# Numerical Analysis of Non-Newtonian Fluid in a Non-Darcy Porous Channel

Numerical Analysis of Non-Newtonian Fluid in a Non-Darcy Porous Channel

Funmilayo H. Oyelami* Moses S. Dada

Department of Mathematical and Physical sciences, Afe Babalola University, Ado Ekiti 360001, Nigeria

Department of Mathematics, University of Ilorin, Ilorin 240101, Nigeria

Corresponding Author Email:
Page:
83-91
|
DOI:
https://doi.org/10.18280/mmc_b.870204
22 May 2018
|
Accepted:
27 June 2018
|
Published:
30 June 2018
| Citation

OPEN ACCESS

Abstract:

In this work, non-Newtonian fluid properties in a non-Darcy porous channel, specifically Darcy-Forchheimer porous channel is investigated with focus on a numerical analysis of Eyring-Powell type of non-Newtonian fluid. The unsteady state problem is considered under the influence of thermal radiation and transversely applied magnetic field. The governing non-linear partial differential equations were non-dimensionalized and then solved using Crank-Nicolson concept. Significance of non-Newtonian fluid properties as well as other fluid parameters is considered on the velocity, temperature and concentration profiles with the aid of graphs.

Keywords:

eyring-powell fluid, porous channel, darcy-forchheimer, crank-nicolson, unsteady

1. Introduction
2. Problem Formulation
3. Solution Method
4. Discussion of Results
5. Conclusion
Nomenclature
References

[1] Manisha P, Timol MG. (2009). Numerical treatment of powell-eyring fluid flow using method of satisfaction of asymptotic boundary conditions. Journal of Applied Numerical Mathematics 59: 2584-2592. https://doi.org/10.1016/j.apnum.2009.04.010

[2] Malik MY, Hussian A, Nadeems. (2013). Boundary layer flow of an Eyring-Powell model fluid due to a stretching cylinder with variable viscosity. Journal of Scientia Iranica 20(2): 313-321. https://doi.org/10.1016/j.scient.2013.02.028

[3] Powell RE, Eyring H. (1944). Mechanism for relaxation theory of viscosity. Nature 154: 427-428.

[4] Bird RB, Stewart WE, Lightfoot EM. (1960). Transport phenomena. John Wiley, New York.

[5] Adesanya SO, Gbadeyan JA. (2011). Adomian Decomposition approach to steady visco-elastic flow with slip through a planar channel. Journal of Nonlinear Science 11(1): 86-94.

[6] Islam S, Shah A, Zhou CY, Ali I. (2009). Homotopy pertubation analysis of slider bearing with Powell-Eyring fluid. Z. Angew. Math. Phys. 60: 178-1193. https://doi.org/10.1007/s00033-009-7034-9

[7] Patel M, Timol MG. (2009). Numerical treatment of Powell Eyring fluid flow using method of asymptotic boundary conditions. Appl. Numer. Math. 59: 2584-2592. https://doi.org/10.1016/j.apnum.2009.04.010

[8] Patel M, Timol MG. (2011). Numerical treatment of MHD Powell Eyring fluid flow using method of satisfaction of asymptotic boundary conditions. Int. J. Math. Sci. Comput. 2: 71-78.

[9] Hayat T, Iqbal Z, Qasim M, Obaidat S. (2012). Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions. Int. J. Heat Mass Transfer 55: 1817-1822. https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.046

[10] Khader MM, Megahed AM. (2013). Numerical studies for flow and heat transfer of the Powell-Eyring fluid thin film over an unsteady stretching sheet with internal heat generation using the finite difference method. Journal of Applied Mechanics Technical Phys. 5(4): 440-450. https://doi.org/10.1134/S0021894413030139

[11] Eldaebe NTM, Hassan AA, Mona AA. (2003). Effect of couple stresses on the MHD of a non-Newtonian unsteady flow between two parallel porous plates. Journal of physics 58a: 204-210.

[12] Zueco J, Beg OA. (2009). Network numerical simulation applied to pulsatile non-Newtonian flow through a channel with couple stress and wall mass effects. International Journal of Applied Mathematics and Mech. 5: 1-16.

[13] Eldabe NTM, Sallam N, Sallam Mohamed Y, Abou-zeid (2012). Numerical study of viscous dissipation effect on free convection heat and mass transfer of MHD non-Newtonian fluid flow through a porous medium. Journal of the Egyptian Mathematical Society 20: 139-151. https://doi.org/10.1016/j.joems.2012.08.013

[14] Ara A, Khan NA, Khan H, Sultan F. (2014). Radiation effects on boundary layer flow of an Eyring-Powell fluid over an exindent potentially shrinking sheet. Ain Shams Engineering Journal 5: 1337-1342. https://doi.org/10.1016/j.asej.2014.06.002

[15] Hayat T, Asad S, Mustafa M, Alsaedi A. (2014). Radiation effects on the flow of Powell Eyring fluid past an unsteady inclined stretching sheet with non-uniform Heat Source/Sink. PLOS ONE 9(7): e103214. https://doi.org/10.1371/journal. pone. 0103214

[16] Darji RM, Timol MG. (2013). Group-theoretic similarity analysis for natural convection boundary layer flow of a class of non-newtonian fluids. International Journal of Advanced Scientific and Technical Research 3(1): 54-69.

[17] Gbadeyan JA, Dada MS. (2013). On the Influence of radiation radiation and heat transfer on an unsteady MHD Non-Newtonian fluid flow with slip in a porous medium. Journal of Mathematical Research 5(3): 40-49. http://dx.doi.org/10.5539/jmr.v5n3p40

[18] Oyelami FH, Dada MS. (2016). Unsteady magnetohydrodynamic flow of some non-Newtonian fluids with slip in a porous channel. International Journal of Heat and Technology 36(2): 709-713. https://doi.org/10.18280/ijht.360237

[19] Parmar A., Jain S. (2018). MHD Powell-Eyring fluid flow with non-linear radiation and variable thermal conductivity over a permeable cylinder. International Journal of Heat and Technology 36(1): 56-64. https://doi.org/10.18280/ijht

[20] Modest MF. (1993). Radiation heat transfer. Mac Graw-Hill, New York.

[21] Rapits A, Perdikis C. (2004). Unsteady flow through a highly porous medium in the presence of radiation. Transport Porous Media 57(2): 171-179. https://doi.org/10.1023/B:TIPM.0000038262.65594.e8