年間 4 号発行
ISSN 印刷: 2151-4798
ISSN オンライン: 2151-562X
Indexed in
FLOW OF MICROPOLAR FLUID PAST A POROUS SPHERE EMBEDDED IN ANOTHER POROUS MEDIUM
要約
The steady axisymmetric uniform flow of an incompressible micropolar fluid past a porous sphere embedded in another porous medium has been studied analytically. The stream function solution for both the inner and outer flow field is acquired by using the Brinkman equation. Explicit expressions are determined for both the flow fields by taking the appropriate boundary conditions across the surface of the porous sphere. Furthermore, the non-dimensional drag experienced by a porous sphere embedded in another porous medium of micropolar fluid is calculated. Effects of drag force and shearing stress on permeability parameter, the viscosity ratio for the porous sphere is presented graphically and numerically. Some special cases of flow past a porous sphere have been validated with earlier well-known cases.
-
Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, New York: Dover, 1970.
-
Ansari, I.A. and Deo, S.,MagnetohydrodynamicViscous Fluid Flow past a Porous Sphere Embedded in Another PorousMedium, Special Topics Rev. Porous Media, vol. 9, no. 2, pp. 191-200, 2018.
-
Barman, B., Flow of a Newtonian Fluid past an Impervious Sphere Embedded in a Porous Medium, Indian J. Pure Appl. Math., vol. 27, no. 12, pp. 1249-1256, 1996.
-
Chamkha, A.J.,MHD-Free Convection from a Vertical Plate Embedded in a Thermally Stratified PorousMediumwith Hall Effects, Appl. Math. Model., vol. 21, pp. 603-609, 1997.
-
Chamkha, A.J., Solar Radiation Assisted Natural Convection in Uniform Porous Medium Supported by a Vertical Flat Plate, J. Heat Transf., vol. 119, pp. 89-96, 1997.
-
Chamkha, A.J. and Khaled, A.R.A., Hydromagnetic Combined Heat and Mass Transfer by Natural Convection from a Permeable Surface Embedded in a Fluid-Saturated Porous Medium, Int. J. Num. Heat Fluid Flow, vol. 10, no. 5, pp. 455-477, 2000.
-
Chamkha, A.J. and Khaled, A.R.A., Similarity Solutions for Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow through Porous Media, Int. J. Num. Methods Heat Fluid Flow, vol. 10, no. 1, pp. 94-115, 2000.
-
Chamkha, A.J., Coupled Heat and Mass Transfer by Natural Convection about a Truncated Cone in the Presence ofMagnetic Field and Radiation Effects, J. Num. Heat Transf., vol. 39, pp. 511-530, 2001.
-
Chamkha, A.J., Issa, C., and Khanafer, K., Natural Convection from an Inclined Plate Embedded in a Variable Porosity Porous Medium due to Solar Radiation, Int. J. Therm. Sci., vol. 41, pp. 73-81, 2002.
-
Chamkha, A.J., Mohamed, R.A., and Ahmed, S.E., Unsteady MHD Natural Convection from a Heated Vertical Porous Plate in a Micropolar Fluid with Joule Heating, Chemical Reaction and Radiation Effects, Meccanica, vol. 46, pp. 399-411, 2011.
-
Chamkha, A.J., Abbasbandy, S., and Rashad, A.M., Radiation Effects on Mixed Convection about a Cone Embedded in a Porous Medium Filled with a Nanofluid, Meccanica, vol. 48, pp. 275-285, 2013.
-
Damesh, R.A., Al-Odat, M.Q., Chamkha, A.J., and Shannak, B.A., Combined Effect of Heat Generation or Absorption and Firstorder Chemical Reaction onMicropolar Fluid Flows over a Uniformly Stretched Permeable Surface, Int. J. Therm. Sci., vol. 48, pp. 1658-1663, 2009.
-
Deo, S., Stokes Flow past a Swarm of Deformed Porous Spheroidal Particles with Happel Boundary Condition, J. Porous Media, vol. 12, no. 4, pp. 347-359, 2009.
-
Deo, S. and Ansari, I.A., Brinkman Flow through a Porous Cylinder Embedded in Another Unbounded PorousMedium, J. Porous Media, vol. 22, no. 6, pp. 681-692, 2019.
-
Deo, S. and Gupta, B.R., Stokes Flow past a Swarm of Porous Aproximately Spheroidal Particles with Kuwabara Boundary Condition, Acta Mech., vol. 203, no. 3, pp. 241-254, 2009.
-
Deo, S. and Gupta, B.R., Drag on a Porous Sphere Embedded in Another Porous Medium, J. Porous Media, vol. 13, no. 11, pp. 1009-1016, 2010.
-
Deo, S. and Shukla, P., Drag on a Fluid Sphere Embedded in a Porous Medium, Adv. Theor. Appl. Mech., vol. 3, no. 1, pp. 45-52, 2010.
-
Gorla, R.S.R. and Chamkha, A.J., Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid, J. Modern Phys., vol. 2, pp. 62-71, 2011.
-
Gupta, B.R. and Deo, S., Stokes Flow of Micropolar Fluid past a Porous Sphere with Non-Zero Boundary Condition for Microrotations, Int. J. Fluid Mech., vol. 37, no. 5, pp. 424-434, 2010.
-
Hoffmann, K.H., Marx, D.M., and Botkin, N.D., Drag on Spheres in Micropolar Fluids with Non-Zero Boundary Conditions for Microrotations, J. Fluid Mech., vol. 590, pp. 319-330, 2007.
-
Jaiswal, B.R., A Non-Newtonian Liquid Sphere Embedded in a Polar Fluid Saturated Porous Medium: Stokes Flow, Appl. Math. Comp., vol. 316, pp. 488-503, 2018.
-
Jaiswal, B.R. and Gupta, B.R., Stokes Flow over a Non-Newtonian Encapsulated Drop of Another Liquid: Effect of Stress Jump, J. Porous Media, vol. 20, no. 9, pp. 807-821, 2017.
-
Khedr, M.E.M., Chamkha, A.J., and Bayomi, M.,MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption, Nonlin.: Model. Control, vol. 14, no. 1, pp. 27-40, 2009.
-
Mudhaf, A.A. and Chamkha, A.J., Similarity Solutions for MHD Thermosolutal Marangoni Convection over a Flat Surface in the Presence of Heat Generation or Absorption Effects, J. Heat Mass Transf., vol. 42, pp. 112-121, 2005.
-
Pal, D. and Mondal, H., Radiation Effects on Combined Convection over a Vertical Flat Plate Embedded in a Porous Medium of Variable Porosity, Meccanica, vol. 44, no. 2, pp. 133-144, 2009.
-
Pop, I. and Ingham, D.B., Flow past a Sphere Embedded in a Porous Medium based on the Brinkman Model, Int. Commun. Heat Mass Transf., vol. 23, no. 6, pp. 865-874, 1996.
-
Qin, Y. and Kaloni, P.N., A Cartesian-Tensor Solution of Brinkman Equation, J. Eng. Math., vol. 22, pp. 177-188, 1988.
-
Qin, Y. and Kaloni, P.N., Creeping Flow past a Spherical Shell, J. Appl. Math. Mech., vol. 73, no. 2, pp. 77-84, 1993.
-
Ramkisson, H., Flow of Micropolar Fluid past a Newtonian Fluid Sphere, ZAMM-J. Appl. Math. Mech., vol. 65, no. 12, pp. 635-637, 1985.
-
Reddy, P.S. and Chamkha, A.J., Soret and Dufour Effects on MHD Convective Flow of Al2O3-Water and TiO2-Water Nanofluids past a Stretching Sheet in Porous Media with Heat Generation or Absorption, Adv. Powder Technol., vol. 27, pp. 1207-1218, 2016.
-
Reddy, P.S., Sreedevi, P., and Chamkha, A.J., MHD Boundary Layer Flow, Heat and Mass Transfer Analysis over a Rotating Disk through Porous Medium Saturated by Cu-Water and Ag-Water Nanofluid with Chemical Reaction, Powder Technol., vol. 307, pp. 46-55, 2017.
-
Srinivasacharya, D., Creeping Flow past a Porous Aproximate Sphere, Z Angew Math. Mech., vol. 83, no. 7, pp. 1-6, 2003.
-
Srinivasacharya, D. and Ramana Murthy, J.V., Flow past an Axisymmetric Body Embedded in a Saturated Porous Medium, C.R. Mecanique, vol. 330, no. 6, pp. 417-423, 2002.
-
Srinivasacharya, D. and Rajyalakshmi, I., Creeping Flow of Micropolar Fluid past a Porous Sphere, Appl. Math. Comp., vol. 153, no. 3, pp. 843-854, 2004.
-
Stokes, G.G., On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, J. Trans. Camb. Philos. Soc., vol. 9, pp. 8-106, 1851.
-
Takhar, H.S., Chamkha, A.J., and Nath, G., Unsteady Mixed Convection Flow from a Rotating Vertical Cone with a Magnetic Field, J. Heat Mass Transf., vol. 39, pp. 297-304, 2003.
-
Umavathi, J.C., Kumar, J.P., Chamkha, A.J., and Pop, I., Mixed Convection in a Vertical Porous Channel, Transp. Porous Media, vol. 61, pp. 315-335, 2005.
-
Yadav, P.K. and Deo, S., Stokes Flow past a Porous Spheroid Embedded in Another Porous Medium, Meccanica, vol. 47, no. 6, pp. 1499-1516, 2012.
-
Yadav, P.K., Deo, S., Singh, S.P., and Filippov, A., Effect of Magnetic Field on the Hydrodynamic Permeability of a Membrane Built up by Porous Spherical Particles, Colloid J., vol. 79, pp. 160-171, 2017.
-
Yadav, P.K., Tiwari, A., Deo, S., Filippov, A., and Vasin, S., Hydrodynamic Permeability of Membranes Built up by Spherical Particles Covered by Porous Shells: Effect of Stress Jump Condition, Acta Mechanica, vol. 215, pp. 193-209, 2010.
-
Zlatanovski, T., Axisymmetric Creeping Flow past a Porous Prolate Spheroidal Particle Using the Brinkman Model, QJ Mech. Appl. Math., vol. 52, no. 1, pp. 111-126, 1999.
-
Taid Bijoy Krishna, Ahmed Nazibuddin, Das Nabanita, Transient MHD convective flow of a micropolar fluid past a moving vertical plate in the presence of thermal diffusion, Heat Transfer, 51, 6, 2022. Crossref
-
Mishra Vandana, Gupta Bali Ram, Drag exerted by a micropolar fluid on a dense swarm of permeable spherical particles, Archive of Applied Mechanics, 92, 11, 2022. Crossref