A study of Jeffery Fluid Flow in a Vertical Channel with wall slip and Hall current

K. Nirmala

doi:https://doi.org/10.14445/22315373/IJMTT-V66I6P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 6 | Year 2020 | Article Id. IJMTT-V66I6P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I6P503

A study of Jeffery Fluid Flow in a Vertical Channel with wall slip and Hall current

K. Nirmala

Abstract

This paper is devoted to the study of MHD Jeffrey fluid in a vertical channel in presence of wall slip and Hall current. The channel is caused due to peristaltic transport on the walls having different amplitudes and phase. The analytical solution has been carried out by using the long-wave approximation and low Reynolds number. Closed form expressions for velocity and temperature are developed. The expressions for the zeroth-order and the first order solutions are obtained and the results are presented graphically for different values of parameters entering into the problem.

Keywords

MHD, Hall current, wall slip, Jeffery fluid, asymmetric channel.

References

[1] T. W. Latham, Fluid motion in Peristaltic Pump, M.S. Thesis, MIII, Cambridge, Mass, 1966.
[2] T. Hayat, Y. Wang, A. M. Siddiqui, K. Hutter and S. Asghar, Peristaltic transport of a third-order fluid in a circular cylindrical tube, Math. Models and methods in Appl. Sci., 12 (2002)1691 - 1706.
[3] M. Mishra and A. Ramachandra Rao, Peristaltic transport of a Newtonian fluid in an asymmetric channel, ZAMP, 54 (2003) 532 - 550.
[4] T. Hayat, N. Ali, S. Asghar and A.M. Siddiqui, Exact peristaltic flow in tubes with an endoscope, Applied Math. Computation, 182 (2006) 359 – 368.
[5] M. Kothandapani and S. Srinivas, Non-linear peristaltic transport of Newtonian fluid in an inclined asymmetric channel through a porous medium, Phys. Lett. A, 372 (2008) 1265-1276.
[6] Kh. S. Mekheimer and Y. Abd elmaboud, The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: Application of an endoscope, Phys. Lett. A, 372 (2008) 1657-1665.
[7] T. Hayat and N. Ali, Peristaltically induced motion of a MHD third grade fluid in a deformable tube, Physica A, 370 (2006) 225-239.
[8] T. Hayat, N. Ali and Z. Abbas, Peristaltic flow of a micropolar fluid in a channel with different wave forms, Phys. Lett. A, 370 (2008) 331-344.
[9] S. Srinivas and R.Gayathri, Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium, Appl. Math. Comput. 215 (2009) 185-196.
[10] T. Hayat, R. Sajjad, S. Asghar, Series solution for MHD channel flow of a Jeffery fluid, Commun Nonlinear Sci Numer Simulat., 15 (2010) 2400–2406.
[11] S. Srinivas and R. Muthuraj, Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis, Math. Comput. Model., 54 (2011) 1213-1227.
[12] S. Srinivas and R. Muthuraj, Peristaltic transport of a Jeffrey fluid under the effect of slip in an inclined asymmetric channel, Int. J Appl. Mech. 2 (2010) 437–455.
[13] R. Muthuraj and S. Srinivas, Effects of compliant wall properties and space porosity in the MHD peristaltic transport with Heat and Mass Transfer in a vertical channel, Int. J. of Appl. Math and Mech., 7 (2011) 97-112.
[14] S. Nadeem and S. Akram, Peristaltic flow of a couple stress fluid under the effect of induced magnetic field in an asymmetric channel, Arch. Appl. Mech., 81 (2011) 97–109.
[15] N. T. Eldabe, K. A. Kamel, G. M. Abd- Allah and S.F. Ramadan, Peristaltic motion with Heat and Mass transfer of a Dusty fluid through a Horizontal porous channel under the effect of wall properties, Int. J Research Reviews in Appl. Sciences., 15 (2013) 300-311.
[16] K. Vajravelu S. Sreenadh, P. Lakshminarayana, The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum, Commun Nonlinear Sci Numer Simulat., 16 (2011) 3107-3125.
[17] S. Hina, T. Hayat and A. Alsaedi, Heat and mass transfer effects on the peristaltic flow of Johnson-Segalman fluid in a curved channel with compliant walls, Int. J Heat Mass Transfer., 55 (2012) 3511-3521.
[18] R. Ellahi, T. Hayat, F. M. Mahomed and S. Asghar, Effects of slip on the non-linear flows of a third grade fluid, Nonlinear anal-Real world App., 11(2010) 139-146.
[19] S. Nadeem and S.Akram, Heat transfer in a peristaltic flow of MHD fluid with partial slip, Commun Nonlinear Sci Numer Simulat., 15 (2010) 312–321.
[20] N. S. Akbar, T. Hayat, S. Nadeem and S. Obaidat, Peristaltic flow of a Williamson fluid in an inclined asymmetric channel with partial slip and heat transfer, Int. J. Heat Mass Transfer, 55 (2012) 1855–1862.
[21] M.Ahmad, H. Zaman and N. Rehman, Effects of Hall current on unsteady MHD flows of a second grade fluid, Cent. Eur. J. Phys., 8 (2010) 422-431.
[22] F.M. Ali, R. Nazar, N.M. Arifin and I. Pop, Effect of Hall current on MHD mixed convection boundary layer flow over a stretched vertical flat plate, Meccanica 46 (2011) 1103-1112.
[23] D. Srinivasacharya and K. Kaladhar, Mixed convection flow of couple stress fluid between parallel vertical plates with Hall and Ion-slip effects, Commun Nonlinear Sci Numer Simulat., 17 (2012) 2447–2462.

Citation :

K. Nirmala, "A study of Jeffery Fluid Flow in a Vertical Channel with wall slip and Hall current," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 6, pp. 17-31, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I6P503