Solución de Mhpm al flujo de fluido de Mhd a través de un medio poroso con una permeabilidad exponencialmente variable
Contenido principal del artículo
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.
Descargas
Metrics
Detalles del artículo

Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial 4.0.
Los autores que publiquen en la revista ACI Avances en Ciencias e Ingenierías aceptan los siguientes términos:
- Los autores conservarán sus derechos de autor y garantizarán a la revista el derecho de primera publicación de su obra, la cual estará simultáneamente sujeto a la Licencia de reconocimiento de Creative Commons que permite a terceros compartir la obra siempre que se indique su autor y su primera publicación esta revista.
- Los autores podrán adoptar otros acuerdos de licencia no exclusiva de distribución de la versión de la obra publicada, pudiendo de esa forma publicarla en un volumen monográfico o reproducirla de otras formas, siempre que se indique la publicación inicial en esta revista.
- Se permite y se recomienda a los autores difundir su obra a través de Internet:
- Antes del envío a la revista, los autores pueden depositar el manuscrito en archivos/repositorios de pre-publicaciones (preprint servers/repositories), incluyendo arXiv, bioRxiv, figshare, PeerJ Preprints, SSRN, entre otros, lo cual puede producir intercambios interesantes y aumentar las citas de la obra publicada (Véase El efecto del acceso abierto).
- Después del envío, se recomiendo que los autores depositen su artículo en su repositorio institucional, página web personal, o red social científica (como Zenodo, ResearchGate o Academia.edu).
Citas
[2] H. C. Brinkman, "A Calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles," Appl. Scientific Res., vol. A1, pp. 27-34, 1947.
[3] M. Hamdan and M. Kamel, "Flow through Variable Permeability Porous Layers," Adv. Theor. Appl. Mech., vol. 4, no. 3, p. 135 – 145, 2011.
[4] D. A. Nield and A. Bejan, "Mechanics of Fluid Flow Through Porous Media," in Convection in Porous Media, 3 ed., Springer, 2006, pp. 14-16.
[5] J.-L. Auriault, "On the Domain of Validity of Brinkman’s Equation," Transport in Porous Media, vol. 79, no. 2, pp. 215-223, September 2009.
[6] N. Rudraiah, "Flow past porous layers and their stability," in Encyclopedia of Fluid Mechanics, Slurry Flow Technology, vol. 8, N. P. Cheremisinoff, Ed., Houston, Texas: Gulf Publishing., 1986, pp. 567-647.
[7] M. Parvazinia, V. Nassehi, R. J. Wakeman and M. H. R. Ghoreishy, "Finite element modelling of flow through a porous medium between two parallel plates using the Brinkman equation," Transport in Porous Media, no. 63, p. 71–90, April 2006.
[8] D. A. Nield, "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, vol. 12, no. 3, pp. 269-272, September 1991.
[9] M. Sahraoui and M. Kaviany, "Slip and no-slip velocity boundary conditions at interface of porous, plain media," International Journal of Heat and Mass Transfer, vol. 35, no. 4, pp. 927-943, 1992.
[10] M. Kaviany, "Part I Single Phase Flow. Fluid Mechanics," in Principles of Heat Transfer in Porous Media, 2 ed., Spinger, Mechanical Engineering Series, 1995, pp. 95-100.
[11] T. S. Lundgren, "Slow Flow Through Stationary Random Beds and Suspensions of Spheres," Journal of Fluid Mechanics, no. 51, p. 273–299, 1972.
[12] A. H.-D. Cheng, "Darcy's Flow With Variable Permeability: A Boundary Integral Solution," Water Resources Research, vol. 20, no. 7, pp. 980-984, July 1984.
[13] M. H. Hamdan and M. S. Abu Zaytoon, "Flow over a Finite Forchheimer Porous Layer with Variable Permeability," IOSR Journal of Mechanical and Civil Engineering, vol. 14, no. 3, pp. 15-22, May-June 2017.
[14] P. Kuzhir, G. Bossis, V. Bashtovoi and O. Volkovab, "Flow of magnetorheological fluid through porous media," European Journal of Mechanics B/Fluids, no. 22, pp. 331-343, 2003.
[15] C. Bárcena, A. Sra and J. Gao, "Applications of Magnetic Nanoparticles in Biomedicine," in Nanoscale Magnetic Materials and Applications, J. Ping Liu, E. Fullerton, O. Gutfleisch and D. Sellmyer, Eds., Springer, 2009, pp. 591-626.
[16] H. Attia and M. Abdeen, "Unsteady MHD Flow and Heat Transfer Between Parallel Porous Plates with Exponential Decaying Pressure Gradient," Kragujevac Journal of Science, no. 34, pp. 15-22, 2012.
[17] S. Shehzad and T. A. A. Hayat, "Influence of convective heat and mass conditions in MHD flow of nanofluid," Bull.Polish Acad.Sci. Tech. Sci., vol. 63, no. 2, p. 465–474, 2015.
[18] S. Mishra, S. Baag, G. Dash and M. Acharya, "Numerical approach to MHD flow of power-law fluid on a stretching sheet with non-uniform heat source," Nonlinear Engineering, vol. 9, no. 1, pp. 81-93, 2019.
[19] J. Hartmann and F. Lazarus, "Experimental investigations on the flow of mercury in a homogeneous magnetic field," Matematisk-fysiske meddelelser Kongelige Danske Videnskabernes Selskab, vol. 15, no. 7, pp. 1-45, 1937.
[20] A. Jeffrey, "Incompressible Magnetohydrodynamic Flow.," in Magnetohydrodynamics, First ed., A. Aitken and D. Rutherford, Eds., Edinburgh and London, Oliver & Boyd, 1966, pp. 90-99.
[21] U. Müller and L. Bühler, "Analytical solutions for MHD channel flow," in Magnetofluiddynamics in Channels and Containers, Berlin-Heidelberg, Springer, 2001, pp. 37-56.
[22] A. P. Rothmayer, "Magnetohydrodynamic channel flows with weak transverse magnetic fields," Phil. Trans. R. Soc. A., no. 372, pp. 1-12, 2014.
[23] M. Kaviany, "Laminar flow through a porous channel bounded by isothermal parallel plates," International Journal of Heat and Mass Transfer, vol. 28, no. 4, pp. 851-858, 1985.
[24] S. Liu, A. Afacan and J. Masliyah, "Steady Incompressible Laminar Flow in Porous Media," Chmdml Engineering Science, pp. 3565-3586, 1994.
[25] W.-S. Fu, H.-C. Huang and W.-Y. Liou, "Thermal enhancement in laminar channel flow with a porous block," International Journal of Heat and Mass Transfer, vol. 39, no. 10, p. 2165 2175, 1996.
[26] M. Awartani and M. Hamdan, "Fully developed flow through a porous channel bounded by flat plates," Applied Mathematics and Computation, vol. 2, no. 169, pp. 749-757, October 2005.
[27] D. A. Harwin, Flows in Porous Channels, Bath: University of Bath, 2007, p. 198.
[28] I. Hassanien, A. Salama and A. Elaiw, "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, vol. 146, no. 2-3, pp. 829-847, December 2003.
[29] I. Hassanien, "Variable permeability effects on mixed convection along a vertical wedge embedded in a porous medium with variable surface heat flux," Applied Mathematics and Computation, vol. 138, pp. 41-59, 2003.
[30] J.-Y. Jang and J.-L. Chen, "Variable porosity effect on vortex instability of a horizontal mixed convection flow in a saturated porous medium," International Journal of Heat and Mass Transfer, vol. 36, no. 6, pp. 1573-1582, 1993.
[31] A. Elaiw, F. Ibrahim and A. Bakr, "Variable permeability and inertia effect on vortex instability of natural convection flow over horizontal permeable plates in porous media," Commun Nonlinear Sci Numer Simulat, vol. 14, p. 2190–2201, 2009.
[32] B. Chandrasekhara, A. Hanumanthappa and S. Chandranna, "Influence of Variable Permeability on the Basic Flows in Porous Media," Indian Journal of Technology, vol. 22, no. 8, pp. 281-283, 01 January 1984.
[33] B. Chandrasekhara, P. Namboodiri and A. Hanumanthappa, "Similarity solutions for buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces," Wärme-und Stoffübertragung, vol. 18, no. 1, pp. 17-23, 01 March 1984.
[34] B. Chandrasekhara, P. Namboodiri and A. R. Hanumanthappa, "Mixed convection in the presence of horizontal impermeable surfaces in saturated porous media with variable permeability," Wärme-und Stoffübertragung, vol. 19, no. 3, pp. 195-201, 01 September 1985.
[35] B. Chandrasekhara and P. Namboodiri, "Influence of variable permeability on combined free and forced convection about inclined surfaces in porous media," International Journal of Heat and Mass Transfer, vol. 28, no. 1, pp. 199-206, 01 January 1985.
[36] R. Goldstein, W. Ibele, S. Patankar, T. Simon, T. Kuehn, P. Strykowski, K. Tamma, J. Heberlein, J. Davidson, J. Bischof, F. Kulacki, U. Kortshagen, S. Garrick and V. Srinivasan, "Heat transfer—A review of 2003 literature," International Journal of Heat and Mass Transfer, vol. 49, p. 451–534, 2006.
[37] R. Schiffman and R. Gibson, "Consolidation of Nonhomogeneous Clay Layers," Journal of the Soil Mechanics and Foundations Division, vol. 90, no. 5, pp. 1-30, 1964.
[38] M. S. Mahmoud and H. Deresiewicz, "Settlement of inhomogeneous consolidating soils—I: The single‐drained layer under confined compression," International Journal for Numerical and Analytical Methods in Geomechanics, vol. 4, no. 1, pp. 57-72, January-March 1980.
[39] D. A. S. Rees and I. Pop, "Vertical free convection in a porous medium with variable permeability effects," International Journal of Heat and Mass Transfer, vol. 43, pp. 2565-2571, 2000.
[40] Z. Alloui, R. Bennacer and P. Vasseur, "Variable permeability effect on convection in binary mixtures saturating a porous layer," Heat and Mass Transfer, vol. 45, no. 8, pp. 1117-1127, June 2009.
[41] M. Abu Zaytoon, Flow through and over porous layers of variable thickness and permeability, M. Hamdan, Ed., University of New Brunswick, 2015, p. 288.
[42] K. Choukairy and R. Bennacer, "Numerical and Analytical Analysis of the Thermosolutal Convection in an Heterogeneous Porous Cavity," FDMP-Fluid Dynamics & Materials Processing, vol. 8, no. 2, pp. 155-172, 2012.
[43] K. Pillai, S. Varma and M. S. Babu, "Aligned magnetic effects through varying permeable bed.," Proc. Indian Acad. Sci. (Math. Sci.), vol. 96, no. 1, pp. 61-69, August 1987.
[44] A. Sinha and G. Chadda, "Steady Laminar Viscous Flow Down an Open Inclined Channel with a Bed of Varying Permeability," Indian J. Pure Appl. Math., vol. 15, no. 9, pp. 1004-1013, September 1984.
[45] S. Narasimha Murthy and J. Feyen, "Influence of variable permeability on the dispersion of a chemically reacting solute in porous media," International Journal of Engineering Science, vol. 27, no. 12, pp. 1661-1671, 1989.
[46] S. Mathew, "Mathematical Analysis," in MHD Convective Heat Transfer Through a Porous Medium in a Vertical Channel with periodic permeability, Sri Krishnadevaraya University Anantapur, 2005, pp. 7-10.
[47] B. Srivastava and S. Deo, "Effect of magnetic field on the viscous fluid flow in a channel filled with porous medium of variable permeability," Applied Mathematics and Computation, vol. 219, no. 17, pp. 8959-8964, May 2013.
[48] J. H. He, "Recent Development of the Homotopy Perturbation Method," Topological Methods in Nonlinear Analysis, vol. 31, p. 205–209, 2008.
[49] C. Geindreau and J.-L. Auriault, "Magnetohydrodynamic flows in porous media," Journal of Fluid Mechanics, vol. 466, pp. 343-363, September 2002.
[50] N. Rudraiah, B. Ramaiah and B. Rajasekhar, "Hartmann flow over a permeable bed," International Journal of Engineering Science, vol. 13, no. 1, pp. 1-24, January 1975.
[51] N. Merabet, H. Siyyam and M. Hamdan, "Analytical approach to the Darcy–Lapwood–Brinkman equation," Applied Mathematics and Computation, vol. 196, p. 679–685, 2008.
[52] M. Abu Zaytoon, T. Alderson and M. Hamdan, "Flow through a Layered Porous Configuration with Generalized Variable Permeability," International. Journal of Enhanced Research in Science, Technology & Engineering, vol. 5, no. 6, pp. 1-21, June 2016.
[53] S. Alzahrani, I. Gadoura and M. Hamdan, "Nield- Kuznetsov Functions of the First- and Second Kind," IOSR Journal of Applied Physics, vol. 8, no. 3 Version III, pp. 47-56, May-June 2016.
[54] H. Seyf and S. Rassoulinejad-Mousavi, "He's Homotopy Method for Investigation of Flow and Heat Transfer in a Fluid Saturated Porous Medium," World Applied Sciences Journal, vol. 15, no. 12, pp. 1791-1799, 2011.
[55] J.-H. He, "Homotopy perturbation technique," Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3–4, pp. 257-262, August 1999.
[56] J.-H. He, "A coupling method of a homotopy technique and a perturbation technique for non-linear problems," International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37-43, 2000.
[57] J.-H. He, "Homotopy perturbation method: A new nonlinear analytical technique," Applied Mathematics and Computation, vol. 135, no. 1, pp. 73-79, 15 February 2003.
[58] J.-H. He, "The homotopy perturbation method for non-linear oscillators with discontinuities," Applied Mathematics and Computation, vol. 151, no. 1, pp. 287-292, 30 March 2004.
[59] B. Jazbi and M. Moini, "Application of He’s homotopy perturbation method for Schrodinger equation," Iranian Journal of Mathematical Sciences and Informatics, vol. 3, no. 2, pp. 13-19, February 2008.
[60] M. Usman, Z. Naheed, A. Nazir and S. Mohyud-Din, "On MHD flow of an incompressible viscous fluid," Journal of the Egyptian Mathematical Society, vol. 22, no. 2, pp. 214-219, July 2014.
[61] J. H. He, "Some Asymptotic Methods for Strongly Nonlinear Equations," International Journal of Modern Physics B, vol. 20, no. 10, p. 1141–1199, April 2006.
[62] J. H. He, "New interpretation of homotopy perturbation," International Journal of Modern Physics B, vol. 20, no. 18, p. 2561–2568, 2006.
[63] J. A. Ochoa-Tapia and S. Whitaker, "Momentum transfer at the boundary between a porous medium and a homogeneous fluid — I. Theoretical development.," International Journal of Heat and Mass Transfer, vol. 38, no. 14, pp. 2635-2646, 1 September 1995.
[64] D. Nield, "Modelling Fluid Flow and Heat Transfer in a Saturated Porous Medium," Journal of Applied Mathematics & Decision Sciences, vol. 4, no. 2, pp. 165-173, 2000.
[65] R. Givler and S. Altobelli, "A determination of the effective viscosity for the Brinkman–Forchheimer flow model," Journal of Fluid Mechanics, vol. 258, pp. 355-370, 10 January 1994.
[66] H. Liu, P. Patil and U. Narusawa, "On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders," Entropy, vol. 9, pp. 118-131, 2007.
[67] S. Liu and J. Masliyah, "Dispersion in Porous Media," in Handbook of Porous Media, 2 ed., K. Vafai, Ed., Boca Raton, Florida: Taylor & Francis, 2005, pp. 110-111.