Unsteady Pulsatile Flow through a Vertical Constricted Annulus with Heat Transfer

Abstract

This paper investigates the effects of heat transfer and pulsatile flow of a Newtonian fluid (blood) through a vertical annulus with mild constriction on the outer wall while the inner wall represents the catheter tube. An analytical expression in terms of Bessel functions of the first and second kind is obtained for the heat and the velocity components. The variation of pressure gradient with steady flow rate is given as well as the wall shear stress distribution for different values of time. The pressure gradient and the wall shear stress are calculated, and their variations are discussed with respect to the Grashof number, the height of the constriction, and the size of the catheter. It is observed that an increase in the catheter size increases the pressure gradient as well as the wall shear stress