Abstract
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.
Highlights
The theory of Newtonian fluids well enough describes the mechanical behavior of many real fluids
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
The orientation stress tensor is incorporated by taking Hookean dumbbells on Brownian configuration fields in the Oldroyd-B model
Summary
The theory of Newtonian fluids well enough describes the mechanical behavior of many real fluids. Still we have a lot of fluids which are not properly entertained by Newtonian fluid such as ketchup, blood, paints, shampoo, pulps, honey, oil and drilling mud etc. These fluids are known as non Newtonian fluids. As we know, these fluids are commonly used in daily life and have many applications toward industries as well as to academics. Many researchers have attempted to develop a single model which represents all these fluids but they haven’t found any success in their struggle. Which are commonly divided into three main classes namely, fluids of differential type, integral type and rate type
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