For steady, incompressible flows, temperature is just a transported scalar. I assume that your flow part is correctly solved. I also guess you are using a constant velocity profile at inlet, so that the two cases (channel and pipe) will have slightly different flow development zones and fully developed profiles.

I am sure that Fluent can correctly solve this case but, in Fluent, you are not free to use an outlet bc and also assign a temperature (backflow temperature is used only in certain cases that are supposed to not be present at convergence here). So, first question first, what conditions/schemes are you using in Fluent?

Second question: what schemes are you using in your Fortran code? Do they match the Fluent ones, at least roughly?

Third question: is your Fortran code solving the flow part correctly?

Considering your case, you seem to then be interested in a pseudo 1D case, where the difference between channel and pipe is only due to the different profiles and development zones (which, however, I expect to be quite similar). However, a constant temperature profile and Neumann at walls, really imply that temperature just behaves as a 1D field because, assuming a sufficiently long channel/pipe, the transversal velocity is non negligible only in the development zone where the temperature is uniform, with no practical effect on it. This brings the fourth question:

What sort of convective effects do you see in Fluent? A temperature profile at a given section (as opposed to a constant profile at the same section) or the classical effect you see in the 1D steady, convection-diffusion equation?