Solución de Mhpm al flujo de fluido de Mhd a través de un medio poroso con una permeabilidad exponencialmente variable
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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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Silva, R., Hamdan, M. H., Erazo-Bone, R., Chuchuca-Aguilar, F., & Escobar-Segovia, K. (2021). Solución de Mhpm al flujo de fluido de Mhd a través de un medio poroso con una permeabilidad exponencialmente variable. ACI Avances En Ciencias E Ingenierías, 13(2), 24. https://doi.org/10.18272/aci.v13i2.2259
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Citas
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[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.
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[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.
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[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.
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[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.
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