Abonnement à la biblothèque: Guest
Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections
Journal of Porous Media
Facteur d'impact: 1.752 Facteur d'impact sur 5 ans: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

Volume 23, 2020 Volume 22, 2019 Volume 21, 2018 Volume 20, 2017 Volume 19, 2016 Volume 18, 2015 Volume 17, 2014 Volume 16, 2013 Volume 15, 2012 Volume 14, 2011 Volume 13, 2010 Volume 12, 2009 Volume 11, 2008 Volume 10, 2007 Volume 9, 2006 Volume 8, 2005 Volume 7, 2004 Volume 6, 2003 Volume 5, 2002 Volume 4, 2001 Volume 3, 2000 Volume 2, 1999 Volume 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.2020024935
pages 865-881


Rakesh Kumar
Department of Mathematics, Central University of Himachal Pradesh, Dharamshala, India
Sabir Ali Shehzad
Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan
M. N. Bashir
Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan


We present a numerical scheme based on explicit finite difference approximation to handle the three-dimensional boundary layer flow of absorbing, emitting, and electrically conducting grey nanofluid over a flat surface. Nanofluid is designed by suspending iron-oxide nanoparticles (IONPs) in the base fluid. The flow field is assumed to be embedded in the porous medium, which executes vibrational rotations. To maintain the flow, velocity slip is introduced at the liquid-sheet interface. The governing equations are reduced to nondimensional form using dimensionless parameters and variables. The stability and convergence criteria have also been discussed to elaborate the validity of results. The hydromagnetic and convective heat transfer characteristics of magnetite nanofluid have been exhibited through graphs and tables for different related parameters. Substantial influences of oscillations and rotations have been noticed on the velocity profiles, temperature profiles, skin-friction coefficients, and Nusselt number.


  1. Arjun, K.S. and Rakesh, K., Hydrodynamics and Heat Transfer Analysis of Nanofluid Flow in a Circular Microchannel by Simulations, J. Porous Media, vol. 8, no. 2, pp. 193-208, 2016. .

  2. Brinkman, H.C., The Viscosity of Concentrated Suspensions and Solutions, J. Chem. Phys., vol. 20, no. 4, Article ID 571, 1952. .

  3. Chand, K. and Kumar, R., Hall Effect on Heat and Mass Transfer in the Flow of Oscillating Viscoelastic Fluid through Porous Medium with Wall Slip Conditions, Indian J. Pure Appl. Phys, vol. 50, no. 3, pp. 149-155, 2012. .

  4. Chand, K., Kumar, R., and Sharma, S., Rarefaction and Darcy Effects on the Hydromagnetic Flow of Radiating and Reacting Fluid in a Vertical Channel, Turk. J. Eng. Env. Sci., vol. 37, no. 2, pp. 137-145, 2013. .

  5. Chand, R. and Rana, G.C., Electrothermo Convection of Rotating Nanofluid in Brinkman Porous Media, J. Porous Media, vol. 7, no. 2, pp. 181-194,2016. .

  6. Choi, S.U.S., Enhancing Thermal Conductivity of Fluids with Nanoparticles, Int. Mech. Eng. Cong. Exhib., San Francisco, CA, vol. 66, pp. 99-103,1995. .

  7. Eegunjobi, A.S., Makinde, O.D., and Jangili, S., Unsteady MHD Chemically Reacting and Radiating Mixed Convection Slip Flow past a Stretching Surface in a Porous Medium, Defect Diffusion Forum, vol. 377, pp. 200-210, 2017. .

  8. Hamilton, R. and Crosser, O.K., Thermal Conductivity of Heterogeneous Two-Component Systems, Ind. Eng. Chem. Fundam., vol. 1, no. 3, pp. 187-191, 1962. .

  9. Hosseinzadeh, M., Heris, S.Z., Beheshti, A., and Shanbedi, M., Convective Heat Transfer and Friction Factor of Aqueous Fe3O4 Nanofluid Flow under Laminar Regime, J. Therm. Anal. Calorim., vol. 124, no. 2, pp. 827-838, 2016. .

  10. Jang, S.P. and Choi, S.U.S., Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids, Appl. Phys. Lett:., vol. 84, no. 21, pp. 436-438,2004. .

  11. Khan, S.U., Ali, N., and Abbas, Z., Hydromagnetic Flow and Heat Transfer over a Porous Oscillating Surface in a Viscoelastic Fluid with Porous Medium, Plos One, vol. 10, no. 12, Article ID 0144299, 2015. .

  12. Kumar, R., Numerical Exploration of Thermal Radiation and Rotation Effects on the 3-Dimensional Flow of Cu-Water Nanofluid over an Oscillating Flat Surface, Int. J. Appl. Comput. Math., vol. 4, Article ID 9, 2018. .

  13. Kumar, R., Kumar, R., Shehzad, S.A., and Sheikholeslami, M., Rotating Frame Analysis of Radiating and Reacting Ferro-Nanofluid Considering Joule Heating and Viscous Dissipation, Int. J. Heat Mass Transf., vol. 120, pp. 540-551,2018. .

  14. Kumar, R., Raju, C.S.K., Sekhar, K.R., and Reddy, G.V., Three Dimensional MHD Ferrous Nanofluid Flow over a Sheet of Variable Thickness in Slip Flow Regime, J. Mech, 2017a. DOI: 10.1017/jmech.2017.95 .

  15. Kumar, R. and Singh, K.D., Mathematical Modeling of Soret and Hall Effects on Oscillatory MHD Free Convective Flow of Radiating Fluid in a Rotating Vertical Porous Channel Filled with Porous Medium, Int. J. Appl. Math. Mech, vol. 8, pp. 49-68, 2012. .

  16. Kumar, R. and Sood, S., Combined Influence of Fluctuations in the Temperature and Stretching Velocity of the Sheet on MHD Flow of Cu-Water Nanofluid through Rotating Porous Medium with Cubic Auto-Catalysis Chemical Reaction, J. Mol. Liq., vol. 237, pp. 347-360,2017. .

  17. Kumar, R. and Sood, S., Effect of Quadratic Density Variation on Mixed Convection Stagnation Point Heat Transfer and MHD Fluid Flow in Porous Medium towards a Permeable Shrinking Sheet, J. Porous Media, vol. 19, no. 12, pp. 1083-1097, 2016. .

  18. Kumar, R., Sood, S., Shehzad, S.A., and Sheikholeslami, M., Radiative Heat Transfer Study for Flow of Non-Newtonian Nanofluid past a Riga Plate with Variable Thickness, J. Mol. Liq., vol. 248, pp. 143-152, 2017b. .

  19. Kumar, R., Sood, S., Sheikholeslami, M., and Shehzad, S.A., Nonlinear Thermal Radiation and Cubic Autocatalysis Chemical Reaction Effects on the Flow of Stretched Nanofluid under Rotational Oscillations, J. Colloid Interf. Sci., vol. 505, pp. 253-265,2017c. .

  20. Lighthill, M.J., The Response of Laminar Skin Friction and Heat Transfer of Fluctuations in Stream Velocity, Proc. Royal Soc., vol. 224, no. 1156, Article ID 1, 1954. .

  21. Lu, A.H., Salabas, E.L., and Schuth, F., Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application, Angew. Chem. Int. Ed, vol. 46, no. 8, pp. 12-22, 2007. .

  22. Mahdy, A., Mansour, M.A., Ahmed, S.E., and Mohamed, S.S., Entropy Generation of Cu-Water Nanofluids through Non-Darcy Porous Medium over a Cone with Convective Boundary Condition and Viscous Dissipation Effects, Spec. Topics Rev. Porous Media: Int. J, vol. 8, no. 1, pp. 59-72, 2017. .

  23. Makinde, O.D. and Animasaun, I.L., Bioconvection in MHD Nanofluid Flow with Nonlinear Thermal Radiation and Quartic Autocatalysis Chemical Reaction past an Upper Surface of a Paraboloid of Revolution, Int. J. Therm. Sci., vol. 109, pp. 159-171,2016. .

  24. Makinde, O.D. and Aziz, A., Boundary Layer Flow of a Nanofluid past a Stretching Sheet with a Convective Boundary Condition, Int. J. Therm. Sci, vol. 50, no. 7, pp. 1326-1332, 2011. .

  25. Makinde, O.D. and Eegunjobi, A.S., Entropy Analysis of Thermally Radiating Magnetohydrodynamics Slip Flow of Casson Fluid in a Microchannel Filled with Saturated Porous Media, J. Porous Media, vol. 19, no. 9, pp. 799-810,2016. .

  26. Makinde, O.D., Khan, W.A., and Culham, J.R., MHD Variable Viscosity Reacting Flow over a Connectively Heated Plate in a Porous Medium with Thermophoresis and Radiative Heat Transfer, Int. J. Heat Mass Transf., vol. 93, pp. 595-604, 2016. .

  27. Makinde, O.D., Khan, W.A., and Khan, Z.H., Stagnation Point Flow of MHD Chemically Reacting Nanofluid over a Stretching Convective Surface with Slip and Radiative Heat, Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng., vol. 231, no. 4, pp. 695-703,2017. .

  28. Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford, UK: Clarendon, 1873. .

  29. Motsumi, T.G. and Makinde, O.D., Effects of Thermal Radiation and Viscous Dissipation on Boundary Layer Flow of Nanofluids over a Permeable Moving Flat Plate, Phys. Scripta, vol. 86, Article ID 045003, 2012. .

  30. Mustafa, M., Mushtaq, A., Hayat, T., and Alsaedi, A., Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation, Plos One, vol. 11, no. 2, Article ID 0149304, 2016. .

  31. Prasher, R.S., Bhattacharya, P., and Phelan, P.E., Brownian-Motion-Based Convective-Conductive Model for the Effective Thermal Conductivity of Nanofluids, J. Heat Transf.-Transact. ASME, vol. 28, no. 6, pp. 588-595, 2006. .

  32. Sandeep, N., Chamkha, A.J., and Animasaun, I.L., Numerical Exploration of Magnetohydrodynamic Nanofluid Flow Suspended with Magnetite Nanoparticles, J. Braz. Soc. Mech. Sci. Eng., vol. 39, no. 9, pp. 3635-3644, 2017. .

  33. Sandeep, N. and Reddy, M.G., Heat Transfer of Nonlinear Radiative Magnetohydrodynamic Cu-Water Nanofluid Flow over Two Different Geometries, J. Mol. Liq., vol. 225, pp. 87-94, 2017. .

  34. Sharifi, I., Shokrollahi, H., and Amiri, S., Ferrite-Based Magnetic Nanofluids Used in Hyperthermia Applications, J. Magnet. Magnet. Mater., vol. 324, no. 6, pp. 903-915,2012. .

  35. Sharma, P.R., Choudhary, S., and Makinde, O.D., MHD Slip Flow and Heat Transfer over an Exponentially Stretching Permeable Sheet Embedded in a Porous Medium with Heat Source, Front. Heat Mass Transf., vol. 9, Article ID 013018, 2017. .

  36. Shehzad, S.A., Hayat, T., Alsaedi, A., and Obid, M.A., Nonlinear Thermal Radiation in Three-Dimensional Flow of Jeffrey Nanofluid, Appl. Math. Comput, vol. 248, pp. 273-286, 2014. .

  37. Sheikholeslami, M., Ganji, D.D., Javed, M.Y., and Ellahi, R., Effect of Thermal Radiation on Magnetohydrodynamics Nanofluid Flow and Heat Transfer by Means of Two Phase Model, J. Magnet. Magnet. Mater., vol. 374, pp. 36-43, 2015. .

  38. Siddiq, M.K., Rauf, A., Shehzad, S.A., Alsaedi, A., and Hayat T., Interaction of Convective andNield's Conditions in Hydromagnetic Flow of Nanofluid Subject to Darcy-Forchheimer Effects, J. Porous Media, vol. 20, no. 11, pp. 989-998, 2017. .

  39. Singh, A.K., Thermal Conductivity of Nanofluids, Defence Sci. J., vol. 58, no. 5, pp. 600-607, 2008. .

  40. Singh, K.D. and Kumar, R., Effects of Chemical Reactions on Unsteady MHD Free Convection and Mass Transfer for Flow past a Hot Vertical Porous Plate with Heat Generation/Absorption through Porous Medium, Ind. J. Phys, vol. 84, no. 1, pp. 93-106, 2010. .

  41. Singh, K.D. and Kumar, R., Fluctuating Heat and Mass Transfer on Unsteady MHD Free Convection Flow of Radiating and Reacting Fluid past a Vertical Porous Plate in Slip-Flow Regime, J. Appl. FluidMech, vol. 4, no. 4, pp. 101-106, 2011. .

  42. Stuart, J.T., A Solution of the Navier-Stokes and Energy Equations Illustrating the Response of Skin-Friction and Temperature of an Infinite Plate Thermometer to Fluctuations in the Stream Velocity, Proc. Royal Soc., vol. 231, no. 1184, Article ID 116, 1955. .

  43. Tiwari, R.K. and Das, M.K., Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids, Int. J. Heat Mass Transf., vol. 50, nos. 9-10, pp. 2002-2018, 2007. .

  44. Verma, V.K. and Dixit, P.K., Flow past a Porous Sphere of Radially Varying Permeability Embedded in Another Porous Medium, Spec. Topics Rev. Porous Media: Int. J, vol. 8, no. 3, pp. 231-243, 2017. .

  45. Wang, Y. and Wu, W., Unsteady Flow of a Fourth-Grade Fluid due to an Oscillating Plate, Int. J. Non-Linear Mech., vol. 42, no. 3, pp. 432-441,2007. .

  46. Yamada, E. and Ota, T., Effective Thermal Conductivity of Dispersed Materials, Warme - und Stoffiibertragung, vol. 13, nos. 1-2, pp. 27-37,1980. .

  47. Zhang, X., Gu, H., and Fujii, M., Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids Containing Spherical and Cylindrical Nanoparticles, Exp. Therm. Fluid Sci., vol. 31, no. 6, pp. 593-599,2007. .

Articles with similar content:

Journal of Porous Media, Vol.14, 2011, issue 11
Muhammad Qasim, S. Mesloub, Tasawar Hayat, Zaheer Abbas
Ioan Pop, Roslinda Nazar, Fadzilah Md. Ali, Norfifah Bachok, Siti Suzilliana Putri Mohd Isa, Norihan Md. Arifin
Journal of Porous Media, Vol.21, 2018, issue 12
Nasir Ali, Sami Ullah Khan, Sabir Ali Shehzad
MHD Stagnation Point Flow and Heat Transfer over a Permeable Surface through a Porous Space
Journal of Porous Media, Vol.12, 2009, issue 2
Zaheer Abbas
Nonsimilar Solutions for Heat and Mass Transfer Flow in an Electrically Conducting Viscoelastic Fluid over a Stretching Sheet Saturated in a Porous Medium with Suction/Blowing
Journal of Porous Media, Vol.11, 2008, issue 2
K. Rajagopal, V. K. Pravin, P. H. Veena