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Dear Ghorrocks,

Can I expect that my post #12 using sub domain option is modeling the periodic part of the temperature profile correctly ?

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For constant heat flux condition, the temperature can be represented as:

T = T(periodic)+gamma*X; gamma is global temperature rise.

T(periodic, X)=T(Periodic, x+L); L is length of period

[Opaque]

Your nomenclature is a bit confusing since it uses 1 or 2 arguments.

For a uniform (and constant) heat flux boundary condition, the fully developed temperature profile is linear in the streamwise direction; therefore, it can be said that for section of the pipe in the developed region and periodic sub-model can be set using a boundary condition such as

Tb (X+L) = Tb(X) + Delta_T

where Delta_T is determined a energy balance between those two sections. Since we know the length of the section, superficial area of the heat flux boundary, mass flow and specific heat capacity, we can write

areaIntegral (density* velocity * Cp * T(X+L)) - areaIntegral (density * velocity * Cp * T(X)) = HeatFlux * Superficial Area

by definition of bulk temperature, the above can be written as

massFlowCp * (Tb(X+L) - Tb(X)) = HeatFlux * Superficial Area

therefore,

Tb(X+L) = Tb(X) + HeatFlux * Superficial Area / massFlowCp

For constant property materials, it can also be written for the local distribution, say radial

T(X+L, r) = T(X,r) + HeatFlux * Superficial Area / massFlowCp

Question: how are you imposing the translational periodicity with a temperature jump ?

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I am following the similar analysis. So, I am solving for the periodic part of temperature using source term in the subdomain (Post # 12). As you can see, the temperature at inlet and outlet are in good match.
Next, to obtain the actual temperature, I have to just subtract Delta_T, which can be obtained using gamma*X.
I get good results; but the only problem is nusselt number value which is coming near about 6.07.

Here, basically I am solving for the periodic temperature using source term giving

T(X+L, r) = T(X,r)

For temperature jump, i need to return back to my actual temperature.