Study of blood viscosity at low shear rate and its flow through viscoelastic tubes and ducts

A nonlinear mathematical model is developed analytically to study the flow characteristics of visco-elastic fluid through a visco-elastic pipe when it is subjected to external body acceleration. The equations governing the motion of the system are solved analytically with the use of appropriate boundary conditions. For the present scope of study the flow of visco-elastic fluid (blood) in smaller artery which is visco-elastic in nature has been taken. The artery is assumed to be a flexible cylindrical tube containing a non-Newtonian fluid. The unsteady flow mechanism in the artery is subjected to a pulsatile pressure gradient arising from the normal functioning of the heart and also the external body acceleration. Numerical models have finally been developed for Newtonian and Non-Newtonian fluid in order to have a thorough quantitative measure of the effects of body acceleration on the flow velocity, volume flow rate and the wall shear stress of blood in normal human artery and when the artery gets stiffer, just to validate the applicability of the present mathematical model.