Analytical Treatments of Non-Newtonian Fluid Flow by Introducing the Conception of Boundary Layer

Abstract

In this paper, it is first shown that the conception of the boundary layer, as in the case of the Newtonian fluid flow, may also be applicable to the non-Newtonian fluid flow at high Reynolds number in a wider sense R6=(ρV2-(1/n)L1/n)/μpsu1/n(ρ : density, V : characteristic velocity, L : characteristic length, μpsu : pseudo viscosity similar to the viscosity of Newtonian fluid, n : rheological constant) ; and the fundamental equations of motion for non-Newtonian fluid can be simplified by the approximations of the boundary layer equation. Then, the relation between the thickness of boundary layer δ and the Reynolds number R6 can also be deduced as follows : [chemical formula] Moreover, as an example of the analytical treatment by the approximations of boundary layer equation, the flow state in the portion of inlet length of a circular pipe is also analysed by means of variational method. Thus, the respective relations between the inlet length xl, the Hagenbach's correction ΔH of non-Newtonian flow and the rheological constant n have been found by the author's researches.