Theoretical study on poiseuille flow of herschel-bulkley fluid in porous media

• Main Authors: Sankarl, D. S., Viswanathan, K. K., Nagar, Atulya K., Jafaars, Nurul Aini
• Format: Article
• Language: English
• Published: Shahid Chamran University of Ahvaz 2022
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/102866/1/KKViswanathan2022_TheoreticalStudyonPoiseuilleFlow.pdf; http://eprints.utm.my/id/eprint/102866/; http://dx.doi.org/10.22055/JACM.2021.36921.2928
• Institution: Universiti Teknologi Malaysia

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 quantities ascend 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.