Effect of Heat Transfer on the Peristaltic Flow of Walters B Fluid in a Vertical Channel with an External Magnetic Field
Publication: Journal of Aerospace Engineering
Volume 29, Issue 2
Abstract
This article describes the effect of heat transfer on the magnetohydrodynamic peristaltic flow of Walters B fluid in a vertical symmetric channel. The flow is investigated in a wave frame of reference moving with the velocity of the wave. A perturbation method is used to obtain the approximate analytical solution for the stream function, temperature, and pressure gradient. The pressure difference and frictional force are obtained numerically. The variation of velocity, pressure gradient, temperature, stream function, pressure difference, and frictional force are sketched for various embedded parameters. The behavior of the Nusselt number and skin friction is presented in tables for the different parameters involved. Graphical results are also presented for four different wave shapes.
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Acknowledgments
The authors are extremely thankful to the anonymous reviewers for their constructive suggestions, which led to the considerable improvement of the quality of the paper.
References
Akbar, N. S. (2014). “Peristaltic Sisko nanofluid in an asymmetric channel.” Appl. Nanosci., 4(6), 663–673.
Akbar, N. S., Nadeem, S., Hayat, T., and Hendi, A. A. (2012). “Peristaltic flow of a nanofluid with slip effects.” Meccanica, 47(5), 1283–1294.
Ali, N., and Hayat, T. (2008). “Peristaltic flow of a micropolar fluid in an asymmetric channel.” Comput. Math. Appl., 55(4), 589–608.
Hayat, T., and Ali, N. (2008). “Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube.” Commun. Nonlinear Sci. Numer. Simul., 13(7), 1343–1352.
Hayat, T., Ali, N., and Asghar, S. (2007a). “An analysis of peristaltic transport for flow of a Jeffrey fluid.” Acta Mech., 193(1-2), 101–112.
Hayat, T., Asghar, Z., Asghar, S., and Mesloub, S. (2010a). “Influence of inclined magnetic field on peristaltic transport of fourth grade fluid in an inclined asymmetric channel.” J. Taiwan Inst. Chem. Eng., 41(5), 553–563.
Hayat, T., and Hina, S. (2010). “The influence of wall properties on the MHD peristaltic flow of a Maxwell fluid with heat and mass transfer.” Nonlinear Anal. Real World Appl., 11(4), 3155–3169.
Hayat, T., Khan, M., Siddiqui, A. M., and Asghar, S. (2007b). “Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel.” Commun. Nonlinear Sci. Numer. Simul., 12(6), 910–919.
Hayat, T., Mahomed, F. M., and Asghar, S. (2005). “Peristaltic flow of a magnetohydrodynamic Johnson-Segalman fluid.” Nonlinear Dyn., 40(4), 375–385.
Hayat, T., and Noreen, S. (2010). “Peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field.” C.R. Mec., 338(9), 518–528.
Hayat, T., Qureshi, M. U., and Hussain, Q. (2009). “Effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space.” Appl. Math. Modell., 33(4), 1862–1873.
Hayat, T., Saleem, N., and Ali, N. (2010b). “Effect of induced magnetic field on peristaltic transport of a Carreau fluid.” Commun. Nonlinear Sci. Numer. Simul., 15(9), 2407–2423.
Hayat, T., Saleem, N., Asghar, S., Alhothuali, M. S., and Alhomaidan, A. (2011). “Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid.” Commun. Nonlinear Sci. Numer. Simul., 16(9), 3559–3577.
Khan, I., Ali, F., Shafie, S., and Qasim, M. (2014). “Unsteady free convection flow in a Walters’-B fluid and heat transfer analysis.” Bull. Malaysian Math. Sci. Soc., 37, 437–448.
Kothandapani, M., and Srinivas, S. (2008). “Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel.” Int. J. Non Linear Mech., 43(9), 915–924.
Mehmood, O. U., and Fetecau, C. (2015). “A note on radiative heat transfer to peristaltic flow of Sisko fluid.” Appl. Bionics Biomech., 1–9.
Mishra, M., and Rao, A. R. (2003). “Peristaltic transport of a Newtonian fluid in an asymmetric channel.” Zeitschrift fur angewandte Mathematik und Physik, 54(3), 532–550.
Nadeem, S., and Akbar, N. S. (2009). “Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: Application of Adomian decomposition method.” Commun. Nonlinear Sci. Numer. Simul., 14(11), 3844–3855.
Nadeem, S., and Akbar, N. S. (2010a). “Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel.” Appl. Math. Mech., 31(8), 969–978.
Nadeem, S., and Akbar, N. S. (2010b). “Effects of temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid in a non-uniform vertical tube.” Commun. Nonlinear Sci. Numer. Simul., 15(12), 3950–3964.
Nadeem, S., and Akbar, N. S. (2010c). “Influence of radially varying MHD on the peristaltic flow in an annulus with heat and mass transfer.” J. Taiwan Inst. Chem. Eng., 41(3), 286–294.
Nadeem, S., and Akbar, N. S. (2010d). “Peristaltic flow of Walters B fluid in a uniform inclined tube.” J. Biorheol., 24(1), 22–28.
Nadeem, S., and Akbar, N. S. (2011). “Influence of heat and mass transfer on the peristaltic flow of a Johnson Segalman fluid in a vertical asymmetric channel with induced MHD.” J. Taiwan Inst. Chem. Eng., 42(1), 58–66.
Nadeem, S., and Akram, S. (2010). “Heat transfer in a peristaltic flow of MHD fluid with partial slip.” Commun. Nonlinear Sci. Numer. Simul., 15(2), 312–321.
Nadeem, S., and Akram, S. (2011). “Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer.” Acta Mech. Sin., 27(2), 237–250.
Noreen, S., and Qasim, M. (2013). “Peristaltic flow of MHD Eyring-Powell fluid in a channel.” Eur. Phys. J. Plus, 128(8), 91–100.
Pandey, S. K., and Chaube, M. K. (2011). “Study of wall properties on peristaltic transport of a couple stress fluid.” Meccanica, 46(6), 1319–1330.
Prakash, O., Kumar, D., and Dwivedi, Y. K. (2012). “Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity.” Pramana, 79(6), 1457–1470.
Radhakrishnamacharya, G., and Srinivasulu, Ch. (2007). “Influence of wall properties on peristaltic transport with heat transfer.” C.R. Mec., 335(7), 369–373.
Ramesh, K., and Devakar, M. (2015). “Effects of heat and mass transfer on the peristaltic transport of MHD couple stress fluid through porous medium in a vertical asymmetric channel.” J. Fluids, 1–19.
Srinivas, S., Gayathri, R., and Kothandapani, M. (2009). “The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport.” Comput. Phys. Commun., 180(11), 2115–2122.
Srinivas, S., Gayathri, R., and Kothandapani, M. (2011). “Mixed convective heat and mass transfer in an asymmetric channel with peristalsis.” Commun. Nonlinear Sci. Numer. Simul., 16(4), 1845–1862.
Srinivas, S., and Muthuraj, R. (2011). “Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis.” Math. Comput. Modell., 54(5–6), 1213–1227.
Tripathi, D. (2011). “Peristaltic transport of a viscoelastic fluid in a channel.” Acta Astronautica, 68(7–8), 1379–1385.
Vajravelu, K., Radhakrishnamacharya, G., and Radhakrishnamurty, V. (2007). “Peristaltic flow and heat transfer in a vertical porous annulus with long wave approximation.” Int. J. Non Linear Mech., 42(5), 754–759.
Walters, K. (1962). “Non-Newtonian effects in some elastico-viscous liquids whose behaviour at small rates of shear is characterized by a general linear equation of state.” Q. J. Mech. Appl. Math., 15(1), 63–76.
Yildirim, A., and Sezer, S. A. (2010). “Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel.” Math. Comput. Modell., 52(3), 618–625.
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Published In
Journal of Aerospace Engineering
Volume 29 • Issue 2 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 10, 2014
Accepted: Jun 22, 2015
Published online: Sep 9, 2015
Discussion open until: Feb 9, 2016
Published in print: Mar 1, 2016
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