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

概要

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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 R_6=(ρV^<2-(1/n)>L^<1/n>)/μ_<psu>^<1/n>(ρ : density, V : characteristic velocity, L : characteristic length, μ_<psu> : 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 R_6 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 x_l, the Hagenbach's correction ΔH of non-Newtonian flow and the rheological constant n have been found by the author's researches.
一般社団法人日本機械学会の論文
1961-02-00