Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
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

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.2019027985
pages 11-26


Aurang Zaib
Department of Mathematical Sciences, Federal Urdu University of Arts, Science and Technology, Gulshan-e-Iqbal Karachi-75300, Pakistan
Rizwan Ul Haq
Department of Electrical Engineering, Bahria University, Islamabad 44000, Pakistan
Mohsen Sheikholeslami
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran; Renewable Energy Systems and Nanofluid Applications in Heat Transfer Laboratory, Babol Noshirvani University of Technology, Babol, Iran
Ali J. Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
Mohammad Mehdi Rashidi
Department of Civil Engineering, School of Engineering, University of Birmingham, Birmingham, UK


The theme of current research is to explore the impact of entropy generation on mixed convective flow of micropolar fluid containing water-based TiO2 nanomaterial toward a vertical surface in a non-Darcy porous medium. The results are confined for opposing and assisting flows. Similarity equations are achieved and then worked out numerically by the Keller box technique. The impacts of substantial parameters on temperature distribution, velocity profile, and microrotation velocity, together with the Nusselt number and the skin friction, are illustrated with the help of graphs. Two solutions are achieved in opposing flow while the solution is unique in assisting flow. It is also observed that the separation of boundary layer accelerates due to volume fraction and delays due to micropolar parameter.


  1. Aman, F., Ishak, A., and Pop, I., Mixed Convection Boundary Layer Flow near Stagnation-Point on Vertical Surface with Slip, Appl. Math. Mech. Eng. E, vol. 32, no. 12, pp. 1599-1606,2011.

  2. Bakar, S.A., Arifin, N.M., Nazar, R., Ali, F.M., Bachok, N., and Pop, I., The Effects of Suction on Forced Convection Boundary Layer Stagnation Point Slip Flow in a Darcy Porous Medium towards a Shrinking Sheet with Presence of Thermal Radiation: A Stability Analysis, J. Porous Media, vol. 21, no. 7, pp. 623-636, 2018.

  3. Butt, A.S. and Ali, A., Entropy Analysis of Magnetohydrodynamic Flow and Heat Transfer over a Convectively Heated Radially Stretching Surface, J. Taiwan Inst. Chem. Eng., vol. 45, pp. 1197-1203, 2014.

  4. Choi, S.U.S., Enhancing Thermal Conductivity of Fluids with Nanoparticle, ASME Fluids Eng. Div, vol. 231, pp. 99-105, 1995.

  5. Das, K. and Duari, P.R., Micropolar Nanofluid Flow over a Stretching Sheet with Chemical Reaction, Int. J. Appl. Comput. Math., vol. 3, pp. 3229-3239,2017.

  6. Eringen, A.C. Theory of Micropolar Fluids, J. Appl. Math. Mech., vol. 16, pp. 1-18, 1966.

  7. Gireesha, B.J., Mahanthesh, B., Manjunatha, P.T., and Gorla, R.S.R., Numerical Solution for Hydromagnetic Boundary Layer Flow and Heat Transfer past a Stretching Surface Embedded in Non-Darcy Porous Medium with Fluid-Particle Suspension, J. Nigerian Math. Soc., vol. 34, pp. 267-285, 2015.

  8. Hayat, T., Nazar, H., Imtiaz, M., and Alsaedi, A., Darcy-Forchheimer Flows of Copper and Silver Water Nanofluids between Two Rotating Stretchable Disks, Appl. Math. Mech. Eng. Ed., vol. 38, no. 12, pp. 1663-1678,2017.

  9. Hsiao, K.L., Micropolar Nanofluid Flow with MHD and Viscous Dissipation Effects towards a Stretching Sheet with Multimedia Feature, Int. J. Heat Mass Transf., vol. 112, pp. 983-990, 2017.

  10. Hussanan, A., Salleh, M.Z., and Khan, I., Microstructure and Inertial Characteristics of a Magnetite Ferrofluid over a Stretching/Shrinking Sheet Using Effective Thermal Conductivity Model, J. Mol. Liq., vol. 255, pp. 64-75,2018.

  11. Hussanan, A., Salleh, M.Z., Khan, I., and Tahar, R.M., Unsteady Free Convection Flow of a Micropolar Fluid with Newtonian Heating: Closed Form Solution, Therm. Sci., vol. 21, pp. 2313-2326,2017.

  12. Iqbal, Z., Ahmed, B., and Miraj, E., A Numerical Study of Ferrofluid in Presence of Magnetic Dipole Inspired by Slip and Viscous Dissipation Effects Submerged in Porous Medium, J. Porous Media, vol. 22, no. 1, pp. 107-117,2019.

  13. Ishak, A., Nazar, R., and Pop, I., Post-Stagnation-Point Boundary Layer Flow and Mixed Convection Heat Transfer over a Vertical, Linearly Stretching Sheet, Arch. Mech., vol. 60, no. 4, pp. 303-322,2008.

  14. Khan, M.I., Hayat, T., Qayyum, S., Khan, M.I., and Alsaedi, A., Entropy Generation (Irreversibility) Associated with Flow and Heat Transport Mechanism in Sisko Nanomaterial, Phys. Lett. A, vol. 382, no. 34, pp. 2343-2353, 2018.

  15. Khan, W.A. and Pop, I., Boundary-Layer Flow of a Nanofluid past a Stretching Sheet, Int. J. Heat Mass Transf., vol. 53, pp. 2477-2483,2010.

  16. Lok, Y.Y., Amin, N., and Pop, I., Unsteady Mixed Convection Flow of a Micropolar Fluid near the Stagnation-Point on a Vertical Surface, Int. J. Therm. Sci., vol. 45, no. 12, pp. 1149-1157, 2006.

  17. Mabood, F., Ibrahim, S.M., Rashidi, M.M., Shadloo, M.S., and Lorenzini, G., Non-Uniform Heat Source/Sink and Soret Effects on MHD Non-Darcian Convective Flow past a Stretching Sheet in a Micropolar Fluid with Radiation, Int. J. Heat Mass Transf., vol. 93, pp. 674-682, 2016.

  18. 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, pp. 1326-1332, 2011.

  19. Makinde, O.D., Mabood, F., Khan, W.A., and Tshehla, M.S., MHD Flow of a Variable Viscosity Nanofluid over a Radially Stretching Convective Surface with Radiative Heat, J. Mol. Liq., vol. 219, pp. 624-630, 2016.

  20. Mukhopadhyay, S., De, P.R., Bhattacharyya, K., and Layek, G.C., Forced Convective Flow and Heat Transfer over a Porous Plate in a Darcy-Forchheimer Porous Medium in Presence of Radiation, Meccanica, vol. 47, pp. 153-161, 2012.

  21. Prasad, V.R., Gaffar, S.A., Reddy, E.K., and Beg, O.A., Numerical Study of Non-Newtonian Boundary Layer Flow of Jeffreys Fluid past a Vertical Porous Plate in a Non-Darcy Porous Medium, Int. J. Comp. Meth. Eng. Sci. Mech., vol. 15, pp. 372-389, 2014.

  22. Rashid, I., Haq, R.U., Khan, Z.H., and Al-Mdallal, Q.M., Flow of Water based Alumina and Copper Nanoparticles along a Moving Surface with Variable Temperature, J. Mol. Liq., vol. 246, pp. 354-362,2017.

  23. Saleh, S.H.M., Arifin, N.M., Nazar, R., and Pop, I., Unsteady Micropolar Fluid over a Permeable Curved Stretching Shrinking Surface, Math. Prob. Eng., vol. 2017, pp. 1-13,2017.

  24. Sandeep, N., Sulochana, C., Raju, C.S.K., Babu, M.J., and Sugunamma, V., Unsteady Boundary Layer Flow of Thermophoretic MHD Nanofluid past a Stretching Sheet with Space and Time Dependent Internal Heat Source/Sink, Appl. Appl. Math., vol. 10, no. 1,pp. 312-327,2015.

  25. Shateyi, S., Motsa, S.S., and Makukula, Z., On Spectral Relaxation Method for Entropy Generation on a MHD Flow and Heat Transfer of a Maxwell Fluid, J. App. Fluid Mech, vol. 8, pp. 21-31,2015.

  26. Spasojevic, M.D., Jankovic, M.R., and Djakovic, D.D., A New Approach to Entropy Production Minimization in Diabatic Distillation Column with Trays, Therm. Sci., vol. 14, pp. 317-328, 2010.

  27. Sreenadh, S., Krishna, G.G., Srinivas, A.N.S., and Sudhakara, E., Entropy Generation Analysis for MHD Flow through a Vertical Deformable Porous Layer, J. Porous Media, vol. 21, no. 6, pp. 523-538, 2018.

  28. Umavathi, J.C. and Sasso, M., Free Convection Flow in a Duct Filled with Nanofluid and Saturated with Porous Medium: Variable Properties, J. Porous Media, vol. 21, no. 1, pp. 1-33,2018.

  29. Wang, X., Xu, X., and Choi, S.U.S., Thermal Conductivity of Nanoparticle Fluid Mixture, J. Thermophys., Heat Transf, vol. 13, pp. 474-480, 1999.

  30. Waqas, H., Hussain, S., Sharif, H., and Khalid, S., MHD Forced Convective Flow of Micropolar Fluids past a Moving Boundary Surface with Prescribed Heat Flux and Radiation, British J. Math. Comput. Sci., vol. 21, no. 1, pp. 1-14, 2017.

  31. Yacob, N.A., Ishak, A., and Pop, I., Falkner-Skan Problem for a Static or Moving Wedge in Nanofluids, Int. J. Therm. Sci., vol. 50, no. 2, pp. 133-139,2011.

  32. Yasmin, A., Ali, K., Ghaffar, M., and Ashraf, M., On Viscous Dissipation and Thermal Characteristics of Magnetohydrodyanics Micropolar Fluid Flow in Porous Channel with Expanding or Contracting Walls, J. Porous Media, vol. 22, no. 2, pp. 243-260, 2019.

  33. Zaib, A., Rashidi, M.M., and Chamkha, A.J., Flow of Nanofluid Containing Gyrotactic Microorganisms over a Static Wedge in Darcy-Brinkman Porous Medium with Convective Boundary Condition, J. Porous Media, vol. 21, no. 10, pp. 911-928,2018.

  34. Zaib, A., Rashidi, M.M., Chamkha, A.J., and Bhattacharyya, K., Numerical Solution of Second Law Analysis for MHD Casson Nanofluid past a Wedge with Activation Energy and Binary Chemical Reaction, Int. J. Num. Meth. Heat Fluid Flow, vol. 27, no. 12, pp. 2816-2834,2017.