Reversing flow in the aorta: a theoretical model.

The viscous boundary layer in a reversing flow in a curved tube is analysed with a view to study the reversing flow in the aorta at the beginning of the diastole. The velocity in the core is taken to vary with time as in a dog's aorta. The flow is considered to be quasi-steady long before the time of reversal. Near the time of reversal, the flow is governed by the diffusion equation--a balance between the unsteady inertia terms and viscous terms. The solution which ensures the continuity of the displacement thickness at the time of take over from the quasi-steady solution to the diffusive solution, is obtained. The knowledge of the distribution of the shearing stress in the circulatory system is essential due to its relevance with regard to atheroma--a disease leading to the hardening of the arteries. With this in mind, the wall shear rate is obtained as a function of time at every cross-section of the tube. The shearing stresses at the inner bend and the outer bend are also plotted. The results are compared with those for the straight tube.