| The problems of convective instability of a fluid layer resulting from buoyancy and surface-tension are examined in this dissertation. The conditions leading to the onset of convective motions in the fluid are determined numerically after a normal mode-type linear stability analysis. The disturbance equations are solved as a Bolza problem in the calculus of variations, using the sequential gradient-restoration algorithm (SGRA) developed for optimal control problems.;The Marangoni instability of a radiating fluid layer is studied. The effects of some radiative parameters, the Planck number, nongrayness of the fluid and the emissivity of the boundaries, are examined. Results indicate that internal radiation suppresses Marangoni convection.;The last part of the dissertation studies the effects of variable viscosity, uniform (internal heating), and non-uniform (external incident radiation) volumetric energy sources on Marangoni convection. The role of the boundary conditions, the temperature gradients, the effect of the temperature-dependent viscosity and surface-tension on the onset of convection are investigated. Viscosity plays an important role on instability as compared to surface-tension. Optically thicker layers are found to be less stable.;The applicability of the SGRA to convective instability is tested by solving the classical Benard problem and the Orr-Sommerfeld equation for liquid film flowing down an inclined plane. Its accuracy is established by comparing the results with those obtained by various methods existing in the literature. The reported results are of high accuracy. |
