Volume 13, no. 3Pages 17 - 28

Mathematical Model of the Acceleration Laminar Flow of a Newtonian Fluid in an Anisotropic Porous Channel of Rectangular Cross Section

V.I. Ryazhskih, A.V. Keller, A.V. Ryazhskih, A.V. Nikolenko, S.V. Dakhin
Based on the Darcy-Brinkman-Forchchimer equations without taking into account the inertia and assuming the unity of the synthesis of the synthesized three-dimensional mathematical model of the accelerating-laminar flow of a viscous incompressible fluid in an anisotropic origin of a rectangular section, taking into account the time of creation of a constant pressure. In order to investigate and analyze the orthopedic structure, all diagonal components were found to determine the primary and boundary value problems for the momentum equations, which solve analytically semilacial and finite Fourier integral sine transforms. It is believed that the application of the developed model for estimating time and differences depending on the time it takes to reach constant pressure gradients, permeability coefficients, and the angle of inclination in an anisotropic system.
Full text
mathematical model; porosity; anisotropy; permeability; channel with a rectangular cross-section; viewing time.
1. Bird R., Stewart W., Lightfoot E. Transport Phenomena. N.Y., John Wiley and Sons, 2002.
2. Vafai K. Handbook of Porous Media. N.Y., CRC Press, 2016. DOI: 10.1201/b18614
3. Guodong Xia, Lei Cao, Guanglong Bi. A Review on Battery Thermal Management in Electric Vehicle Application. Journal of Power Sources, 2017, vol. 367, pp. 90-105. DOI: 10.1016/j.jpowsour.2017.09.046
4. Ellrey J.L., Belmont E.L., Smith C.H. Heat Recirculating Reactors: Fundamental Research and Application. Progress in Energy and Combustion Science, 2019, vol. 72, pp. 32-58. DOI: 10.1016/j.pecs.2018.12.001
5. Kolb G. Microstructured Reactors for Distributed and Renewable Production of Fuels and Electrical Energy. Chemical Engineering and Processing: Process Intensification, 2013, vol. 65, pp. 1-44. DOI: 10.1016/j.cep.2012.10.015
6. Machmoudi Y., Hooman K., Vafai K. Convective Heat Transfer in Porous Media, N.Y., CRC Press, 2019.
7. Lukisha A.P., Prishyakov V.F. The Efficiency of Round Channels Fitted with Porous, Highly Heat-Conducting in Set in a Laminar Fluid Coolant Flow at Boundary Conditions of the Third Kind. International Journal of Heat and Mass Transfer, 2010, vol. 53, pp. 2469-2476. DOI: 10.1016/j.ijheatmasstransfer.2010.01.036
8. Yuanwang Deng, Changling Feng, Jiaqiang E, Hao Zhu, Jingwei Chen, Ming Wen, Huichun Yin. Anisotropic Porous Structure Modeling for 3D Printed Objects. Applied Thermal Engineering, 2018, vol. 10, no. 2, pp. 157-164. DOI: 10.1016/j.applthermaleng.2018.06.043
9. Machamoudi Y., Karimi N., Mazaheri K. Analytical Investigation of Heat Transfer Enhancement In a Channel Partially Filled with a Porous Material Under Local Thermal Non-Equilibrium Conditions: Effects of Different Thermal Boundary Conditions at the Porous-Fluide Interface. International Journal of Heat and Mass Transfer, 2014, vol. 70, pp. 875-891. DOI: 10.1016/j.ijheatmasstransfer.2013.11.048
10. Saberinejad H., Keshavaz A. Payandehdoost M., Azmoodeh M.R., Batooei A. Numerical Study of Heat Transfer Performance in a Pipe Partially Filled with Non-Uniform Porous Media Under the Condition. International Journal of Numerical Methods for Heat and Fluid Flow, 2018, vol. 28, no. 8, pp. 1845-1855. DOI: 10.1108/HFF-12-2017-0495
11. Penha D.J.Lopez, Stols S., Kuerten J.G.M., Nordlund M., Kuczay A.K., Geurts B.J. Fully-Developed Conjugate Heat Transfer in Porous Media With Uniform Heating. International Journal of Heat and Fluid Flow, 2012, vol. 38, pp. 94-106. DOI: 10.1016/j.ijheatfluidflow.2012.08.007
12. Xu Chua, Guang Yang, Sandeep Pandey, Bernhard Weiganda. Direct Numerical Simulation of Convective Heat Transfer in Porous Media. International Journal of Heat and Mass Transfer, 2019, vol. 133, pp. 11-20. DOI: 10.1016/j.ijheatmasstransfer.2018.11.172
13. Gamal A., Furmanski P. Problems of Modeling Flow and Heat Transfer in Porous Media. Journal of Power Technologies, 1997, no. 85, pp. 55-88. DOI: 10.1080/00144940.1997.11484129
14. Yuanwang Deng, Changling Feng, Jiaqiang E, Hao Zhu, Jingwei Chen, Ming Wen, Huichun Yin. Effects of Different Coolants and Cooling Strategies on the Cooling Performance of the Power Lithium Ion Battery System: a Review. Applied Thermal Engineering, 2018, vol. 142, pp. 10-29. DOI: 10.1016/j.applthermaleng.2018.06.043
15. Chakraborty G. A Note on Methods for Analysis of Flow Through Microchannels. International Journal of Heat and Mass Transfer, 2008, vol. 51, no. 17-18, pp. 4583-4588. DOI: 10.1016/j.ijheatmasstransfer.2007.11.058
16. Ryazhskikh V.I., Konovalov D.A., Ryazhskikh A.V., Boger A.A., Dakhin A.V. Analytical Solutions to the Problem of Convective Heat Transfer in a Porous Rectangular Channel for Thermal Boundary Conditions of the Second Genus. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2017, vol. 10, no. 3, pp. 40-53. DOI: 10.14529/mmp170304
17. Gamrat G., Farve-Marinet M., Le Person S. Numerical Study of Heat Transfer Over Banks of Rods in Small Reynolds Number Cross-Flow. International Journal of Heat and Mass Transfer, 2008, vol. 51, no. 3-4, pp. 853-864. DOI: 10.1016/j.ijheatmasstransfer.2007.04.038
18. Benchawan Wiwatanapataphec, Yong Hong Wu, Suharsono Suharsono. Transient flows of Newtonian Fluid Through a Rectangular Microchannel with Slip Boundary. Abstract and Applied Analysis, 2014, article ID: 530605, 13 p.
19. Sefi S., Benissaad S. Heat and Mass Transfer in Anisotropic Porous Media. Advances in Theoretical and Applied Mechanics, 2012, vol. 5, no. 1, pp. 11-22.
20. Qinzhuo Liao, Gang Lei, Dongxiao Zhang, Shirish Patil. Analytical Solution for Upscaling Hydraulic Conductivity in Anisotropic Heterogeneous Formations. Advances in Water Rescurces, 2019, vol. 128, no. 6, pp. 97-116. DOI: 10.1016/j.advwatres.2019.04.011
21. Ryazhskikh V.I., Gromov Yu.Yu., Ryazhskikh A.V., Khvostov А.А.[Analysis of the Operating Modes of a Closed Circulation Cooling Circuit with an Intermediate Coolant]. Prikladnaya fizika i matematika [Applied Physics and Mathematics], 2017, no. 8, pp. 20-26. (in Russian)
22. 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, no. 6, pp. 629-635. DOI: 10.1016/S0142-727X(98)10035-8
23. Chintsau Hsu, Ping Cheng. Thermal Dispersion in Porous Medium. International Journal of Heat and Mass Transfer, 1990, vol. 33, no. 8, pp. 1587-1597. DOI: 10.1016/0017-9310(90)90015-M
24. Soltani H., Ajamin H. Analytical Solution of Forced Convective Heat Transfer in a Horizontal Anisotropic Porous Media Cylinder: Effect of Variatiouse of Frictional Heating and Heat Generation on the Temperature Profile and Nusselt Number. Biochemical Engineering Journal, 2014, vol. 28, no. 3, pp. 301-318.
25. Landau L.D., Lifshic E.M. Teoreticheskaya Fizika. Т.VII. Teoriya uprugosti. [Theoretical Physics. Т.VII. Elasticity Theory], Moscow, Nauka, 1987. (in Russian)
26. Ango A. Matematika dlya elektro-i radio inzhinerov [Mathematical for Electical and Radio Engineers]. Moscow, Nauka, 1964. (in Russian)
27. Dotsch G. Anleitung zum praktischen gebrauch der Laplace-transformation und der z-transformation. Wien, Oldenbourg, 1967. (in German)
28. Sneddon I.N. Fourier Transforms. N.Y., McGraw-Hill, 1951.
29. Degan G., Zjhoun S., Vasseur P. Forced Convection in Horizontal Porous Channels with Hydrodynamic Anisotropy. International Journal of Heat and Mass Transfer, 2002, vol. 45, pp. 3181-3188.