Similarity solutions for mathematical modelling of boundary layer flow and heat transfer in viscous fluids and nanofluid

In this thesis, similarity solutions of boundary layer flow and heat transfer in viscous fluid and nanofluid are considered. The objectives of the thesis are to mathematically model heat and mass transfer problems and to obtain the numerical results of each problem. The scope of this study is restricted to two-dimensional, steady,incompressible, laminar boundary layer flows in viscous fluid or nanofluid. Two problems are considered in viscous fluid and three problems are considered in nanofluid which related to the Marangoni boundary layer flow, boundary layer stagnation point flow and boundary layer flow with the effect of radiation and stretching/ shrinking sheet or cylinder. The radiation effects have important applications in physics and engineering particularly in space technology and high temperature processes. On the other hand, slip flow and permeable surface have also been considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using similarity transformation which is then solved numerically using a shooting function in Maple software to get the similarity solutions. Results and discussion which comprise the analysis of skin friction, temperature gradient, velocity and temperature profiles for some values of the governing parameters are presented in tabular and graphical form. In order to validate the numerical results obtained in this thesis, comparisons with known results from the previous literature have been made and show very good agreements. All the governing parameters influence the flow and heat transfer characteristics. For example, the heat transfer rate at the surface decreases as the radiation parameter increases. Besides, it was also shown that the imposition of suction was to decrease the heat transfer rate at the surface whereas injection showed the opposite effects. Furthermore, dual solutions exist for a certain range of the governing parameters and nanofluid can increase the heat transfer rate.

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