In this paper, the problem of steady laminar boundary layer flow of an incompressible viscous fluid over a moving thin needle is considered. The governing boundary layer equations were first transformed into non-dimensional forms. These non-dimensional equations were then transformed into similarity equations using the similarity variables, which were solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions were obtained for a blunt-nosed needle. Numerical computations were carried out for various values of the dimensionless parameters of the problem which included the Prandtl number Pr and the parameter a representing the needle size. It was found that the heat transfer characteristics were significantly
influenced by these parameters. However, the Prandtl number had no effect on the flow characteristics due to the decoupled boundary layer equations.
Linear stability analysis was used to investigate the onset of Marangoni convection in a two-layer system. The system comprised a saturated porous layer over which was a layer of the same fluid. The fluid was heated from below and the upper free surface was deformable. At the interface between the fluid and the porous layer, the Beavers-Joseph slip condition was used and in the porous medium the Darcy law was employed to describe the flow. Predictions for the onset of convection were obtained from the analysis by the perturbation technique. The effect of surface deformation and depth ratio, z (which is equal to the depth of the fluid layer/depth of the porous layer) on the onset of fluid motion was studied in detail.