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Reacting Flow of Temperature-Dependent Variable Permeability Through a Porous Medium in the Presence of Arrhenius Reaction

American Journal of Mathematical and Computational Sciences
Vol.4 , No. 1, Publication Date: Mar. 6, 2019, Page: 11-18

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Authors

[1]	Benjamin Aina Peter, School of Engineering and Applied Sciences, Kamapala International University, Kampala, Uganda.
[2]	Amos Wale Ogunsola, Departmentof Pure and Applied Mathematics, University of Technology, Ogbomoso, Nigeria.
[3]	Anthony EjehItodo, School of Engineering and Applied Sciences, Kamapala International University, Kampala, Uganda.
[4]	Idowu Sabiki Adebola, Departmentof Mathematical Sciences, Olabisi Onabanjo University, Ago-Iwoye, Nigeria.
[5]	Mundu Muhamad Mustapha, School of Engineering and Applied Sciences, Kamapala International University, Kampala, Uganda.

Abstract

In this work, a reacting flow of temperature-dependent variable permeability through a porous medium has studied and analyzed. It is assumed that the viscosity is temperature-dependent. Absolute permeability is said to be the ability of a porous medium to transmit its fluid content under an applied pressure gradient. The permeability of a porous medium is an intrinsic property that measures its ability to transmit fluids or a medium that allow fluids to pass through it. It is determined by the macroscopic properties of the medium namely porosity, pore size distribution, tortuosity and specific surface. It is a well known fact that the value of permeability is independent of the type of fluid used in the porous medium where Newtonian fluids are used for measurements. Since a porous medium contains pores, the applications of thermal science to the system leads to an intuitive believe that the thermal expansion coefficient of the solid component will cause volumetric expansion with changes in temperature variation of the medium. The governing partial differential equations are transformed into ordinary differential equations in terms of a suitable similarity variable. Galerkin weighted residual method is employed to solve the resulting non-linear equations and the effects of various physical parameter s involve in the system of flow were reported graphically. Furthermore, the effect of variable permeability parameter on the velocity profile is investigated. Some special cases with their physical significance are discussed and compared with the existing published work.

Keywords

Unsteady Gravity Flow, Weighted Residual Method, Power-Law Fluid and Viscous Dissipation

Reference

[01]	Philip Iyiola Farayola. On Steady Flow of a Reactive Viscous Fluid in a Porous Cylindrical Pipe. Open Journal of Fluid Dynamics, 7, 359-370, 2017.
[02]	Adango Miadonye and Mumuni Amadu. Analytical Derivation of the Temperature Dependence of Absolute Permeability of a Porous Medium. Journal of Petroleum Science Research (JPSR) Volume 3 Issue 4, October 2014.
[03]	Mahesh P. Ediriweera and Britt M. Halvorsen. A Study of the Effect of Relative Permeability and Residual Oil Saturation on Oil Recovery. Proceedings of the 56th SIMS October 07-09, 2015, Linköping, Sweden.
[04]	T. Chevalier, C. Chevalier1, X. Clain, J. C. Dupla, J. Canou, S. Rodts, and P. Coussot. Darcy’s law for yield stress fluid flowing through a porous medium. Journals of Non-Newtonian Fluid Mechanics, Elsevier, 195, pp. 57-66, 2018.
[05]	I. J. Uwanta, M. M. Hamza and M. O Ibrahim. Heat and Mass Transfer Flow through a Porous Medium with Variable Permeability and Periodic Suction. International Journal of Computer Applications (0975 – 8887) Volume 36– No. 2, December 2011.
[06]	K. Hooman, and H. Gurgenci. Effects of temperature-dependent viscosity variation on entropy generation, heat, and fluid flow through a porous-saturated duct of rectangular cross-section. Retrieved from URL on 18th December, 2018.
[07]	S. K. Parida and B. R. Rout. Free Convective Flow through Porous Medium with Variable Permeability in Slip Flow Regime with Couple Stress in the Presence of Heat Source. Journal of Engineering Thermophysics, Vol. 26, (1), 125–138, 2017.
[08]	T. Pesso and S. Piva. An Analytical Solution for the Laminar Forced Convection in a Pipe with Temperature-Dependent Heat Generation. Journal of Applied Fluid Mechanics, Vol. 8, No. 4, pp. 641-650, 2015.
[09]	Temitope E. Akinbobola, Samuel S. Okoya. The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink. Journal of the Nigerian Mathematical Society, 34, 331–342, 2015.
[10]	Debasish Dey. Viscoelastic fluid flow through an annulus with relaxation, retardation effects and external heat source/sink. Alexandria Engineering Journal 2017.www.elsevier.com/locate/aej.
[11]	Kumar, B. and Prasad (2014): Pulsatile flow through a porous medium. J. of Appl. Fluid Mech., Vol. 7, No. 1, pp 63-74, 2014.
[12]	Vajravelu, K, Prasad, K. V. Santh, S. R. and Umesh, V. (2014): Fluid flow and heat transfer over a permeable stretching cylinder. J. of Applied Fluid Mechanics, Vol. 7, No, pp 111-120, 2014.
[13]	Salem, A. M. (2013): The effects of variable viscosity, viscous dissipation and chemical reaction on heat and mass transfer flow of MHD micropolar fluid along a permeable stretching sheet in a non-Darcian porous medium. Journal of Mathematical Problems in Engineering, Vol., 2013.
[14]	Gitima Patowanj (2012): Effect of variable viscosity and thermal conductivity of micro polar fluid in a porous channel in the presence of magnetic field. Int. J. of Basic Sciences and Social Sciences, Vol. 3, pp. 69-77.
[15]	Rafael Cortell Bataller (2008): Unsteady gravity flows of a power- law fluid througha porous medium. Applied Maths. and Computation 196 pp 356-362.
[16]	Ogunsola, A. W. and Ayeni, R. O. (2007). Temperature distribution of an Arrheniusly reacting unsteady flow through a porous medium with variable permeability. Research Journal of Applied Sciences, Issue 2, Vol. 4, pp 400-403.
[17]	Hupper. H. E. and Woods, A. W. Gravity-driven flows in porous layers. J. Fluid Mech., Vol. 292, pp 55-69, 1995.
[18]	Pascal, J. P. and Pascal, H. (1993): Similarity solutions to some gravity flows of non-Newtonian fluids through a porous medium. Int. J. Non-Linear Mech. 38 pp, 157.
[19]	Singh, P. K. (2013): Viscous dissipation and variable viscosity effects on MHD boundary layer flow in porous medium past a moving vertical plate with suction. Int. Journal of Engineering Science and Technology.
[20]	Vittorio Di Federico, Renata Archetti and Sandro Longo. Similarity solutions for spreading of a two dimensional non-Newtonian gravity current in a porous layer. Journal of Non-Newtonian Fluid Mechanics 177-178, pp 46-53, 2012.
[21]	Kumar, B. and Prasad (2014): Pulsatile flow through a porous medium. J. of Appl. Fluid Mech., Vol. 7, No. 1, pp 63-74, 2014.
[22]	Fatin Nabila Kamal and Khairy Zaimi. Heat and mass transfer in MHD stagnation point flow over a permeable stretching/shrinking sheet in the presence of radiation effect, so ret effect and slip parameter. Applied Mathematics and Computational Intelligence. 6, 53-62, 2017.