Volume 14, no. 2Pages 5 - 16

Hydrodynamic Entrance Region in a Flat Porous Channel with a Pressure Head Isothermal Laminar Flow of a Newtonian Medium

A.V. Ryazhskih, A.V. Nikolenko, D.A. Konovalov, V.I. Ryazhskih, A.V. Keller
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.
Full text
flat porous channel; pressure head laminar flow; Newtonian fluid; Darcy–Brinkman equation; hydrodynamic initial section.
1. Bear J., Bachmat Y. Introduction to Modeling of Transport Phenomena in Porous Media. Dordrecht, Kluwer Academic Publishers, 1990.
2. Novyi spravochnik himika i technologa. Processy i apparaty himicheskih thenologii [The New Handbook of the Chemist and Technologist. Processes and Apparatuses of Chemical Technologies]. St. Petersburg, Professional, 2004. (in Russian)
3. Vafai K., Tien C.-L. Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media. International Journal of Heat Mass Transfer, 1981, vol. 24, pp. 195-203.
4. Vafai K. Handbook of Porous Media. New York, CRC Press, 2015.
5. Posnov A., Baltrunas P., Kagan A., Zagorskis A. Aerodinamika vozduhoochistnyh ustroistv s zernistym sloem [The Aerodynamics of Air Treatment Devices with a Granular Layer]. Vilnius, Tehnika, 2010. (in Russian)
6. Tien C. Adsorption Calculations and Modeling. Boston, Butter-Heinemann, 1994.
7. Metal Foams. New York, Elsevier, 2000.
8. Tribok G., Gnanasekaran N. Numerical Study on Maximizing Heat Transfer and Minimizing Flow Resistance Behavior of Metal Foams Owing to Their Structural Properties. International Journal of Thermal Sciences, 2021, vol. 159, article ID: 106617, 15 p.
9. Bagci O., Dakhan N. Experimental Hydrodynamics of High-Porosity Metal Foam: Effect of Pore Density. International Journal of Heat and Mass Transfer, 2016, vol. 103, pp. 879-885.
10. Kaviany M. Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates. International Journal of Heat and Mass Transfer, 1985, vol. 28, no. 4, pp. 851-858.
11. Tien-Chien Jen, Yan T.Z. Developing Fluid Flow and Heat Transfer in a Channel Partially Filled with Porous Medium. International Journal of Heat and Mass Transfer, 2005, vol. 49, pp. 3995-4009.
12. Kaviany M. Principles of Heat Transfer in Porous Media. New York, Springer Science and Business Media, 1995.
13. Akowanou C., Degan G., Prodjinonto V. Effect of Permeability Anisotropy on Forced Convection Thermal-Hydrodynamics of Entrance and Developed Flow Regimes in Porous Saturated Circular Tube. International Journal of Applied Science and Techology, 2016, vol. 20, pp. 1-9.
14. Ryazhskih V.I., Keller A.V., Ryazhskih A.V., Nikolenko A.V. Dakhin S.V. Mathematical Model of the Acceleration Laminar Flow of a Newtonian Fluid in a Anisotropic Porous Channel of Rectangular Cross Section. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2020, vol. 13, no. 3, pp. 17-28.
15. Tianwang Lai, Xiangyang Liu, Sa Xue, Jimin Xu, Maogang He, Ying Zhang. Extension of Ergun Equation for the Calculation of the Flow Resistance in Porous Media with Higher Porosity and Open-Celled Structure. Applied Thermal Engineering, 2020, vol. 173, article ID: 115262, 13 p.
16. Izadpanah M.R., Muller-Steinhagen H., Jamilahmadi M. Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium. International Journal of Heat and Fluid Flow, 1998, vol. 19, pp. 629-635.
17. Nield D.A., Bejan A. Convection in Porous Media, New York, Springer, 2006.
18. Mobedi M., Cokmer O., Pop I. Forced Convection Heat Transfer Inside an Anisotropic Porous Channel with Olique Principal Axes: Effect of Viscous Dissipation. International Journal of Thermal Sciences, 2010, vol. 49, pp. 1984-1993.
19. Slezkin N.A. Dinamika vyazkoi neszhimaemoyi zhidkosti [Dynamics of a Viscous Incompressible Fluid], Moscow, Gosudarstvennoe izdatel'stvo tehniko-teoreticheskoi literatury, 1955. (in Russian)
20. Handbook of Mathematical Formulas and Integrals. New York, Academic Press, 2004.
21. Handbook of Differential Equations. New York, Elsevier, 1992.
22. Schlichting H. Teoriya pogranichnogo sloya [The Theory of the Boundary Layer]. Moscow, Nauka, 1974. (in Russian)