NUMERICAL STUDY FOR LAMINAR FLOW OF NON-NEWTONIAN FLUID BASED ON FRACTAL DERIVATIVE

Non-Newtonian fluid has complex rheological characteristics.It is very helpful to reveal these characteristics for the applications of non-Newtonian fluid in industry and agriculture.The classical rheological models of nonNewtonian fluid usually have sophisticated forms and the limitations of specific materials or rheological situations.Fractional models have been successfully applied to describe the motion of non-Newtonian fluid due to their simplicity and few parameters.As an alternative method, the Hausdorff fractal derivative possesses simpler form and higher computational efficiency compared with the fractional derivative.This paper proposes a fractal dashpot model that improves the current Newton's Law by using the Hausdorff fractal derivative.By investigating the apparent viscosity, the creep and recovery characteristics of the fractal dashpot, it shows that the proposed fractal dashpot model is suitable to describe the non-Newtonian fluid with viscoelasticity (the so-called fractal fluid).Combined the fractal dashpot model with the continuity and motion equations, the basic equation for the fractal fluid for the laminar flow between two parallel plates is derived.Moreover, the velocity distributions between two plates are numerically calculated in three cases, which can be obtained through whether there is horizontal pressure gradient or the initial velocity of upper plate.It is found that the horizontal pressure gradient can change the shape of velocity over time and delay the arrival of stable velocity.The fractal fluid with different orders has the same velocity distribution and evolution when the horizontal pressure gradient doesn't exist.In addition, the velocity of upper plate doesn't influence the difference of stable velocity between different orders of fractal fluid when the horizontal pressure gradient exists.