Application of Caputo-Fabrizio Fractional Order Derivative (NFDt) in Simulating the MHD Flow of the Third Grade non-Newtonian Fluid in the Porous Artery

  • Authors

    • Salah Uddin
    • M. Mohamad
    • Suliadi Sufahani
    • M. Ghazali Kamardan
    • Obaid Ullah Mehmood
    • Fazli Wahid
    • R. Roslan
  • Caputo-Fabrizio fractional derivative, Incompressible fluid, Unsteady pulsatile.
  • In this paper, the third grade non-Newtonian MHD blood flow in the porous arteries subjected to the periodic pressure gradient was studied using the Caputo-Fabrizio (NFDt ) time fractional order derivative. The time fractional model was solved by taking the Laplace and the finite Hankel transforms. Results were compared with those reported in the previous studies and good agreement was found. The Mathematica software was used to simulate the velocity profile and the Bessel functions with zero order and first order of first kind. The correlations between the flow velocity and the third grade non-Newtonian fluid parameter, the magnetic field and the porosity were negative. Nevertheless, the flow velocity increased with respect to the Womersely number.



  • References

    1. [1] Abdullah M, Rashid A, Raza N, Saleh A, & Alzahrani AK (2018), Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional caputo derivatives, J. of Mag. and Mag. Mater., 446, pp.28–36

      [2] Akbar NS (2016), Non-Newtonian model study for blood flow through a tapered artery with a stenosis, Alex. Eng. J., 55(1), pp.321–329

      [3] Akbar NS & Nadeem S (2014), Carreau fluid model for blood flow

      through a tapered artery with a stenosis, Ain. Shams. Eng. J., 5(17),


      [4] Akbarzadeh P (2016), Pulsatile magneto-hydrodynamic blood flows through porous blood vessels using a third grade non-Newtonian fluids model, Com. Methods. and Prog. in Biomed., 126, pp.3–19

      [5] Akinshilo AT & Sobamowo GM (2017), Perturbation solutions for

      the study of mhd blood as a third grade nano fluid transporting gold

      nanoparticles through a porous channel, J. of App. And Comp. Mech., 3(2), pp.103–113

      [6] Bao S, Zhang R, Wang K, Zhi X & Qiu L (2017), Free surface flow

      • of liquid oxygen under non-uniform magnetic field, Cryogenics., 81,


      [7] Das UJ (2013), Viscoelastic effects on unsteady two-dimensional and mass transfer of a viscoelastic fluid in a porous channel with radiative heat transfer, Eng., pp.67–72

      [8] Eldesoky IM (2012), Mathematical analysis of unsteady MHD blood flow through parallel plate channel with heat source, W. J. of Mech., pp.131–137

      [9] Fardad AA, Sedaghatizadeh M, Sedaghatizadeh N & Soleimani S

      (2011), Temperature, velocity and micro rotation analysis of blood

      flow in cosserat continuum using homotopy perturbation method, Wor. App. Sci. J., 14(7), pp.1042–1047

      [10] Gupta AK & Agrawal SP (2015), Computational modeling and analysis of the hydrodynamic parameters of blood through stenotic artery, Pro. Comp. Sci., 57, pp.403–410

      [11] Krasnov D, Zikanov O & Boeck T (2011), Comparative study of

      finite difference approaches in simulation of magnetohydrodynamic

      turbulence at low magnetic Reynolds number, Comp. and Fluids, 50(1), pp.46–59

      [12] Mekheimer KS & Kot MAE (2015), Engineering science and technology, an international journal suspension model for blood flow through catheterized curved artery with time-variant overlapping stenosis, Eng. Sci. and Tech. an Int. J., 18(3), pp.452–462

      [13] Okuyade WIA (2013), On the pressure velocity and temperature factors and the effect of viscosity on the arterial blood flow in relation to the hypertension patient, part-1, flow without out flow, Afr. J. Sci. Tech., 12(2), pp.99–104

      [14] Parmar A & Jain S (2017), Comparative study of flow and heat transfer behavior of Newtonian and non-Newtonian fluids over a permeable stretching surface, Gl. and Sto. Ana., 25, pp.41–50

      [15] Ram P, Kumar A & Singh H (2013), Effect of porosity on unsteady

      MHD flow past a semi-infinite moving vertical plate with time dependent suction, Ind. J. of Pur. and App. Phy., 51, pp.461–470

      [16] Singh J & R. Rathee (2010), Analytical solution of two-dimensional model of blood flow with variable viscosity through an indented artery due to LDL effect in the presence of magnetic field, Int. J. of the. Phy. Sci., 5(12), pp.1857–1868

      [17] Venkateswarlu K & Rao JA (2004), Numerical solution of unsteady blood flow through an indented tube with atherosclerosis, Ind. J. of Bioch. and Biophy., 41, pp.241–245

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  • How to Cite

    Uddin, S., Mohamad, M., Sufahani, S., Ghazali Kamardan, M., Ullah Mehmood, O., Wahid, F., & Roslan, R. (2018). Application of Caputo-Fabrizio Fractional Order Derivative (NFDt) in Simulating the MHD Flow of the Third Grade non-Newtonian Fluid in the Porous Artery. International Journal of Engineering & Technology, 7(4.30), 527-532.