Laminar pipe flow has an analytical solution, have you checked that? What about the temperature BCs?

I mean here, laminar mixed convection.

regarding to boundary condition,

inlet section: we have inlet velocity and inlet temperature.

outlet section: we have pressure outlet (gauge pressure = 0) and back flow temperature (300 as default).

at the wall: constant heat flux.

regarding to material:

*density sets as boussinesq hypothesis and reference temperature is the same of inlet temperature.

*thermal expansion coefficient of water,

operating conditions:

*activate gravity in the opposite y direction,

*refernce temperature is the same of inlet temperature,

Methods:

SIMPLE algorithm for velocity-pressure,

Seconde order upwind scheme for pressure, momentum,and energy,

Under relaxation factor as a default,

initialization:

standard intialization for all zones,

Am I correct?

How do you know that the coupling with temperature is relevant and the temperature field is not just like a passive tracer?

Do you add or subtract heat at the walls ?

I do not understand what do you say exactly?

As noted previously, this does allow classical analytical solution. There must always be temperature gradients if the heat flux is constant or no heat can flow. The outlet temperature gradient depends mainly on the fluid properties and the L/D ratio, but will always exist.

Dear Ammar Laichi,

Fluid motion in free convection is driven by density change and gravity.

Thus the assumption of constant density cannot be made in the analysis of

free convection problems. Instead an alternate simplification called the

Boussinesq approximation is made. The basic approach in this

approximation is to treat the density as constant in the continuity equation

and the inertia term of the momentum equation, but allow it to change with

temperature in the gravity term.

The importance of this approximation lies in the

elimination of density as a variable in the analysis of free convection

problems. However, the momentum and energy equations remain coupled.

assumption in the Boussinesq approximation, that the dimensionless product

β(T − T∞) is considerably smaller than unity.

concept of local temperature differnce, is difference between the suface and fluid temperature(or bulk fluid temperature).

Kind regards,

jafar behtarinik

Thank you for your answer,

I mean here (concept of local temperature difference, is difference between the surface and fluid temperature(or bulk fluid temperature)) the difference between the max temperature (wall) and the min temperature in the fluid at the same isosurface or plane (cross section 3D pipe).

Kind regards,

Ammar Laichi