Stability analysis on convection boundary layer stagnation-point flows over a permeable stretching/shrinking surface

In this thesis, several problems of convection boundary layer flow and heat transfer towards a stretching/shrinking surface along with stability analysis for viscous, nanofluid and micropolar fluids are investigated. There are five problems considered, namely (i) stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect; (ii) magnetohydrodynamic stagnation-point flow towards a permeable stretching/shrinking sheet with slip and heat source/sink effects; (iii) effect three-dimensional stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effects in viscous fluid; (iv) MHD stagnation-point flow towards a permeable stretching/shrinking sheet in a nanofluid with chemical reaction; and (v) stagnation-point flow and heat transfer in a micropolar fluid towards a nonlinearly permeable stretching/shrinking sheet. The study starts with the formulations of the mathematical models for every problems. Next, in solving these problems, the governing nonlinear partial differential boundary layer equations are transformed into ordinary differential equations using similarity transformations before being solved numerically using the boundary value problem solver, bvp4c built in Matlab software. The numerical results are then presented in tables and graphs for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and concentration profiles. The effects of governing parameters have been analysed such as the heat source parameter, the chemical reaction parameter, the suction/injection parameter, the micropolar parameter and the stretching/shrinking parameter. It is observed that the suction/injection effect increase the skin friction coefficient, the local Nusselt number, and the local Sherwood number. Heat source effect has decrease the heat transfer rate. Furthermore, the effect of chemical reaction effect has decrease the local Sherwood number while Micropolar parameter has decrease the skin friction coefficient and heat transfer rate. Further, dual solutions are found for a certain range of the stretching/shrinking parameter. A stability analysis has been carried out to determine which solution is stable for dual solutions exist in all problems considered. The first solution is found to be stable and physically reliable, whereas the second solution is unstable as time passes, thus impractical in the real world applications for a long run.