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SECCIÓN A: CIENCIAS EXACTAS

Vol. 13 Núm. 2 (2021)

Solución de Mhpm al flujo de fluido de Mhd a través de un medio poroso con una permeabilidad exponencialmente variable

DOI
https://doi.org/10.18272/aci.v13i2.2259
Enviado
mayo 1, 2021
Publicado
2021-11-05

Resumen

En este artículo se estudia y analiza el flujo completamente desarrollado de un fluido magneto-reológico a través de un medio poroso no isotrópico bajo el efecto de un campo magnético externo, uniforme y transversal. La permeabilidad se toma como una función de distribución exponencial de la dirección transversal. Para esto se ha utilizado la ecuación de Darcy-Brinkman-Lapwood-Lorentz para el flujo de fluidos en medios porosos y se ha resuelto en condiciones de límite antideslizantes mediante el método modificado de perturbación homotópica y los resultados fueron validados por el método numérico del disparo. El análisis de los resultados se ha realizado a través de las variables: velocidad, flujo volumétrico y esfuerzo de deformación en la pared. Estos demuestran que los parámetros más importantes son el número de Darcy y la relación de viscosidad. Asimismo, se demuestra que valores bajos de estos parámetros minimizan los efectos de cizallamiento viscoso de Brinkman.

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Citas

  1. Nield, D. A., & Bejan, A. (2006). Mechanics of Fluid Flow Through Porous Media. In D. A. Nield, & A. Bejan, Convection in Porous Media (3 ed., pp. 14-16). USA: Springer.
  2. Rudraiah, N. (1986). Flow past porous layers and their stability. In N. P. Cheremisinoff (Ed.), Encyclopedia of Fluid Mechanics, Slurry Flow Technology (Vol. 8, pp. 567-647). Houston, Texas, USA: Gulf Publishing. Retrieved from https://archive.org/details/in.ernet.dli.2015.148666/page/n3/mode/2up
  3. Alzahrani, S., Gadoura, I., & Hamdan, M. (2016, May-June). Nield- Kuznetsov Functions of the First- and Second Kind. IOSR Journal of Applied Physics, 8(3 Version III), 47-56. Retrieved from http://www.iosrjournals.org/iosr-jap/papers/Vol8-issue3/Version-3/H0803034756.pdf
  4. Attia, H., & Abdeen, M. (2012). Unsteady MHD Flow and Heat Transfer Between Parallel Porous Plates with Exponential Decaying Pressure Gradient. Kragujevac Journal of Science(34), 15-22. Retrieved from https://www.pmf.kg.ac.rs/KJS/images/volumes/vol34/kjs34attiaabdeen15revision.pdf
  5. Barcena, C., Sra, A., & Gao, J. (2009). Applications of Magnetic Nanoparticles in Biomedicine. In J. Ping Liu, E. Fullerton, O. Gutfleisch, & D. Sellmyer (Eds.), Nanoscale Magnetic Materials and Applications (pp. 591-626). Springer. doi: https://doi.org/10.1007/978-0-387-85600-1
  6. Mishra, S., Baag, S., Dash, G., & Acharya, M. (2019). Numerical approach to MHD flow of power-law fluid on a stretching sheet with non-uniform heat source. Nonlinear Engineering, 9(1), 81-93. doi: https://doi.org/10.1515/nleng-2018-0026
  7. Shehzad, S., & Hayat, T. A. (2015). Influence of convective heat and mass conditions in MHD flow of nanofluid. Bull. PolishAcadSc. Tech. Sci., 63(2), 465-474. doi: https://doi.org/10.1515/bpasts-2015-0053
  8. Hamdan, M., Kamel, M., & Siyyam, H. (2009). A permeability function for Brinkman’s equation. Proceedings of the 11th Conf. on Mathematical Methods, System Theory and Control (pp. 198-205). WSEAS Publications. Retrieved from https://pdfs.semanticscholar.org/b2b7/8e0741d09e511c6a461d3b22a01a5d4151e7.pdf
  9. Brinkman, H. C. (1947). A Calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Scientific Res., A1, 27-34. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.454.3769&rep=rep1&type=pdf
  10. Hamdan, M., & Kamel, M. (2011). Flow through Variable Permeability Porous Layers. Adv. Theor. Appl. Mech., 4(3), 135 - 145. Retrieved from http://m-hikari.com/atam/atam2011/atam1-4-2011/hamdanATAM1-4-2011-2.pdf
  11. Auriault, J.-L. (2009, September). On the Domain of Validity of Brinkman’s Equation. Transport in Porous Media, 79(2), 215-223. doi: https://doi.org/10.1007/s11242-008-9308-7
  12. Parvazinia, M., Nassehi, V., Wakeman, R. J., & Ghoreishy, M. H. (2006, April). Finite element modelling of flow through a porous medium between two parallel plates using the Brinkman equation. Transport in Porous Media(63), 71-90. doi: https://doi.org/10.1007/s11242-005-2721-2
  13. Nield, D. A. (1991, September). The Limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface. International Journal of Heat and Fluid Flow, 12(3), 269-272. doi: https://doi.org/10.1016/0142-727X(91)90062-Z
  14. Sahraoui, M., & Kaviany, M. (1992). Slip and no-slip velocity boundary conditions at interface of porous, plain media. International Journal of Heat and Mass Transfer, 35(4), 927-943. doi: http://dx.doi.org/10.1016/0017-9310(92)90258-T
  15. Kaviany, M. (1995). Part I Single Phase Flow. Fluid Mechanics. In M. Kaviany, Principles of Heat Transfer inPorous Media (2 ed., pp. 95-100). Spinger, Mechanical Engineering Series. doi: https://doi.org/10.1007/978-1-4684-0412-8
  16. Lundgren, T. S. (1972). Slow Flow Through Stationary Random Beds and Suspensions of Spheres. Journal of Fluid Mechanics(51), 273-299. doi: http://dx.doi.org/10.1017/S002211207200120X
  17. Cheng, A. H.-D. (1984, July). Darcy’s Flow With Variable Permeability: A Boundary Integral Solution. (A. G. Union, Ed.) Water Resources Research, 20(7), 980-984. doi: https://doi.org/10.1029/WR020i007p00980
  18. Hamdan, M. H., & Abu Zaytoon, M. S. (2017, May-June). Flow over a Finite Forchheimer Porous Layer with Variable Permeability. IOSR Journal of Mechanical and Civil Engineering, 14(3), 15-22. doi: https://doi.org/10.9790/1684-1403041522
  19. Elaiw, A., Ibrahim, F., & Bakr, A. (2009). Variable permeability and inertia effect on vortex instability of natural convection flow over horizontal permeable plates in porous media. Commun Nonlinear Sci Numer Simulat, 14, 2190­2201. doi: https://doi.org/10.1016/j.cnsns.2008.06.022
  20. Hassanien, I. (2003). Variable permeability effects on mixed convection along a vertical wedge embedded in a porous medium with variable surface heat flux. Applied Mathematics and Computation, 138, 41-59. doi: https://doi.org/S0096-3003(02)00098-X
  21. Hassanien, I., Salama, A., & Elaiw, A. (2003, December). Variable permeability effect on vortex instability of mixed convection flow in a semi-infinite porous medium bounded by a horizontal surface. Applied Mathematics and Computation, 146(2-3), 829-847. doi: https://doi.org/10.1016/S0096-3003(02)00635-5
  22. Jang, J.-Y., & Chen, J.-L. (1993). Variable porosity effect on vortex instability of a horizontal mixed convection flow in a saturated porous medium. International Journal of Heat and Mass Transfer, 36(6), 1573-1582.
  23. Chandrasekhara, B., Namboodiri, P., & Hanumanthappa, A. (1984, March 01). Similarity solutions for buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces. Wärme-und Stoffübertragung, 18(1), 17-23.
  24. Abu Zaytoon, M. (2015). Flow through and over porous layers of variable thickness and permeability. Canada: University of New Brunswick. Retrieved from https://unbscholar.lib.unb.ca/islandora/object/unbscholar%3A7625
  25. Chandrasekhara, B., Hanumanthappa, A., & Chandranna, S. (1984, January 01). Influence of Variable Permeability on the Basic Flows in Porous Media. Indian Journal of Technology, 22(8), 281-283.
  26. Goldstein, R., Ibele, W., Patankar, S., Simon, T., Kuehn, T., Strykowski, P., . . . Srinivasan, V. (2006). Heat transfer—A review of 2003 literature. International Journal of Heat and Mass Transfer, 49, 451-534. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2005.11.001
  27. Schiffman, R., & Gibson, R. (1964). Consolidation of Nonhomogeneous Clay Layers. Journal of the Soil Mechanics and Foundations Division, 90(5), 1-30.
  28. Mahmoud, M. S., & Deresiewicz, H. (1980, January-March). Settlement of inhomogeneous consolidating soils—I: The single-drained layer under confined compression. International Journal for Numerical and Analytical Methods in Geomechanics, 4(1), 57-72. doi: https://doi.org/10.1002/nag.1610040105
  29. Rees, D. A., & Pop, I. (2000). Vertical free convection in a porous medium with variable permeability effects. International Journal of Heat and Mass Transfer, 43, 2565-2571. Retrieved from https://people.bath.ac.uk/ensdasr/PAPERS/PAPERS.bho/paper51.pdf
  30. Alloui, Z., Bennacer, R., & Vasseur, P. (2009, June). Variable permeability effect on convection in binary mixtures saturating a porous layer. Heat and Mass Transfer, 45(8), 1117-1127. doi: https://doi.org/10.1007/s00231-009-0488-7
  31. Choukairy, K., & Bennacer, R. (2012). Numerical and Analytical Analysis of the Thermosolutal Convection in an Heterogeneous Porous Cavity. FDMP-Fluid Dynamics & Materials Processing, 8(2), 155-172. doi: https://doi.org/10.3970/fdmp.2012.008.155
  32. Hartmann, J., & Lazarus, F. (1937). Experimental investigations on the flow of mercury in a homogeneous magnetic field. Matematisk-fysiske meddelelser Kongelige Danske Videnskabernes Selskab, 15(7), 1-45.
  33. He, J.-H. (2003, February 15). Homotopy perturbation method: A new nonlinear analytical technique. Applied Mathematics and Computation, 135(1), 73-79. doi: https://doi.org/10.1016/S0096-3003(01)00312-5
  34. Müller, U., & Bühler, L. (2001). Analytical solutions for MHD channel flow. In U. Müller, & L. Bühler, Magnetofluiddynamics in Channels and Containers (pp. 37-56). Berlin-Heidelberg, Germany: Springer.
  35. Rothmayer, A. P. (2014). Magnetohydrodynamic channel flows with weak transverse magnetic fields. Phil. Trans. R. Soc. A. (372), 1-12. doi: https://doi.org/10.1098/rsta.2013.0344
  36. Awartani, M., & Hamdan, M. (2005, October). Fully developed flow through a porous channel bounded by flat plates. Applied Mathematics and Computation, 2(169), 749-757. doi: https://doi.org/10.1016/j.amc.2004.09.087
  37. Fu, W.-S., Huang, H.-C., & Liou, W.-Y. (1996). Thermal enhancement in laminar channel flow with a porous block. International Journal of Heat and Mass Transfer, 39(10), 2165 2175.
  38. Harwin, D. A. (2007). Flows in Porous Channels. Bath, United Kingdom: University of Bath. Retrieved from https://people.bath.ac.uk/masjde/Theses/Thesis-Harwin.pdf
  39. Kaviany, M. (1985). Laminar flow through a porous channel bounded by isothermal parallel plates. International Journal of Heat and Mass Transfer, 28(4), 851-858.
  40. Liu, S., Afacan, A., & Masliyah, J. (1994). Steady Incompressible Laminar Flow in Porous Media. Chmdml Engineering Science, 3565-3586.
  41. Pillai, K., Varma, S., & Babu, M. S. (1987, August). Aligned magnetic effects through varying permeable bed. Proc. Indian Acad. Sci. (Math. Sci.), 96(1), 61-69. Retrieved from https://www.ias.ac.in/article/fulltext/pmsc/096/01/0061-0069
  42. Sinha, A., & Chadda, G. (1984, September). Steady Laminar Viscous Flow Down an Open Inclined Channel with a Bed of Varying Permeability. Indian J. Pure Appl. Math., 15(9), 1004-1013. Retrieved from https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a6e_1004.pdf
  43. Narasimha Murthy, S., & Feyen, J. (1989). Influence of variable permeability on the dispersion of a chemically reacting solute in porous media. International Journal of Engineering Science, 27(12), 1661-1671. doi: https://doi.org/10.1016/0020-7225(89)90159-6
  44. Mathew, S. (2005). Mathematical Analysis. In S. Mathew, MHD Convective Heat Transfer Through a Porous Medium in a Vertical Channel with periodic permeability (pp. 7-10). India: Sri Krishnadevaraya University Anantapur. Retrieved from http://hdl.handle.net/10603/64940
  45. Srivastava, B., & Deo, S. (2013, May). Effect of magnetic field on the viscous fluid flow in a channel filled with porous medium of variable permeability. Applied Mathematics and Computation, 219(17), 8959-8964. doi: https://doi.org/10.1016/j.amc.2013.03.065
  46. He, J. H. (2008). Recent Development of the Homotopy Perturbation Method. Topological Methods in Nonlinear Analysis, 31, 205-209. Retrieved from https://projecteuclid.org/download/pdf_1/euclid.tmna/1463150264
  47. Geindreau, C., & Auriault, J.-L. (2002, September). Magnetohydrodynamic flows in porous media. Journal of Fluid Mechanics, 466, 343-363. doi: https://doi.org/10.1017/S0022112002001404
  48. Rudraiah, N., Ramaiah, B., & Rajasekhar, B. (1975, January). Hartmann flow over a permeable bed. International Journal of Engineering Science, 13(1), 1-24. doi: https://doi.org/10.1016/0020-7225(75)90070-1
  49. Merabet, N., Siyyam, H., & Hamdan, M. (2008). Analytical approach to the Darcy-Lapwood-Brinkman equation. Applied Mathematics and Computation, 196, 679-685. doi: https://doi.org/10.1016/j.amc.2007.07.003
  50. Abu Zaytoon, M., Alderson, T., & Hamdan, M. (2016, June). Flow through a Layered Porous Configuration with Generalized Variable Permeability. International. Journal of Enhanced Research in Science, Technology & Engineering, 5(6), 1-21. Retrieved from http://www.erpublications.com/uploaded_files/download/download_05_06_2016_16_55_43.pdf
  51. Seyf, H., & Rassoulinejad-Mousavi, S. (2011). He’s Homotopy Method for Investigation of Flow and Heat Transfer in a Fluid Saturated Porous Medium. World Applied Sciences Journal, 15(12), 1791-1799. Retrieved from http://www.idosi.org/wasj/wasj15(12)11/21.pdf
  52. He, J. H. (2006). New interpretation of homotopy perturbation. International Journal of Modern Physics B, 20(18), 2561-2568. Retrieved from https://works.bepress.com/ji_huan_he/3/
  53. He, J. H. (2006, April). Some Asymptotic Methods for Strongly Nonlinear Equations. International Journal of Modern Physics B, 20(10), 1141-1199. doi: https://doi.org/10.1142/S0217979206033796
  54. He, J.-H. (1999, August). Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering, 178(3-4), 257-262. doi: https://doi.org/10.1016/S0045-7825(99)00018-3
  55. He, J.-H. (2000). A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-Linear Mechanics, 35(1), 37-43. doi: https://doi.org/10.1016/S0020-7462(98)00085-7
  56. He, J.-H. (2003, February 15). Homotopy perturbation method: A new nonlinear analytical technique. Applied Mathematics and Computation, 135(1), 73-79. doi: https://doi.org/10.1016/S0096-3003(01)00312-5
  57. He, J.-H. (2004, March 30). The homotopy perturbation method for non-linear oscillators with discontinuities. Applied Mathematics and Computation, 151(1), 287-292. doi: https://doi.org/10.1016/S0096-3003(03)00341-2
  58. Jazbi, B., & Moini, M. (2008, February). Application of He’s homotopy perturbation method for Schrodinger equation. Iranian Journal of Mathematical Sciences and Informatics, 3(2), 13-19. https://ijmsi.ir/browse.php?a_id=51&sid=1&slc_lang=en
  59. Usman, M., Naheed, Z., Nazir, A., & Mohyud-Din, S. (2014, July). On MHD flow of an incompressible viscous fluid. Journal of the Egyptian Mathematical Society, 22(2), 214-219. doi: https://doi.org/10.1016/j.joems.2013.07.003
  60. Ochoa-Tapia, J. A., & Whitaker, S. (1995, September 1). Momentum transfer at the boundary between a porous medium and a homogeneous fluid — I. Theoretical development. International Journal of Heat and Mass Transfer, 38(14), 2635-2646. doi: https://doi.org/10.1016/0017-9310(94)00346-W
  61. Nield, D. (2000). Modelling Fluid Flow and Heat Transfer in a Saturated Porous Medium. Journal of Applied Mathematics & Decision Sciences, 4(2), 165-173. Retrieved from http://www.kurims.kyoto-u.ac.jp/EMIS/journals/HOA/JAMDS/Volume4_2/173.pdf
  62. Givler, R., & Altobelli, S. (1994, January 10). A determination of the effective viscosity for the Brinkman-Forchheimer flow model. Journal of Fluid Mechanics, 258, 355-370. doi: https://doi.org/10.1017/S0022112094003368
  63. Liu, S., & Masliyah, J. (2005). Dispersion in Porous Media. In K. Vafai (Ed.), Handbook of Porous Media (2 ed., pp. 110­111). Boca Raton, Florida, USA: Taylor & Francis.