Once modeling convective heat transfer problems through internal channels we normally ignore axial heat conduction. How valid is this assumption? I believe it has a relationship with the Pecelet number.
I am not master on the subject but recently we were doing heat transfer problem within the laminar boundary layer over a certain type of body. At parameters where the curvature of the body was large we found that the local Nusselt number was decreasing. We concluded that conduction dominated while at other parts of the body where the curvature was smaller the Nusselt number increased comparatively. There it was sensible that convection effects dominated. Your problem might be totally of different nature. Like you may work in potential inviscid flows and I don't know in that case.
Axial heat conduction in the fluid becomes more important at low Peclet number. It's hard to say what is a low Peclet number exactly. Axial conduction through the channel walls may also be significant even if conduction in the fluid is not.
Peclet number based on the channel length (or alternatively thermal entry length) needs to be approximately 1 or less than 1, in order for the axial conduction to have an effect that is similar to or stronger than the convection. If it is approximately one, then axial conduction has similar strength as the convection, while if it is less than one it is stronger. Pe_l = (u_c * l )/alpha .
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