The Oscillatory Motion of Oldroyd-B Fluid by Incorporating Some of the Mechanical Factors

The aim of this paper is to present a numerical study of oscillatory motion of Oldroyd-B fluid in a uniform magnetic field through a small circular pipe. First, we derive the orientation stress tensor by considering the Brownian force. Then, the orientation stress tensor is incorporated by taking Hookean dumbbells on Brownian configuration fields in the Oldroyd-B model. The Oldroyd-B model is then reformulated coupled with the momentum equation and the total stress tensor. Finally, we analyze the orientation stress tensor in the pipe by the numerical simulations of the model and showed that the effect of orientation stress tensor is considerable although the Brownian force is sufficiently small.