# Unsteady magnetohydrodynamic flow of some non-Newtonian fluids with slip through porous channel

Unsteady magnetohydrodynamic flow of some non-Newtonian fluids with slip through porous channel

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:
709-713
|
DOI:
https://doi.org/10.18280/ijht.360237
20 December 2017
| |
Accepted:
3 April 2018
| | Citation

OPEN ACCESS

Abstract:

The numerical analysis for transfer of heat by natural convection on an unsteady Magnetohydrodynamic flow of non-Newtonian fluids through porous channel is considered. Equations governing the model are formulated, simplified and non-dimensionalised. The solution is obtained by employing Crank Nicolson’s type of finite difference discritization. Velocity as well as the temperature distributions for both Prandtl-Eyring and Eyring-Powell non-Newtonian fluid models are examined. Comparism between these two diverse liquid models is made with their graphical illustrations on velocity and temperature profiles. It is observed that the velocity is higher for Prandtl Eyring model than Eyring Powell model. Also, the temperature variation for Prandtl number in Eyring-Powell fluid is a little slower than that of Prandtl-Eyring fluid.

Keywords:

non-Newtonian fluid, slip, porous medium, eyring-powell model, prandtl-eyring model

1. Introduction
2. Problem Formulation
3. Numerical Solution
4. Results and Discussion
5. Conclusion
Nomenclature
References

[1] Timol MG, Kalthia NL. (1985). Group theoretic approach to similarity solutions in non-Newtonian natural convection flows. Journal of Energy Heat and Mass Transfer 7(4): 251-288.

[2] 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 58: 204-210. http://dx.doi.org/10.1515/zna-2003-0405

[3] 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: 1-1ֱ6.

[4] 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.

[5] 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

[6] 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:10.1371/journal. pone. 0103214

[7] 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

[8] Arifuzzaman SM, Khan MS, Hossain KE, Islam MS, Akter S, Roy R. (2017). Chemically reactive viscoelastic fluid flow in presence of nano particle through porous stretching sheet. Frontiers in Heat and Mass Transfer 9(5): 1-11. http://dx.doi.org/10.5098/hmt.9.5

[9] Khan MS, Karim I, Ali LE, Islam A. (2012). Unsteady MHD free convection boundary-layer flow of a nanofluid along a stretching sheet with thermal radiation and viscous dissipation effects. International Nano Letters 2(24). https://doi.org/10.1186/2228-5326-2-24

[10] Arifuzzaman SM, Rana BMJ, Ahmed R, Ahmmed SF. (2017). Cross diffusion and MHD effect on a high order chemically reactive micropolar fluid of naturally convective heat and mass transfer past through an infinite vertical porous medium with a constant heat sink. AIP Conference Proceedings 1851, 020006. http://dx.doi.org/10.1063/1.4984635

[11] Arifuzzaman SM, Khan MS, Islam MS, Islam MM, Rana BMJ, Biswas P, Ahmmed SF. (2017). MHD Maxwell fluid flow in presence of nano-particle through a vertical porous–plate with heat- generation, radiation absorption and chemical reaction. Frontiers in Heat and Mass Transfer 9(25): 1-14.  http://dx.doi.org/10.5098/hmt.9.25

[12] Zaman H. (2013). unsteady incompressible couette flow problem for the Eyring-Powell model with porous walls. American Journal of Computational Mathematics 3: 313-32ֳ5. http://doi 10.4236/ajcm.2013.34041

[13] 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

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

[15] Mahmoudi A, Mejri I. (2015). Analysis of conduction-radiation heat transfer with variable thermal conductivity and variable refractive index: Application of the Lattice Boltzmann method. International Journal of Heat and Technology 33(1): 1-8. https://doi.org/10.18280/ijht.330101

[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.