A Note on Kirchhoff’s Junction Rule for Power-Law Fluids
Eduard Marušić‐Paloka, Igor Pažanin · Zeitschrift für Naturforschung A · 2015
Abstract We study a multiple pipe system filled with non-Newtonian fluid being in stationary regime and obeying the power law. Introducing the small parameter ε , being the ratio between the cross-section area and the length of the pipes, we find the effective flow via singular perturbation as ε tends to zero. The flow in each pipe of the system remains in the power-law Poiseuille form governed by the pressure drop between pipe’s end and the junction. Kirchhoff’s law providing the value of pressure at the junction point is derived, and its solvability is discussed. In the vicinity of junction, an interior layer appears, so we correct the asymptotic solution by introducing a non-Newtonian Leray’s problem. The error analysis is also provided.