Hey there Ammar Laichi,

When it comes to mixed convection in water flowing through a circular pipe, considering the Boussinesq hypothesis can provide valuable insights into temperature distribution.

In this scenario, the temperature range within each cross-section of the pipe is influenced by the balance between buoyancy-driven flow and forced convection. The Boussinesq approximation assumes that the density variation due to temperature differences is negligible, except for the buoyancy force term in the momentum equation.

Typically, in mixed convection, the temperature gradient across the pipe's cross-section varies, with warmer fluid accumulating near the center and cooler fluid closer to the pipe walls. This temperature profile is influenced by factors such as the Reynolds number, Grashof number, and Prandtl number, along with the imposed heat flux.

The precise range of temperatures within each cross-section depends on various parameters such as flow rate, pipe diameter, fluid properties, and boundary conditions. However, generally speaking, in mixed convection, the temperature difference between the center and the wall of the pipe may vary within a certain range, often with the central region being warmer than the outer regions.

To get a more specific understanding of the temperature distribution in your particular setup, it's essential to conduct detailed simulations or experiments considering the specific geometrical and flow conditions.

Hope this sheds some light on your query! If you Ammar Laichi need further clarification or have more questions, feel free to ask.

Thank you so much for your discussion, I found a paragraphe in article discussed boussinesq hypothesis [The Boussinesq model can be used successfully for incompressible flows, and in the cases where the density variation is driven by small temperature variations (i.e.: < 10 °C at a given cross-section for water based fluids). Nevertheless, as limitations, the Boussinesq model should not be used if the temperature differences in the domain are large, which is not the case, as can be seen clearly from Annex 1. In this regard, the natural convection flow was approached using the Boussinesq model for test cases A - E],

What do you say here?

I have other question in setup of mixed convection of water flow in circular tube under an isothermal heat flux using Ansys fluent,gravity is on, In term of density the boussinesq hypothesis is done, also reference density set at reference temperature (inlet temperature), is it necessary to go to operating conditions to more setup?