Caputo-Fabrizio Time Fractional Derivative Applied to Visco Elastic MHD Fluid Flow in the Porous Medium


  • Salah Uddin
  • M. Mohamad
  • M. A. H. Mohamad
  • Suliadi Sufahani
  • M. Ghazali Kamardan
  • Obaid Ullah Mehmood
  • Fazli Wahid
  • R. Roslan





Laminar flow, Porosity, Hartmann number.


In this paper the laminar fluid flow in the axially symmetric porous cylindrical channel subjected to the magnetic field was studied. Fluid

model was non-Newtonian and visco elastic. The effects of magnetic field and pressure gradient on the fluid velocity were studied by using a new trend of fractional derivative without singular kernel. The governing equations consisted of fractional partial differential equations based on the Caputo-Fabrizio new time-fractional derivatives NFDt. Velocity profiles for various fractional parameter a, Hartmann number, permeability parameter and elasticity were reported. The fluid velocity inside the cylindrical artery decreased with respect to Hartmann number, permeability parameter and elasticity. The results obtained from the fractional derivative model are significantly different from those of the ordinary model.




[1] Gul T, Rehman I, Islam S, Khan MA, Ullah W & Shah Z (2017), Unsteady third order fluid flow with heat transfer between two vertical oscillating plates, J. Appl. Environ. Biol. Sci, 5(4), pp.72–79.

[2] Raza N (2017), Unsteady rotational flow of a second grade fluid with non- integer Caputo time fractional derivative, Journal of Mathematics, 49(3), pp.15–25.

[3] Abro KA (2017), Heat transfer in magnetohydrodynamic second grade fluid with porous impacts using Caputo-Fabrizio fractional derivatives, Journal of Mathematics, 49(2), pp.113–125.

[4] Abro KA, Hussain M & Baig MM (2017), Slippage of magnetohydrodynamic fractionalized Oldroyd-B fluid in porous medium, Journal of Mathematics, 80(1), pp. 69–80.

[5] Sharma k & Gupta S (2016), Analytical study of MHD boundary layer flow and heat transfer towards a porous exponentially stretching sheet in presence of thermal radiation, International Journal of Advances in Applied Mathematics and Mechanics, 4(1), pp. 1–10.

[6] Eldesoky IM, Kamel MH & Abumandour RM (2014), Numerical study of slip effect of unsteady MHD pulsatile flow through porous medium in an artery using generalized differential quadrature method (Comparative Study), World Journal of Engineering and Technology, pp. 131–148.

[7] Ahmad I, Ilyas H & Bilal M (2014), Numerical solution for nonlinear MHD Jeery-Hamel blood flow problem through neural networks optimized techniques, J. Appl. Environ. Biol. Sci., 4, pp. 33–43.

[8] Sedaghatizadeh N, Barari A, Soleimani S & Modi M (2013), Analytical and numerical evaluation of steady flow of blood through artery, Biomedical Research, 24(1), pp. 88–98.

[9] Rathod VP & Ravi M (2014), Blood flow through stenosed inclined tubes with periodic body acceleration in the presence of magnetic field and its applications to cardiovascular diseases, International Journal of Research in Engineering and Technology, pp. 96–101.

[10] Elshahed M (2000), MHD flow of an elastico-viscous fluid under periodic body acceleration, Int. J. Math. & Math. Sci., 23(11), pp. 795–799.

[11] Ibraheem GH & Abdulhadi AM (2014), Exact solutions for MHD flow of a viscoelastic fluid with the fractional Burgers’ model in an annular pipe, International Journal Of Modern Engineering Research (IJMER), 4(3), pp. 58–64.

[12] Mohan V, Prasad V & Varshney NK (2013), Effect of magnetic field on blood flow (elastico-viscous) under periodic body acceleration in porous medium, Journal of Mathematics, 6(4), pp. 43–48.

[13] Kumar D (2010), Application of Sumudu transform in the timefractional Navier-Stokes equation with MHD flow in porous media, Journal of Applied Sciences Research, 16(11), pp. 1814–1821.

[14] Liu Y & Ma J (2015) Accelerating MHD flow of a generalized Oldroyd-B, Frontiers in Heat and Mass Transfer, 17, pp. 1–5.

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