Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
The aim for this report is to investigate for what non-dimensional parameters a fluid, at rest, starts to develop a non-zero velocity when the fluid is heated from below and cooled from the top. Starting with the governing equations the goal is to derive the linear stability theory for a fluid at rest located between two horizontal plates. This is done by using the three conservation equations for the fluid and then simplifying it with the Boussinesq approximation. First, a two-dimensional problem is considered: The most unstable eigenvalue is found for the vertical velocity component and through that the linear stability can be calculated. Thecritical Rayleigh number is determined to be Rac ≈ 1708. To verify the linear stability calculations the simulation code Nek5000 is used to calculate the nonlinear development of the flow, and the linear stability results could be confirmed with great accuracy. Then the simulations are extended into three spatial dimensions, that is done for three different geometries; a square, a cylinder and a hexagon. This is done to investigate the shape of the convection cells that will build up due to the convective motion, affected by the lateral boundary geometry.
Place, publisher, year, edition, pages
2015. , 39 p.
IdentifiersURN: urn:nbn:se:kth:diva-169484OAI: oai:DiVA.org:kth-169484DiVA: diva2:821561