We derived the unidirectional shear flows appropriate for Hele Shaw cell when there is no buoyancy driving force. Using the Galerkin spectral method, the linear stability of Hele Shaw convection in shear flows has been analyzed. The results show that all shear flows stabilize the convection. / Using a modified perturbation method with a two parameter expansion and a strained time coordinate, we successfully obtained the oscillatory (steady) finite amplitude solutions with (without) imposed shear flows. The two parameters are $\epsilon$ Pe, where $\epsilon$ is the amplitude of the stream function to leading order, and Pe is the Peclet number. It has been found that the flow pattern in Couette flow tilted more strongly with the stream as the Prandtl number was decreased. The temperature pattern was symmetric about the vertical axis when the Prandtl number is large. As the Prandtl number is decreased the temperature pattern becomes an intense narrow hot center and relatively weak broad cold center and then the cold center splits into a cats-eyes pattern and the hot center remains narrow and intense. This kind of pattern change has also been observed as the Peclet number is increased. / The generated mean flow and the momentum flux in both shear flows were derived analytically and were increased whereas the Prandtl number decreases. The momentum flux in all shear flows is found to be always up the gradient of the mean flow and results in the energy transformation from the the convective kinetic energy into the mean kinetic energy. / The study reported here might be very helpful for understanding the porous medium convection in shear flows. Therefore, the consequence of these results to ground water transport as well as industrial processes might be significant. / Source: Dissertation Abstracts International, Volume: 52-04, Section: B, page: 1926. / Major Professor: Ruby Krishnamurti. / Thesis (Ph.D.)--The Florida State University, 1991.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76395 |
| Contributors | Yang, Huijun., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 257 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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