Neural Computing and Applications

, Volume 29, Issue 2, pp 501–508 | Cite as

A finite element investigation of the flow of a Newtonian fluid in dilating and squeezing porous channel under the influence of nonlinear thermal radiation

  • Naveed Ahmed
  • Umar Khan
  • Syed Tauseef Mohyud-DinEmail author
  • Bandar Bin-Mohsin
Original Article


The influence of nonlinear thermal radiation on the flow of a viscous fluid between two infinite parallel plates is investigated. The lower plate is solid, fixed and heated, while the upper is porous and capable of moving toward or away from the lower plate. The effects of nonlinear thermal radiation are incorporated in the energy equation by using Rosseland approximation. The similarity transformations have been used to obtain a system of ordinary differential equations. A finite element algorithm, known as Galerkin method, has been employed to obtain the solution of the resulting system of differential equations. It is observed that the radiation parameter Rd increases the temperature of the fluid in all the cases considered. Same is the case with temperature ratio parameter θ w . The influence of the concerned parameters on the local rate of heat transfer is also displayed with the help of graphs.


Nonlinear thermal radiation Deformable walls Porous channel Heat transfer Numerical solutions 



The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research Group No. RG-1437-019.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.


  1. 1.
    Berman AS (1953) Laminar flow in channels with porous walls. J Appl Phys 24:1232–1235MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Dauenhauer EC, Majdalani J (1999) Unsteady flows in semi-infinite expanding channels with wall injection. In: 30th AIAA fluid dynamics conference, NorfolkGoogle Scholar
  3. 3.
    Majdalani J, Zhou C, Dawson CA (2002) Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. J Biomech 35:1399–1403CrossRefGoogle Scholar
  4. 4.
    Xinhui S, Liancun Z, Xinxin Z, Jianhong Y (2011) Homotopy analysis method for the heat transfer in a asymmetric. Appl Math Model 35:4321–4329MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ahmed N, Khan U, Zaidi ZA, Jan SU, Waheed A, Mohyud-Din ST (2014) MHD flow of an incompressible fluid through porous medium between dilating and squeezing permeable walls. J Porous Med 17(10):861–867CrossRefGoogle Scholar
  6. 6.
    Xinhui S, Liancuna Z, Xinxin Z, Xinyi S, Min L (2014) Asymmetric viscoelastic flow through a porous channel with expanding or contracting walls: a model for transport of biological fluids through vessels. Comput Methods Biomech Biomedical Eng 17(6):623–631CrossRefGoogle Scholar
  7. 7.
    Ahmed N, Mohyud-Din ST, Hassan SM (2016) Flow and heat transfer of nanofluid in an asymmetric channel with expanding and contracting walls suspended by carbon nanotubes: a numerical investigation. Aerosp Sci Technol 48:53–60CrossRefGoogle Scholar
  8. 8.
    Ciancio A (2007) Analysis of time series with wavelets. Int J Wavelets Multiresolut Inf Process 5(2):241–556MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ciancio V, Ciancio A, Farsaci F (2008) On general properties of phenomenological and state coefficients for isotropic viscoanelastic media. Phys B 403(18):3221–3227CrossRefGoogle Scholar
  10. 10.
    Ciancio A, Quartarone A (2013) A hybrid model for tumor-immune competition. UPB Sci Bull Ser A 75(4):125–136MathSciNetzbMATHGoogle Scholar
  11. 11.
    Sheikholeslamia M, Ellahi R (2015) Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid. Int J Heat Mass Transf 89:799–808CrossRefGoogle Scholar
  12. 12.
    Ellahi R, Hassan M, Zeeshan A (2015) Study on magnetohydrodynamic nanofluid by means of single and multi-walled carbon nanotubes suspended in a salt water solution. IEEE Trans Nanotechnol 14(4):726–734CrossRefGoogle Scholar
  13. 13.
    Kandelousi MS, Ellahi R (2015) Simulation of ferrofluid flow for magnetic drug targeting using the lattice Boltzmann method. Z Naturforsch A 70(2):115–124CrossRefGoogle Scholar
  14. 14.
    Haq RU, Khan ZH, Noor NFM (2016) Numerical simulation of water base magnetite nanoparticles between two parallel disks. Adv Powder Technol. doi: 10.1016/j.apt.2016.05.020 Google Scholar
  15. 15.
    Hussain ST, Haq RU, Noor NFM, Nadeem S (2015) Non-linear radiation effects in mixed convection stagnation point flow along a vertically stretching surface. Int J Chem Reactor Eng. doi: 10.1515/ijcre-2015-0177 Google Scholar
  16. 16.
    Ciancio A, Ciancio V, Francesco F (2007) Wave propagation in media obeying a thermoviscoanelastic model. UPB Sci Bull Ser A 69:69–81Google Scholar
  17. 17.
    Rashidi MM, Pour SM, Abbasbandy S (2011) Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation. Commun Nonlinear Sci Numer Simul 16(4):1874–1889CrossRefGoogle Scholar
  18. 18.
    Noor NFM, Abbasbandy S, Hashim I (2012) Heat and mass transfer of thermophoretic MHD flow over an inclined radiate isothermal permeable surface in the presence of heat source/sink. Int J Heat Mass Transf 55(7–8):2122–2128CrossRefGoogle Scholar
  19. 19.
    Haq RU, Nadeem S, Akbar NS, Khan ZH (2015) Buoyancy and radiation effect on stagnation point flow of micropolar nanofluid along a vertically convective stretching surface. IEEE Trans Nanotechnol 14(1):42–50CrossRefGoogle Scholar
  20. 20.
    Mohyud-Din ST, Khan SI (2016) Nonlinear radiation effects on squeezing flow of a Casson fluid between parallel disks. Aerosp Sci Technol 48:186–192CrossRefGoogle Scholar
  21. 21.
    Khan U, Ahmed N, Mohyud-Din ST, Bin-Mohsin B (2016) Nonlinear radiation effects on MHD flow of nanofluid over a nonlinearly stretching/shrinking wedge. Neural Comput Appl 1–10. doi: 10.1007/s00521-016-2187-x
  22. 22.
    Rybick GB, Lightman AP (1985) Radiative processes in astrophysics. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  23. 23.
    Goto M, Uchida S (1990) Unsteady flow in a semi-infinite contracting expanding pipe with a porous wall. In: Proceeding of the 40th Japan national congress applied mechanics NCTAM-40, TokyoGoogle Scholar
  24. 24.
    Boutros ZY, Mina B, Abd-el-Malek B (2007) Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. Appl Math Model 31:1092–1108CrossRefzbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Naveed Ahmed
    • 1
  • Umar Khan
    • 1
  • Syed Tauseef Mohyud-Din
    • 1
    Email author
  • Bandar Bin-Mohsin
    • 2
  1. 1.Department of Mathematics, Faculty of SciencesHITEC UniversityTaxila CanttPakistan
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia

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