Mathematical model of the acceleration laminar flow of a Newtonian fluid in an anisotropic porous channel of rectangular cross section. (Russian. English summary) Zbl 1455.35204
Summary: 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.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
mathematical model; porosity; anisotropy; permeability; channel with rectangular cross-section; viewing timeReferences:
| [1] | R. Bird, W. Stewart, E. Lightfoot, Transport Phenomena, John Wiley and Sons, N.Y., 2002 |
| [2] | K. Vafai, Handbook of Porous Media, CRC Press, N.Y., 2016 · Zbl 1315.76005 · 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, 367 (2017), 90-105 · doi:10.1016/j.jpowsour.2017.09.046 |
| [4] | J.L. Ellrey, E.L. Belmont, C.H. Smith, “Heat Recirculating Reactors: Fundamental Research and Application”, Progress in Energy and Combustion Science, 72 (2019), 32-58 · doi:10.1016/j.pecs.2018.12.001 |
| [5] | G. Kolb, “Microstructured Reactors for Distributed and Renewable Production of Fuels and Electrical Energy”, Chemical Engineering and Processing: Process Intensification, 65 (2013), 1-44 · doi:10.1016/j.cep.2012.10.015 |
| [6] | Y.Machmoudi, K. Hooman, K. Vafai, Convective Heat Transfer in Porous Media, CRC Press, N.Y., 2019 |
| [7] | A.P. Lukisha, V.F. Prishyakov, “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, 53 (2010), 2469-2476 · doi:10.1016/j.ijheatmasstransfer.2010.01.036 |
| [8] | Jianming Ying, Lin Lu, Lihao Tian, Xin Yan, Baoquan Chen, “Anisotropic Porous Structure Modeling for 3D Printed Objects”, Computers and Graphics, 10:2 (2018), 157-164 · doi:10.1016/j.applthermaleng.2018.06.043 |
| [9] | Y. Machamoudi, N. Karimi, K. Mazaheri, “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, 70 (2014), 875-891 · doi:10.1016/j.ijheatmasstransfer.2013.11.048 |
| [10] | H. Saberinejad, A. Keshavaz, M. Payandehdoost, M.R. Azmoodeh, A. Batooei, “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, 28:12 (2018), 1845-1855 · doi:10.1108/HFF-12-2017-0495 |
| [11] | D.J. Lopez Penha, S. Stols, J.G.M. Kuerten, M. Nordlund, A.K. Kuczay, B.J. Geurts, “Fully-Developed Conjugate Heat Transfer in Porous Media with Uniform Heating”, International Journal of Heat and Fluid Flow, 38 (2012), 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, 133 (2019), 11-20 · doi:10.1016/j.ijheatmasstransfer.2018.11.172 |
| [13] | A. Gamal, P. Furmanski, “Problems of Modeling Flow and Heat Transfer in Porous Media”, Journal of Power Technologies, 85 (1997), 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, 142 (2018), 10-29 · doi:10.1016/j.applthermaleng.2018.06.043 |
| [15] | G. Chakraborty, “A Note on Methods for Analysis of Flow Through Microchannels”, International Journal of Heat and Mass Transfer, 51:17-18 (2008), 4583-4588 · Zbl 1144.76048 · 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, 10:3 (2017), 40-53 · Zbl 1386.76166 · doi:10.14529/mmp170304 |
| [17] | G. Gamrat, M. Farve-Marinet, S. Le Person, “Numerical Study of Heat Transfer Over Banks of Rods in Small Reynolds Number Cros-Flow”, International Journal of Heat and Mass Transfer, 51:3-4 (2008), 853-864 · Zbl 1133.80307 · 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, 530605, 13 pp. |
| [19] | S. Sefi, S. Benissaad, “Heat and Mass Transfer in Anisotropic Porous Media”, Advances in Theoretical and Applied Mechanics, 5:1 (2012), 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, 128:6 (2019), 97-116 · doi:10.1016/j.advwatres.2019.04.011 |
| [21] | Ryazhskikh V. I., Gromov Yu.Yu., Ryazhskikh A. V., Khvostov A. A., “Analysis of the Operating Modes of a Closed Circulation Cooling Circuit with an Intermediate Coolant”, Applied Physics and Mathematics, 2017, no. 8, 20-26 (in Russian) |
| [22] | M.R. Izadpanah, H. Muller-Steinhagen, M. Jamialahmadi, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium”, International Journal of Heat and Fluid Flow, 19:6 (1998), 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, 33:8 (1990), 1587-1597 · Zbl 0703.76079 · doi:10.1016/0017-9310(90)90015-M |
| [24] | H. Soltani, H. Ajamin, “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, 28:3 (2014), 301-318 |
| [25] | Landau L. D., Lifshic E. M., Theoretical Physics, v. VII, Elasticity Theory, Nauka, M., 1987 (in Russian) |
| [26] | Ango A., Mathematical for Electical and Radio Engineers, Nauka, M., 1964 (in Russian) |
| [27] | G. Dotsch, Anleitung zum praktischen gebrauch der Laplace-transformation und der z-transformation, Oldenbourg, Wien, 1967 (in German) · Zbl 0166.10001 |
| [28] | I.N. Sneddon, Fourier Transforms, McGraw-Hill, N.Y., 1951 · Zbl 0038.26801 |
| [29] | G. Degan, S. Zjhoun, P. Vasseur, “Forced Convection in Horizontal Porous Channels with Hydrodynamic Anisotropy”, International Journal of Heat and Mass Transfer, 45 (2002), 3181-3188 · Zbl 1016.76074 · doi:10.1016/S0017-9310(02)00032-7 |
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