Flows driven by a combination of source/sink part 2: Interior creeping flows

In this paper, two-dimensional creeping flows generated by source and sink inside a circular cylinder are studied in the presence of different boundary conditions. For simplicity, line source and sink are assumed to be parallel to the cylinder axis, all axes in the same plane. The interior boundary value problem associated with these flows is solved in terms of a stream function. Analytical solutions for the flow field are obtained by straight forward application of the Fourier method. These solutions are used to plot streamline topologies of these flows and the flow patterns are sketched for a number of special cases where the boundary conditions is varying from no slip to perfect slip boundary conditions. Eddies of various sizes and shapes appear as the parameter is varied. Some interesting flow patterns are observed in the parameter space which may have applications in vortex mixing flows.