Influence of time-dependent viscosity on wall shear stresses in unsteady pipe flows

The behaviour of wall shear stresses in unsteady flows in pipes is investigated for flows in which the effective kinematic viscosity varies in time. Such variations can arise through the effects of temperature, pressure, shear or chemical change. The theoretical approach is founded on an analytical method of solution using finite Hankel transforms. It is well suited to studying trends arising in flows with viscosity that is uniform spatially, but varies in time. The method is applied to a range of flows driven by pulsed pressure gradients. The overall wall shear stress is found to follow trends similar to those followed by the mean velocity, but the unsteady component of the wall shear stress is much more strongly influenced by the acceleration. The kinematic behaviour tends to be influenced more strongly by the instantaneous viscosity (or, strictly, by its local temporal average) than by the local rate of change of viscosity.