ライブラリ登録: Guest

SLOW MOTION OF A POROUS SPHERE OF VARIABLE PERMEABILITY IN A BOUNDED MEDIUM: EFFECT OF STRESS JUMP CONDITION

巻 10, 発行 6, 2019, pp. 607-623
DOI: 10.1615/SpecialTopicsRevPorousMedia.2020028891
Get accessGet access

要約

In this paper, we present the study of the slow motion of a porous sphere of variable permeability in a spherical container, filled by a viscous incompressible fluid, at an instant it passes the center of the container. Flow in the spherical container and the porous sphere is governed by the Stokes equation and Brinkman's equation, respectively. Two cases are considered here: (i) when the permeability of the porous sphere varies quadratically with radial distance and (ii) when the permeability of the sphere is uniform. An analytical solution of the problem is obtained for both cases of permeability variation by using continuity of the velocity and normal stress and jump in tangential shear stress at the interface of the fluid and porous sphere as a boundary condition. Exact expression of the relevant hydrodynamical quantities such as streamlines, velocity, pressure, wall correction factor Wc, and drag D on the surface of the sphere are obtained. The influence of various parameters, such as stress jump coefficient β permeability parameter a and separation parameter λ, on streamlines, wall correction factor, and drag force, have been discussed and exhibited graphically. One figure shows that the drag force and wall correction parameter on the porous sphere increase with the decrease in stress jump coefficient β. We find that this parameter has a remarkable effect on Wc and drag D. Also, we compare the obtained results for both cases of permeability variation.

参考
  1. Alamri, S.Z., Ellahi, R., Shehzad, N., and Zeeshan, A., Convective Radiative Plane Poiseuille Flow of Nanofluid through Porous Medium with Slip: An Application of Stefan Blowing, J. Mol. Liq., vol. 273, pp. 292-304,2019.

  2. Beavers, G.S. and Joseph, D.D., Boundary Conditions at a Naturally Permeable Wall, J. Fluid Mech, vol. 30,no. 1,pp. 197-207, 1967.

  3. Bhatti, M.M., Abbas, T., Rashidi, M.M., Ali, M.E., and Yang, Z., Entropy Generation on MHD Eyring-Powell Nanofluid through a Permeable Stretching Surface, Entropy, vol. 18, no. 6, pp. 1-4,2016.

  4. Bhatti, M.M., Zeeshan, A., Ellahi, R., and Shit, G.C., Mathematical Modeling of Heat and Mass Transfer Effects on MHD Peristaltic Propulsion of Two-Phase Flow through a Darcy-Brinkman-Forchheimer Porous Medium, Adv. Powder Technol., vol. 29, no. 5, pp. 1189-1197,2018.

  5. Brinkman, H.C., A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles, Appl. Sci. Res. A, vol. 1,pp. 27-34,1947.

  6. Chikh, S., Boumedien, A., Bouhadef, K., and Lauriat, G., Analytical Solution of Non-Darcian Forced Convection in an Annular Duct Partially Filled with a Porous Medium, Int. J. Heat Mass Transf., vol. 38, pp. 1543-1551,1995.

  7. Ellahi, R., Bhatti, M.M., Riaz, A., and Sheikholeslami, M., The Effects of Magnetohydrodynamics on Peristaltic Flow of Jeffrey Fluid in a Rectangular Duct through a Porous Medium, J. Porous Media, vol. 17, no. 2, pp. 143-157,2014a.

  8. Ellahi, R., Nadeem, S., Riaz, A., and Akbar, N.S., Mathematical Model for the Peri-Staltic Flow of Nanofluid through Eccentric Tubes Comprising Porous Medium, Appl. Nanosci., vol. 4, no. 6, pp. 733-743,2014b.

  9. Ellahi, R., Nadeem, S., Riaz, A.. and Ali, M., Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium, Math. Probl. Eng., vol. 2012, pp. 1-24,2012.

  10. Grosan, T., Postelnicu, A., and Pop, I., Brinkman Flow of a Viscous Fluid through a Spherical Porous Medium Embedded in Another Porous Medium, Transp. Porous Media, vol. 81, pp. 89-103,2010.

  11. Haberman, W.L. and Sayre, R.M., Wall Effects for Rigid and Fluid Spheres in Slow Motion with a Moving Liquid, David Taylor Model, Basin Report No. 1143, Washington, DC, 1958.

  12. Keh, H.J. andChou, J., Creeping Motion of a Composite Sphere in Spherical Cavity, Chem. Eng. Sci., vol. 59, pp. 407-415,2004.

  13. Khan, J.A., Numerical Study of Nanofluid Flow and Heat Transfer over a Rotating Disk Using Buongiornos Model, Int. J. Numer. Methods Heat Fluid Flow, vol. 27, no. 1, pp. 221-234,2017.

  14. Kim, A.S. and Yuan, R., Hydrodynamics of an Ideal Aggregate with Quadratically Increasing Permeability, J. Colloid Interface Sci, vol. 285, no. 2, pp. 627-633,2005.

  15. Kuo, J. and Keh, H.J., Motion of a Colloid Sphere Covered by a Layer of Adsorbed Polymers Normal at a Plane Surface, J. Colloid Interface Sci, vol. 210, no. 2, pp. 296-308,1999.

  16. Masliyah, J.H., Afacan, A., and Liu, S., Flow through a Tube with an Annual Porous Medium Layer, J. Porous Media, vol. 8, no. 2, pp. 193-210,2005.

  17. Maskeen, M.M., Mehmood, O.U., and Zeeshan, A., Hydromagnetic Solidliquid Pulsatile Flow through Concentric Cylinders in a Porous Medium, J. Visualization, vol. 21, no. 3, pp. 407-419,2018.

  18. Mishra, S.R., Baag, S., and Bhatti, M.M., Study of Heat and Mass Transfer on MHD Walters B Nanofluid Flow Induced by a Stretching Porous Surface, Alexandria Eng. J, vol. 57, no. 4, pp. 2435-2443,2018.

  19. Ochoa-Tapia, J.A. and Whitaker, S., Momentum Jump Condition at the Boundary between a Porous Medium and a Homogeneous Fluid: Inertial Effects, J. Porous Media, vol. 1, pp. 201-217,1998.

  20. Padmavathi, B.S., Amaranath, T., and Nigam, S.D., Stokes Flow past a Porous Sphere Using Brinkman Model, Z. Angew. Math. Phys, vol. 44, pp. 929-939,1993.

  21. Ramkissoon, H. and Rahman, K., NonNewtonian Fluid Sphere in a Spherical Container, Acta Mech, vol. 149, pp. 239-245,2001.

  22. Ramkissoon, H. and Rahman, K., Wall Effects on a Spherical Particle, Int. J. Eng. Sci., vol. 41, pp. 283-290,2003.

  23. Riaz, A., Razaq, A., and Awan, A.U., Magnetic Field and Permeability Effects on Jeffrey Fluid in Eccentric Tubes Having Flexible Porous Boundaries, J. Magn, vol. 22, no. 4, pp. 642-648,2017.

  24. Saad, E.I., Translation and Rotation of a Porous Spheroid in a Spheroidal Container, Can. J. Phys., vol. 88, pp. 689-700,2010.

  25. Saad, E.I. and Faltas, M.S., Slow Motion of a Porous Sphere Translating along the Axis of a Circular Cylindrical Pore Subject to a Stress Jump Condition, Transp. Porous Media, vol. 102, no. 1, pp. 91-109,2014.

  26. Sheikholeslami, M. and Zeeshan, A., Numerical Simulation of Fe3O4-Water Nanofluid Flow in a Non-Darcy Porous Media, Int. J. Numer. Methods Heat Fluid Flow, vol. 28, no. 3, pp. 641-660,2018.

  27. Srinivasacharya, D., Motion of a Porous Sphere in a Spherical Container, C.R. Mec., vol. 333, pp. 612-616,2005.

  28. Srinivasacharya, D., Axisymmetric Motion of a Porous Approximate Spherical Container, Arch. Mech., vol. 65, no. 6, pp. 485-509, 2013.

  29. Turkyilmazoglu, M., Flow and Heat Simultaneously Induced by Two Stretchable Rotating Disks, Phys. Fluids, vol. 28, 043601, 2016.

  30. Turkyilmazoglu, M., Unsteady Flow over a Decelerating Rotating Sphere, Phys. Fluids, vol. 30, no. 3, 033601,2018a.

  31. Turkyilmazoglu, M., Fluid Flow and Heat Transfer over a Rotating and Vertically Moving Disk, Phys. Fluids, vol. 30, 063605, 2018b.

近刊の記事

HYDROMAGNETIC CASSON FLUID FLOW ACROSS AN INCLINED VERTICAL SURFACE IN POROUS CHANNEL WITH BUOYANCY AND THERMO-DIFFUSION EFFECTS Sowmiya C, Rushi Kumar B Effect of Helical Force on Thermal Convection of a Ferrofluid: A Weakly Non-linear Theory Jagathpally Sharathkumar Reddy, Kishan N, Shiva Kumar Reddy G, Ravi Ragoju STABILITY ANALYSIS OF A COUPLE-STRESS FLUID WITH VARIABLE GRAVITY IN A POROUS MEDIUM FOR DIFFERENT CONDUCTING BOUNDARIES Shalu Choudhary, Reeta Devi, Amit Mahajan, Sunil Sunil CREEPING FLOW ABOUT A TAINTED LIQUID DROP WITH A MICROPOLAR FLUID AND ALIGNED IN A POROUS MEDIUM FILLED WITH VISCOUS FLUID UTILISING SLIP PHANI KUMAR MEDURI, VIJAYA LAKSHMI KUNCHE Reviewing the Impact of Magnetic Prandtl Number and Magnetic Force Parameter on Convective Heat Transfer in Boundary Layers Hossam Nabwey, Muhammad Ashraf, Zia Ullah, Ahmed M. Rashad, Ali J. Chamkha Spectral Analysis for Entropy Generation and Irreversibility on NiZnFe_2O_4 – Engine Oil based Fluids RamReddy Chetteti, Sweta ., Pranitha Janapatla Study of global stability of rotating partially-ionized plasma saturating a porous medium Vishal Chandel, Sunil Kumar, Poonam Sharma Porous Medium Influenced Dissipative Hybrid Casson Nanofluid Flow over a Nonlinearly Stretching Sheet under Inclined Ohmic Lorentz Force Field A. R. Deepika, K. Govardhan, Hussain Basha, G Janardhana Reddy Effect of Motile Gyrotactic Microorganisms on Arterial Stenosis Sisko Nanofluid Flow Through Porous Medium : A Numerical Study Galal Moatimid, Mona Mohamed, Khaled Elagamy, Ahmed Gaber ELECTROTHERMOSOLUTAL CONVECTION IN NANOFLUID SATURATING POROUS MEDIUM Pushap Lata Sharma, Mohini Kapalta EFFECT OF VARIABLE GRAVITY ON THERMAL CONVECTION IN ROTATING JEFFREY NANOFLUID: DARCY-BRINKMAN MODEL Deepak Bains, Pushap Lata Sharma, Gian C. Rana Activation energy effect on MHD convective Maxwell nanofluid flow with Cattaneo-Christove heat flux over a porous stretching sheet JYOTHI NAGISETTY, VIJAYA KUMAR AVULA GOLLA Effects of different fins on Maxwell liquid under hybrid surveys of magnetic and porous material in presence of radiation factors Pooya Pasha, Payam Jalili, Bahram Jalili, Loghman Mostafa, Ahmed Mohammed Mahmood, Hussein Abdullah Abbas, D.D. Ganji
Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集 価格及び購読のポリシー Begell House 連絡先 Language English 中文 Русский Português German French Spain