A New Approach for Study the Electrohydrodynamic Oscillatory Flow Through a Porous Medium in a Heating Compliant Channel

M.H. Haroun 1
  • 1 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Abstract

The governing equations of an electrohydrodynamic oscillatory flow were simplified, using appropriate nondimensional quantities and the conversion relationships between fixed and moving frame coordinates. The obtained system of equations is solved analytically by using the regular perturbation method with a small wave number. In this study, modified non-dimensional quantities were used that made fluid pressure in the resulting equations dependent on both axial and vertical coordinates. The current study is more realistic and general than the previous studies in which the fluid pressure is considered functional only in the axial coordinate. A new approach enabled the author to find an analytical form of fluid pressure while previous studies have not been able to find it but have found only the pressure gradient. Analytical expressions for the stream function, electrical potential function and temperature distribution are obtained. The results show that the electrical potential function decreases by the increase of the Prandtl number, secondary wave amplitude ratio and width of the channel.

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  • [1] Latham T.W. (1966): Fluid motion in a peristaltic pump. – M. SC. Thesis, MIT, Cambridge, M.A.

  • [2] Fung Y.C. and Yih C.S. (1968): Peristaltic transport. J. Appl. Mech., vol.35, pp.669-675.

  • [3] Shapiro A.H., Jaffrin M.Y. and Weinberg S.L. (1969): Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech., vol.37, pp.799-825.

  • [4] AbdElnaby M.A. and Haroun M.H. (2008): A new model for study the effect of wall properties on peristaltic transport of a viscous fluid. Communications in Nonlinear Science and Numerical Simulation, vol.13, pp.752-762.

  • [5] Sankad G.C. and Nagathan P.S. (2017): Influence of wall properties on the peristaltic flow of a Jeffrey fluid in a uniform porous channel under heat transfer. Int. J. Res. Ind. Eng., vol.6, No.3, pp.246-261.

  • [6] Nadeem S., Riaz A. and Ellahi R. (2014): Peristaltic flow of viscous fluid in a rectangular duct with compliant walls. Comput. Math. Model., vol.25, No.3, pp.404-415.

  • [7] Haroun M.H. (2006): On non-linear magnetohydrodynamic flow due to peristaltic transport of an Oldroyd 3-constant fluid. Z. Naturforsch. A, vol.61, pp.263-274.

  • [8] Hayat T., Rafiq M. and Ahmad B. (2016): Influences of rotation and thermophoresis on MHD peristaltic transport of Jeffrey fluid with convective conditions and wall properties. Journal of Magnetism and Magnetic Materials, vol.410, pp.89-99.

  • [9] Mekheimer Kh.S., Saleem N. and Hayat T. (2012): Simultaneous effects of induced magnetic field and heat and mass transfer on the peristaltic motion of second-order fluid in a channel. International Journal for Numerical Methods in Fluids, vol.70, pp.342-358.

  • [10] Ranjit N.K. and Shit G.C. (2017): Joule heating effects on electromagnetohydrodynamic flow through a peristaltically induced micro-channel with different zeta potential and wall slip. Physica A, vol.482, pp.458-476.

  • [11] Tripathi D., Sharma A. and Beg O.A. (2017): Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel: Effects of Joule heating and Helmholtz-Smoluchowski velocity. International Journal of Heat and Mass Transfer, vol.111, pp.138-149.

  • [12] El-Sayed M.F., Haroun M.H. and Mostapha D.R. (2015): Electroconvection peristaltic flow of viscous dielectricliquid sheet in asymmetrical flexible channel. Journal of Atomization and Sprays, vol.25, pp.985-1011.

  • [13] Landau L.D. and Lifshitz E.M. (1960): Electrodynamics of Continuous Media. New York: The Macmillan Company.

  • [14] Tropea C., Yarin A.L. and Foss J.F. (2007): Hand Book of Experimental Fluid Mechanics. Berlin: Springer.

  • [15] Takashima M. and Ghosh A.K. (1979): Electrohydrodynamic instability of viscoelastic liquid layer. J. Physical Society of Japan, vol.47, pp.1717-1722.

  • [16] Davies C. and Carpenter P.W. (1997): Instabilities in a plane channel flow between compliant walls. J. Fluid Mech., vol.352, pp.205-243.

  • [17] Nayfeh A.H. (1981): Introduction to Perturbation Techniques. – New York: John Wiley and Sons.

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