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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.2019026922
pages 27-49


Santosh Chaudhary
Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, India
K. M. Kanika
Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, India


A numerical study of the effect of viscous dissipation and Joule heating on steady two-dimensional incompressible stagnation point flow of electrically conducting nanofluids along with suction/injection at a stretching/shrinking surface embedded in saturated porous medium and magnetic field is considered. The impact of different types of nanoparticles with base fluid, heat generation/absorption, and thermal radiation are also dealt with. Similarity transformations are applied to reduce the governing partial differential equations into a system of nonlinear ordinary differential equations, which are solved numerically using a Galerkin finite element method. Influences in velocity and temperature distributions due to various nanofluids and appropriate controlling parameters such as mass flux, velocity, solid volume fraction, permeability, magnetization, radiation, heat source/sink, and Eckert number are evaluated through graphs and discussed in detail. Computational values of local skin friction and local Nusselt number against various physical parameters are presented via tables. Moreover, the effectiveness and accuracy of the proposed method are compared with previously published research.


  1. Ahmed, S.E. and Elshehabey, H.M., Buoyancy-Driven Flow of Nanofluids in an Inclined Enclosure Containing an Adiabatic Obstacle with Heat Generation/Absorption: Effects of Periodic Thermal Conditions, Int. J. Heat Mass Transf., vol. 124, pp. 58-73,2018.

  2. Akbar, N.S. and Khan, Z.H., Effect of Variable Thermal Conductivity and Thermal Radiation with CNTS Suspended Nanofluid over a Stretching Sheet with Convective Slip Boundary Conditions: Numerical Study, J. Mol. Liq., vol. 222, pp. 279-286,2016a.

  3. Akbar, N.S. and Khan, Z.H., Magnetic Field Analysis in a Suspension of Gyrotactic Microorganisms and Nanoparticles over a Stretching Surface, J. Magn. Magn. Mater., vol. 410, pp. 72-80, 2016b.

  4. Ali, F., Gohar, M., and Khan, I., MHD Flow of Water-Based Brinkman Type Nanofluid over a Vertical Plate Embedded in a Porous Medium with Variable Surface Velocity, Temperature and Concentration, J. Mol. Liq., vol. 223, pp. 412-419,2016.

  5. Alsaedi, A., Khan, M., Farooq, M., Gull, N., and Hayat, T., Magnetohydrodynamic (MHD) Stratified Bioconvective Flow of Nanofluid due to Gyrotactic Microorganisms, Adv. Powder Technol, vol. 28, pp. 288-298,2017.

  6. Attia, H.A., Unsteady MHD Flow and Heat Transfer of Dusty Fluid between Parallel Plates with Variable Physical Properties, Appl. Math. Model, vol. 26, pp. 863-875, 2002.

  7. Bhattacharyya, K., Dual Solution in Unsteady Stagnation-Point Flow over a Shrinking Sheet, Chinese. Phys. Lett., vol. 28, p. 084702,2011.

  8. Bhattacharyya, K., Mukhopadhyay, S., and Layek, G.C., Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Shrinking Sheet, Int. J. Heat Mass Transf., vol. 54, pp. 308-313, 2011.

  9. Chaudhary, S. and Choudhary, M.K., Heat and Mass Transfer by MHD Flow near the Stagnation Point over a Stretching or Shrinking Sheet in a Porous Medium, Indian J. Pure Appl. Phys., vol. 54, pp. 209-217,2016.

  10. Chaudhary, S. and Choudhary, M.K., Partial Slip and Thermal Radiation Effects on Hydromagnetic Flow over an Exponentially Stretching Surface with Suction or Blowing, Therm. Sci., vol. 22, pp. 797-808,2018.

  11. Chaudhary, S. and Kumar, P., MHD Forced Convection Boundary Layer Flow with a Flat Plate and Porous Substrate, Meccanica, vol. 49, pp. 69-77, 2014.

  12. Chaudhary, S. and Kumar, P., Magnetohydodynamic Stagnation Point Flow past a Porous Stretching Surface with Heat Generation, Indian J. Pure Appl. Phys. vol. 53, pp. 291-297, 2015.

  13. Chaudhary, S., Choudhary, M.K., and Sharma, R., Effects of Thermal Radiation on Hydromagnetic Flow over an Unsteady Stretching Sheet Embedded in a Porous Medium in the Presence of Heat Source or Sink, Meccanica, vol. 50, pp. 1977-1987, 2015a.

  14. Chaudhary, S., Singh, S., and Chaudhary, S., Thermal Radiation Effects on MHD Boundary Layer Flow over an Exponentially Stretching Surface, Appl. Math, vol. 6, pp. 295-303, 2015b.

  15. Choi, S.U.S., Enhancing Thermal Conductivity of Fluids with Nanoparticles, Publ. Fed, vol. 231ASME, pp. 99-106, 1995.

  16. Crane, L.J., Flow past a Stretching Plate, J. Appl. Math. Phys, vol. 21, pp. 645-647, 1970.

  17. Darcy, H.P.G., Les Fontaines Publiques de la villa de Dijon, Paris: Dalmont, 1856.

  18. Fang, T. and Zhang, J., Closed-Form Exact Solutions of MHD Viscous Flow over a Shrinking Sheet, Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 2853-2857, 2009.

  19. Hamad, M.A.A. and Ferdows, M., Similarity Solution of Boundary Layer Stagnation-Point Flow towards a Heated Porous Stretching Sheet Saturated with a Nanofluid with Heat Absorption/Generation and Suction/Blowing: A Lie Group Analysis, Commun. Nonlinear Sci. Numer. Simul., vol. 17, pp. 132-140,2012.

  20. Hiemenz, K., Die Grenzschicht an Einem in den Gleichformigen Fliissigkeitsstrom Eingetauchten Geraden Kreiszylinder, Dingler's Polytech. J, vol. 326, pp. 321-324, 1911.

  21. Homann, F., Der Einfluss Grosser Zahigkeit Bei der Stromung um den Zylinder und um Die Kugel, Z. Angew. Math. Phys., vol. 16, pp. 153-164, 1936.

  22. Ja'fari, M. and Rahimi, A.B., Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Plate with Time-Dependent Axial Velocity and Uniform Transpiration, Scientia Iran, vol. 20, pp. 152-161,2013.

  23. Jat, R.N. and Chaudhary, S., MHD Stagnation Flows with Slip, IL Nuovo Cimento B, vol. 122, pp. 823-831,2007.

  24. Jat, R.N. and Chaudhary, S., Unsteady Magnetohydrodynamic Boundary Layer Flow over a Stretching Surface with Viscous Dissipation and Joule Heating, Il Nuovo Cimento B, vol. 124, pp. 53-59,2009.

  25. Jat, R.N. and Chaudhary, S., Radiation Effects on the MHD Flow near the Stagnation Point of a Stretching Sheet, Z. Angew. Math. Phys, vol. 61, pp. 1151-1154,2010.

  26. Kechil, S.A. and Hashim, I., Approximate Analytical Solution for MHD Stagnation-Point Flow in Porous Media, Commun. Non-linear Sci. Numer. Simul., vol. 14, pp. 1346-1354,2009.

  27. Khan, A., Khan, I., Ali, F., and Shafie, S., A Note on Entropy Generation in MHD Flow over a Vertical Plate Embedded in a Porous Medium with Arbitrary Shear Stress and Ramped Temperature, J. Porous Media, vol. 19, pp. 175-187, 2016.

  28. Khanafer, K., Vafai, K., and Lightstone, M., Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids, Int. J. Heat Mass Transf., vol. 46, pp. 3639-3653,2003.

  29. Kun, D., Liming, S., Jun, Li., and Bengt, S., Effects of the Mainstream Turbulence Intensity and Slot Injection Angle on the Endwall Cooling and Phantom Cooling of the Vane Suction Side Surface, Int. J. Heat Mass Transf, vol. 112, pp. 427-440, 2017.

  30. Liao, S.J., A New Branch of Solutions of Boundary Layer Flows over a Permeable Stretching Plate, Int. J. Non-Linear Mech, vol. 42, pp. 819-830, 2007.

  31. Mahajan, A. and Sharma, M.K., Convection in Magnetic Nanofluids in Porous Media, J. Porous Media, vol. 17, pp. 439-455, 2014.

  32. Mahapatra, T.R. and Sidui, S., Heat Transfer in Non-Axisymmetric Homann Stagnation-Point Flows towards a Stretching Sheet, Euro. J Mech.-B/Fluids, vol. 65, pp. 522-529, 2017.

  33. Mahmoud, M.A.A. and Megahed, A.M., Non-Uniform Heat Generation Effect on Heat Transfer of a Non-Newtonian Power-Law Fluid over a Non-Linearly Stretching Sheet, Meccanica, vol. 47, pp. 1131-1139, 2012.

  34. Miklavcic, M. and Wang, C.Y., Viscous Flow due to a Shrinking Sheet, Q. Appl. Math., vol. 64, pp. 283-290, 2006.

  35. Nasir, N.A.A.M., Ishak, A., and Pop, I., Stagnation-Point Flow and Heat Transfer past a Permeable Quadratically Stretching/Shrinking Sheet, Chinese J. Phys., vol. 55, pp. 2081-2091, 2017.

  36. Pal, D. and Mandal, G., Influence of Thermal Radiation on Mixed Convection Heat and Mass Transfer Stagnation-Point Flow in Nanofluids over Stretching/Shrinking Sheet in a Porous Medium with Chemical Reaction, Nucl. Eng. Des., vol. 273, pp. 644-652,2014.

  37. Pal, D., Mandal, G., and Vajravelu, K., Flow and Heat Transfer of Nanofluids at a Stagnation Point Flow over a Stretching/Shrinking Surface in a Porous Medium with Thermal Radiation, Appl. Math. Comput., vol. 238, pp. 208-224, 2014.

  38. Ramesh, K., Effects of Slip and Convective Conditions on the Peristaltic Flow of Couple Stress Fluid in an Asymmetric Channel through Porous Medium, Comput. Methods Programs Biomed., vol. 135, pp. 1-14, 2016.

  39. Ramzan, M., Bilal, M., and Chung, J.D., Effects of Thermal and Solutal Stratification on Jeffrey Magneto-Nanofluid along an Inclined Stretching Cylinder with Thermal Radiation and Heat Generation/Absorption, Int. J. Mech. Sci., vols. 131-132, pp. 317-324,2017.

  40. Rassoulinejad-Mousavi, S.M., Seyf, H.R., and Abbasbandy, S., Heat Transfer through a Porous Saturated Channel with Permeable Walls Using Two-Equation Energy Model, J. Porous Media, vol. 16, pp. 241-254,2013.

  41. Rassoulinejad-Mousavi, S.M. and Yaghoobi, H., Effect of Non-Linear Drag Term on Viscous Dissipation in a Fluid Saturated Porous Medium Channel with Various Boundary Conditions at Walls, Arabian J. Sci. Eng., vol. 39, pp. 1231-1240, 2014.

  42. Rossow, V.J., On Flow of Electrically Conducting Fluids over a Flat Plate in the Presence of a Transverse Magnetic Field, N.A.C.A.T.N., vol. 1, pp. 489-508,1957.

  43. Reddy, P.S. and Chamkha, A.J., Heat and Mass Transfer Characteristics of Al2O3-Water and Ag-Water Nanofluid through Porous Media over a Vertical Cone with Heat Generation/Absorption, J. Porous Media, vol. 20, pp. 1-17,2017.

  44. Sajid, M. and Hayat, T., Influence of Thermal Radiation on the Boundary Layer Flow due to an Exponentially Stretching Sheet, Int. Commun. Heat Mass Transf., vol. 35, pp. 347-356,2008.

  45. Salem, A.M. and El-Aziz, M.A., Effect of Hall Currents and Chemical Reaction on Hydromagnetic Flow of a Stretching Vertical Surface with Internal Heat Generation/Absorption, Appl. Math. Model., vol. 32, pp. 1236-1254,2008.

  46. Seyf, H.R. and Rassoulinejad-Mousavi, S.M., An Analytical Study for Fluid Flow in Porous Media Imbedded inside a Channel with Moving or Stationary Walls Subjected to Injection/Suction, J. Fluids Eng., vol. 133, p. 091203, 2011.

  47. Sheikholeslami, M. and Rokni, H.B., Effect of Melting Heat Transfer on Nanofluid Flow in Existence of Magnetic Field Considering Buongiorno Model, Chinese J. Phys, vol. 55, pp. 1115-1126, 2017.

  48. Shit, G.C., Haldar, R., and Mandal, S., Entropy Generation on MHD Flow and Convective Heat Transfer in a Porous Medium of Exponentially Stretching Surface Saturated by Nanofluids, Adv. Powder Technol., vol. 28, pp. 1519-1530, 2017.

  49. Su, X. and Zheng, L., Hall Effect on MHD Flow and Heat Transfer of Nanofluids over a Stretching Wedge in the Presence of Velocity Slip and Joule Heating, Central Euro. J. Phys., vol. 11, pp. 1694-1703,2013.

  50. Tamayol, A., Hooman, K., and Bahrami, M., Thermal Analysis of Flow in a Porous Medium over a Permeable Stretching Wall, Transp. Porous Media, vol. 85, pp. 661-676, 2010.

  51. Wang, C.Y., Free Convection on a Vertical Stretching Surface, J. Appl. Math. Mech, vol. 69, pp. 418-420, 1989.

  52. Wang, C.Y. and Cheng, P., Multiphase Flow and Heat Transfer in Porous Media, Adv. Heat Transf., vol. 30, pp. 93-196, 1997.

  53. Wei, X. and Wang, L., Synthesis and Thermal Conductivity of Microfluidic Copper Nanofluids, Particuology, vol. 8, pp. 262-271, 2010.