24-04-2012, 02:55 PM
Forced Convection over a Flat Plate
Forced Convection over a Flat Plate.doc (Size: 3.19 MB / Downloads: 55)
In our problem, we have a flat plate at a constant temperature of 413K. The plate is infinitely wide. The velocity profile of the fluid is uniform at the point x = 0. The free stream temperature of the fluid is 353K. The assumption of incompressible flow becomes invalid increasingly less valid for larger temperature differences between the plate and freestream. Because of this, we will treat this as a compressible flow. We will analyze a fluid flow with the following non-dimensional conditions:
Preliminary Analysis
We expect the turbulent boundary layer to grow along the plate. As the boundary layer grows in thickness, the rate of heat transfer (q'') and thus the heat transfer coefficient (h) will decrease.
Strategy for creating flow field geometry
In creating the geometry for our flow field we must consider what is necessary for our model to approximate real flow. A boundary layer grows along the plate, which must satisfy the no slip condition. The flow velocity at the plate must be zero. Continuity requires that this condition gives rise to a y-velocity. Although the y-velocity is significantly smaller in magnitude than the x-velocity, it can affect the solution significantly if not taken into consideration when creating the geometry of the flow field.
Mesh Geometry in GAMBIT
We'll now create a mesh on the rectangular face with 100 divisions in the vertical direction and 30 divisions in the horizontal direction. We'll first mesh the four edges and then the face. The desired grid spacing is specified through the edge mesh.
Mesh Edges
Operation Toolpad > Mesh Command Button > Edge Command Button > Mesh Edges
Mesh Strategy
In creating this mesh, it is desirable to have more cells near the plate (Edge 1) because we want to resolve the turbulent boundary layer, which is very thin compared to the height of the flow field.