This dissertation presents a numerical method to study the two dimensional incompressible thermal boundary layer flows. The governing equations are the Prandtl's thermal boundary layer equations. Analytically, these equations are difficult to solve. Numerically, standard methods such as finite difference method may suffer from problems associated with the use of grids and the discretization of gradients, especially within an extremely thin boundary layer where large velocity and temperature gradient exist The proposed numerical method is a particle method in which the computational elements carry concentrations of vorticity and heat flux. These elements are convected at the fluid velocity and undergo a random walk to simulate the diffusion. New elements are created to simulate the interaction between the vorticity and the heat flux and to satisfy the boundary conditions. At any instant of time, the velocity and temperature field can be recovered from the location and the concentration of the elements by integration The method is grid-free and it does not suffer from problems associated with the use of a very fine grid in the boundary layer where sharp gradients exist. It introduces no numerical diffusion and automatically concentrates computational effort near steep gradients The method is applied to a forced parallel flow past a heated horizontal flat plate and a natural flow around a heated vertical plate. The numerical results are compared with the steady-state similarity solutions and good agreement is observed / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_25709 |
| Date | January 1993 |
| Contributors | Chui, Wing Kwong (Author), Sod, Gary A (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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