# Problem position

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 m2/s. Therefore, the Reynolds number is approximately 327.15. Thus, the test case is a laminar flow.
• The plate's temperature is equal to Tp=90°C while the air temperature is T0=60°C.

The next figure shows the domain at initial instant of simulation Figure:  the domain at initial instant of simulation