Exact solutions of flow between two concentric pipes and flow over porous wall by a new couple-stress theory

A lot of research has been done to study force-tractions and couple-tractions acting on the surface of solid and fluid elements. Navior-Stokes equations have been developed based on these researches in the domain of fluid mechanics. However, a number of researchers have emphasized that the Navior-Stokes equations are not sufficient and they should be modified because regardless of couple-stress effects. In this paper, after presenting couple-stress theory, two flow geometry between two concentric pipes and flow over porous wall are considered and the behavior of them are compared with classical case. It has been shown that the force-stress tensor is not symmetric by calculating two components of the force-stress tensor for flow between two concentric pipes. In addition, it can be considered that length scale is an effective parameter on small scale flow by calculating flow velocity profile for these two geometries and by comparing them with classical solution. However, the effects of length scale on the velocity profile and the flow rate decrease with increasing geometrical scales of the problem. These results can be used to study fluid flows with small-scale characteristics such as biofluids, lubrication and microelectromechanical systems