In this thesis, the two-dimensional, transient, laminar flow of
viscous and incompressible fluids is solved by using the dual
reciprocity boundary element method (DRBEM). Natural convection and
mixed convection flows are also solved with the addition of energy
equation. Solutions of natural convection flow of nanofluids and
micropolar fluids in enclosures are obtained for highly large values
of Rayleigh number. The fundamental solution of Laplace equation is
used for obtaining boundary element method (BEM) matrices whereas
all the other terms in the differential equations governing the
flows are considered as nonhomogeneity. This is the main advantage
of DRBEM to tackle the nonlinearities in the equations with
considerably small computational cost. All the convective terms are
evaluated by using the DRBEM coordinate matrix which is already
computed in the formulation of nonlinear terms. The resulting
systems of initial value problems with respect to time are solved
with forward and central differences using relaxation parameters,
and the fourth-order Runge-Kutta method. The numerical stability
analysis is developed for the flow problems considered with respect
to the choice of the time step, relaxation parameters and problem
constants. The stability analysis is made through an eigenvalue
decomposition of the final coefficient matrix in the DRBEM
discretized system. It is found that the implicit central difference
time integration scheme with relaxation parameter value close to
one, and quite large time steps gives numerically stable solutions
for all flow problems solved in the thesis. One-and-two-sided
lid-driven cavity flow, natural and mixed convection flows in
cavities, natural convection flow of nanofluids and micropolar
fluids in enclosures are solved with several geometric
configurations. The solutions are visualized in terms of
streamlines, vorticity, microrotation, pressure contours, isotherms
and flow vectors to simulate the flow behaviour.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12611605/index.pdf |
| Date | 01 February 2010 |
| Creators | Gumgum, Sevin |
| Contributors | Tezer, Munevver |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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