Stability analysis on boundary layer flow and heat transfer over a permeable surface in presence of thermal radiation

The study of stability analysis on boundary layer flow and heat transfer over a permeable surface in presence of thermal radiation is numerically studied in this thesis. The aim of this thesis is to analyze the following five problems, which are: (i) forced convection stagnation point slip flow in a Darcy porous medium towards a shrinking sheet in presence of thermal radiation and suction; (ii) forced convection flow over a permeable stretching sheet with variable thickness in presence of free stream, magnetic field and thermal radiation; (iii) mixed convection boundary layer flow over a permeable surface embedded in a porous medium saturated by a nanofluid with thermal radiation, MHD (magnetohydrodynamics) and heat generation; (iv) mixed convection boundary layer flow over a permeable vertical cylinder embedded in a porous medium saturated by a nanofluid with thermal radiation; and (v) unsteady mixed convection stagnation point flow over a permeable moving surface along the flow impingement direction with thermal radiation. Similarity transformation is used in all problems to reduce the governing system of partial differential equations into a system of ordinary differential equations, which is numerically solved using shooting method and bvp4c function. The programming codes for the shooting method are built using MAPLE software, while the programming codes for the bvp4c function are built using MATLAB software. The characteristics of the reduced skin friction coefficient and Nusselt number, together with velocity and temperature profiles, for various existence of parameters are discussed and analyzed in details. It is observed that the reduced skin friction coefficient increases with the increasing of permeability and thermal radiation parameter, where the boundary layer thickness and velocity gradient are seen to be affected by those parameters. Further, the problems possessed dual solutions for a certain range of parameters, in which we performed a stability analysis by solving the linear eigenvalue problems to identify which of the two solution is stable. Our analysis reveals that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

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