Geodesic
Hydrodynamic entrance region in a flat porous channel with a pressure head isothermal laminar flow of a Newtonian medium
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 5-16

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The problem of the hydrodynamic initial section of an isothermal pressure laminar flow of a Newtonian fluid in a horizontal flat porous channel of semi-infinite length, formulated in the initial-boundary formulation for the Darcy–Brinkman equation with partial consideration of the convective component, provided that the pressure depends only on the axial coordinate, is analytically solved. For a channel without a porous matrix, the results correlate with the classical data. An explicit relation was proposed for calculating the length of the hydrodynamic initial section, which does not contradict the results based on macroscopic boundary layer concepts
Keywords: flat porous channel, pressure head laminar flow, Newtonian fluid, Darcy–Brinkman equation, hydrodynamic initial section. 
@article{VYURU_2021_14_2_a0,
     author = {A. V. Ryazhskikh and A. V. Nikolenko and D. A. Konovalov and V. I. Rjazhskih and A. V. Keller},
     title = {Hydrodynamic entrance region in a flat porous channel with a pressure head isothermal laminar flow of a {Newtonian} medium},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {5--16},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a0/}
}
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A. V. Ryazhskikh; A. V. Nikolenko; D. A. Konovalov; V. I. Rjazhskih; A. V. Keller. Hydrodynamic entrance region in a flat porous channel with a pressure head isothermal laminar flow of a Newtonian medium. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 5-16. http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a0/