Journal of Applied and Computational Mechanics (Oct 2022)

Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in ‎Porous Media‎

  • D.S. Sankar,
  • K.K. Viswanathan,
  • Atulya K. Nagar,
  • Nurul Aini Binti Jaafar,
  • A. Vanav Kumar

DOI
https://doi.org/10.22055/jacm.2021.36921.2928
Journal volume & issue
Vol. 8, no. 4
pp. 1246 – 1269

Abstract

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This theoretical study analyses the effects of geometrical and fluid parameters on the flow metrics in the Hagen-Poiseuille and plane-Poiseuille flows of Herschel-Bulkley fluid through porous medium which is considered as (i) single pipe/single channel and (ii) multi–pipes/multi-channels when the distribution of pores size in the flow medium are represented by each one of the four probability density functions: (i) Uniform distribution, (ii) Linear distribution of Type-I, (iii) Linear distribution of Type-II and (iv) Quadratic distribution. It is found that in Hagen-Poiseuille and plane-Poiseuille flows, Buckingham-Reiner function increases linearly when the pressure gradient increases in the range 1 - 2.5 and then it ascends slowly with the raise of pressure gradient in the range 2.5 - 5.In all of the four kinds of pores size distribution, the fluid’s mean velocity, flow medium’s porosity and permeability are substantially higher in Hagen-Poiseuille fluid rheology than in plane-Poiseuille fluid rheology and, these flow quantitiesascend considerably with the raise of pipe radius/channel width and a reverse characteristic is noted for these rheological measures when the power law index parameter increases.The flow medium’s porosity decreases rapidly when the period of the pipes/channels distribution rises from 1 to 2 and it drops very slowly when the period of the pipes/channels rises from 2 to 11.

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