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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


Magneto-Hydrodynamic Flow of a Viscous Fluid in a Channel with a Porous Bounding Wall of Different Permeabilities

Magneto-Hydrodynamic Flow of a Viscous Fluid in a Channel with a Porous Bounding Wall of Different Permeabilities

Nidhi Pandya
Department of Mathematics & Astronomy, Lucknow University, Lucknow, India.

Pravin Kumar Srivastava
Department of Applied Science & Humanities, Bundelkhand Institute of Engineering & Technology, Jhansi, India.

Ramesh Yadav
Department of Mathematics, Babu Banarasi Das National Institute of Technology and Management, Lucknow, India.

R. P. Pandey
Department of Applied Science & Humanities , Bundelkhand Institute of Engineering & Technology, Jhansi, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.3-056

Received on October 22, 2018
  ;
Accepted on April 03, 2019

Abstract

In this paper, the effects of permeability parameter on the magneto-hydrodynamic laminar flow of a viscous incompressible fluid in a channel with a porous bounding wall have been investigated. A transverse magnetic field has been applied in the channel flow of viscous fluid and the stream function is used to reduce the governing partial differential equations into non-linear ordinary differential equation which is solved by applying Perturbation method. Numerical simulation is used to analyze the problem and the graphs have been plotted using MATLAB. It has been observed that an increase of magnetic parameter increases the velocity of the viscous fluid while the velocity decreases with the increase of permeability parameter. The flow of viscous fluid has also been investigated with the variation of Reynolds number and the slip coefficient.

Keywords- Porous medium, MHD Flow, Reynolds number, Slip coefficient, Laminar flow.

Citation

Pandya, N., Srivastava, P. K., Yadav, R., & Pandey, R. P. (2019). Magneto-Hydrodynamic Flow of a Viscous Fluid in a Channel with a Porous Bounding Wall of Different Permeabilities. International Journal of Mathematical, Engineering and Management Sciences, 4(3), 708-728. https://dx.doi.org/10.33889/IJMEMS.2019.4.3-056.

Conflict of Interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgements

The authors thank the reviewers for their valuable suggestions which led to definite improvement in the paper.

References

Abdou, M.M.M., El-Kabeir, S.M.M., & Gorla, R.S.R. (2007). Effect of mixed thermal boundary conditions and magnetic field on free convection flow about a cone in micropolar fluids. International Journal of Fluid Mechanics Research, 34(5), 387-402.

Abou-Zeid, M.Y. (2009). Numerical treatment of heat and mass transfer of MHD flow of carreau fluid with diffusion and chemical reaction through a Non-Darcy porous medium. The Open Mathematics Journal, 2, 22-35.

Akeem B. Disu, Christie, Y. Ishola & Toyin Olorunnishola (2014). Heat and mass transfer on MHD oscillatory slip flow in a channel filled with porous medium. IOSR Journal of Mathematics, 10(4), 69-77.

Berman, A.S. (1953). Laminar flow in channels with porous walls. Journal of Applied physics, 24(9), 1232-1235.

Bujurke, N., Katagi, N.N., & Awati, V.B. (2010). Analysis of Laminar flow in a channel with one porous bounding wall. International Journal of Fluid Mechanics Research, 37(3), 267-281.

Dey, D. (2019). Mixed convective MHD micro-polar fluid flow in a porous medium with radiation absorption. International Journal of Mathematical, Engineering and Mathematical Sciences, 4(2), 387-399.

Ganesha, S., & Krishnambal, S. (2006). Magneto hydrodynamic flow of viscous fluid between two parallel porous plates. Journal of Applied Sciences, 6(11), 2420-2425.

Hosseini, M., Sheikholeslami, Z., & Ganji, D.D. (2013). Non-Newtonian fluid flow in an axisymmetric channel with porous wall. Propulsion and Power Research, 2(4), 254-262.

Jafaryar, M., Farkhadnia, F., Mohammadian, E., Hosseini, M., & Khazaee, A.M. (2014). Analytical investigation of laminar flow through expanding or contracting gaps with porous walls. Propulsion and Power Research, 3(4), 222-229.

Mahanta, P.K. (2012). Numerical study on heat transfer of Non-Newtonian fluid flow over stretching surface with variable viscosity in uniform magnetic Field. International Journal of Scientific & Research Publications, 2(12), 1-9.

Makinde, O.D. & Osalusi, E. (2006). MHD steady flow in a channel with slip at the permeable boundaries. Romanian Journal of Physics, 51(3-4), 319-328.

Muthuraj, R., & Srinivas, S. (2009). Influence of magnetic field and wall slip conditions on steady flow between parallel flat wall and a long wavy wall with Soret effect. Journal of Naval Architecture and Marine Engineering, 6(2), 62-71.

Naikoti, K., & Vadithya, M. (2014). Thermal radiation effects on magneto hydrodynamic flow and heat transfer in a channel with porous walls of different permeability. Thermal Science, 18(Supplement 2), S563-S572.

Prasad, B.G., & Kumar, A. (2011). Flow of hydro magnetic fluid through porous media between permeable beds under exponentially decaying pressure gradient. Computational Methods in Science and Technology, 17(1-2), 63-74.

Ramadevi, B., Reddy, R.J.V., & Sugunamma V. (2018). Influence of thermodiffusion on time dependent Casson fluid flow past a wavy surface. International Journal of Mathematical, Engineering and Mathematical Sciences, 3(4), 472-490.

Ramakrishnan, K., & Sathish, E. (2018). Influence of porous parameter on MHD flow between porous walls of finite thickness. International Journal of Pure and Applied Mathematics, 119(13), 71-79.

Reddy, P.G., Reddy, T.S., & Varma, S.V.K. (2017). MHD flow of a Newtonian fluid through a porous medium in planer channel. Global Journal of Pure and Applied Mathematics, 13(7), 3811-3832.

Terrill, R.M, & Shrestha, G.M. (1964). Laminar flow through channels with porous walls and with an applied transverse magnetic field. Applied Scientific Research, 11(B), 134-144.

Terrill, R.M. (1965). Laminar flow in a uniformly porous channel with large injection. The Aeronautical Quarterly, 16(4), 323-332.

Terrill, R.M., & Shrestha, G.M. (1966). Laminar flow through a channel with uniformly porous walls of different permeability. Applied Scientific Research, Section A, 15(1), 440-468.

Vafai, K., & Kim, S. (1990). Fluid mechanics of the interface region between a porous medium and a fluid layer—an exact solution. International Journal of Heat and Fluid Flow, 11(3), 254-256.

Yadav, R., & Joseph, V. (2017). Numerical investigation of heat transfer along symmetrical porous wedge and effects of radiation in the presence of variable fluid viscosity of flow. Applied Research Journal, 3(10), 295-303.

Zhang, Y., Lin, P., & Si, X.H. (2014). Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls. Applied Mathematics and Mechanics, 35(2), 203-220.