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

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  • 非ニュートン流動の境界層論的取扱い
  • ヒニュートン リュウドウ ノ キョウカイソウロンテキ トリアツカイ

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In this paper, it is first shown that the idea 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/nL1/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 introducing the approximations of the boundary layer. Then, the relation between the thickness of boundary layer δ and the Reynolds number R6* can also be deduced as follows : δ/L=0(R6*-n/(n+1)) Moreover, as an example of the analytical treatment by the boundary layer approximations, 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.

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