FLOW IN A PIPE DRIVEN BY SUCTION AT AN ACCELERATING WALL

The axisymmetric now of a viscous fluid in a pipe driven by suction at the pipe wall and acceleration of the wall is examined using a similarity form of solution: the particular combination of the two effects chosen is one in which there is a simple analytical solution. The temporal stability of solutions (both this analytical one and other numerical ones) is investigated for various values of the Reynolds number R, and stable and unstable parts of the solution branches are identified. A transcritical bifurcation is found and also a Hopf bifurcation. We consider also the corresponding nonlinear diffusion problem and present some solutions. Finally we examine the continuation from the present problem to the flow in a pipe driven by suction only.