Unsteady boundary layer flow over a permeable curved stretching/shrinking surface

• Unsteady boundary layer flow is numerically studied.
• The flow involves a curved surface.
• Dual solutions are found and discussed along with a stability analysis.
• Different flow behavior is depicted.

The problem of unsteady viscous flow over a curved stretching/shrinking surface with mass suction is studied. A similarity transformation is used to reduce the system of partial differential equations to an ordinary differential equation. This equation is then solved numerically using the function bvp4c from Matlab for different values of the curvature, mass suction, unsteadiness and stretching/shrinking parameters. The physical quantities of interest, such as reduced skin friction, velocity and shear stress are obtained and discussed as functions of these parameters. Results show that for both cases of stretching and shrinking surfaces, multiple (dual, upper and lower branch) solutions exist for a certain range of curvature, mass suction, unsteadiness and stretching/shrinking parameters. This is an opposite situation than that of the plane stretching sheet. In order to establish which of these solutions are stable and which are not, a stability analysis has been performed. It is evident from the results that the pressure inside the boundary layer cannot be neglected for a curved stretching sheet, as distinct from a flat stretching sheet.