Modelling blood flow in coronary arteries: flow in a time-dependent sinuous tube

Coronary cine-angiograms reveal that some arteries on the surface of the heart are sinuous and their amplitude and wavelength vary periodically with time. As part of a program to understand the flow and wall shear stress distribution in coronary artery, a theoretical analysis is conducted of the flow of a viscous fluid at a high Reynolds number in an oscillating, sinuous, tube of constant circular cross-section. The governing equations are derived in a natural, boundary-fitted coordinate system, made rather complicated by the acceleration and rotation of the frame of reference. However, this is more than compensated by the simple boundary conditions of zero relative velocity on the walls, which are at a fixed distance from the centerline of the tube. Attention is then restricted to small amplitude sinusoidal indulations. Periodic end conditions are applied.