**Numerical simulations **

** 1- Problem's geometry**

In this part, we simulate the boundary layer over a flat-plate. For this, we consider a flat plate of length L. This flat-plate is situated in a uniform flow with a uniform velocity U.

*Figure: Flat-plate in a uniform flow*

** Flat-plate's mesh**

We use OpenFoam tools to mesh the domain. The mesh is particularly refined above the plate in order to describe better the evolution of the boundary layer over the flat-plate. The global domain is divided to (100x200) meshes.

The picture below represents the meshed domain viewed by Paraview.

* Figure: Domain mesh *

** 3- "MyIcoFoamT" solver**

OpenFoam doesn't offer any standard solver that can resolve both thermic and dynamic equations. That's why, we create our own solver "**MyIcoFoamT**" in order to simulate the thermic boundary layer. In fact, we modify the standard solver "IcoFoam" that solves the incompressible laminar Navier - Stokes equations using the PISO algorithm, by adding temperature equations.

The next screenshots are representation of modifications that we have done in the source code:

* Figure: Screenshot of source code*

** 4- Test case**

We study the boundary layer over a flat-plate under the following circumstances:

- The flat-plate is situated in a uniform flow of air with a uniform velocity U=0.025m/s. We consider that the air kinematic viscosity is equal to 0.55 10
^{-6}m^{2}/s. Therefore, the Reynolds number is approximately 327.15. Thus, the test case is a laminar flow. - The plate's temperature is equal to T
_{p}=90°C while the air temperature is T_{0}=60°C.

The next figure shows the domain at initial instant of simulation

* Figure: the domain at initial instant of simulation*