Document Type: Research Paper



2 Acharya Nagarjuna University, India


In this paper, we analyze the thermal radiation and chemical reaction impacts on MHD peristaltic motion of the Eyring-Powell fluid through a porous medium in a channel with compliant walls under slip conditions for velocity, temperature, and concentration. Assumptions of a long wave length and low Reynolds number are considered. The modeled equations are computed by using the perturbation method. The resulting non-linear system is solved for the stream function, velocity, temperature, concentration, skin-friction coefficient, heat transfer coefficient and mass transfer coefficient. The flow quantities are examined for various parameters. Temperature depresses with an enhancee in the radiation parameter, while the opposite effect is observed for the concentration. The fluid concentration enhances and depresses with generative and destructive chemical reaction respectively. The trapped bolus whose size diminishes as the Powel-Eyring parameter increases while it enhances as another Powell fluid parameter increases. The trapped bolus whose size rises when Darcy number enhances.

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[1] T.W. Latham, “Fluid motion in a peristaltic pump”, MS. Thesis, Massachusetts Institute of Technology, Cambridge (1966).

[2] A.H. Shapiro, M.Y. Jaffrin, and S.L. Weinberg, “Peristaltic pumping with long wave lengths at low Reynolds numbers”, Journal of Fluid Mechanics, Vol. 37, No. 4, pp. 799 – 825, (1969).

[3] H.L. Agrawal, and B. Anwaruddin, “Peristaltic flow of blood in a branch”, Ranchi University Mathematical Journal, Vol. 15, pp.111 – 125 (1984).

[4] L.M. Srivastava, and V.P. Srivastava, “Peristaltic transport of a power-law fluid: Application to the ductus efferentes of the reproductive tract”, Rheologica Acta , Vol. 27, No. 4, pp. 428 – 433, (1988).

[5] M. Mishra, and A.R. Rao,” Peristaltic transport of a Newtonian fluid in an asymmetric channel”, Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 54, No. 3, pp. 532 – 550, (2003).

[6] Kh. S. Mekheimer, and Y. Abd elmaboud, “Peristaltic flow through a porous medium in an annulus”: Application of an endoscope, Applied Mathematics & Information Sciences, Vol. 2 , No. 1, pp. 103 – 111 (2008).

[7] T. Hayat, S. Hina, A.A. Hendi, and S. Asghar, “Effect of wall properties on the peristaltic flow of a third grade fluid in a curved channel with heat and mass transfer”, International Journal Heat Mass Transfer, Vol. 54 , pp. 5126 – 5136 (2011).

[8] S.K. Pandey, and M.K. Chaube, “Study of wall properties on peristaltic transport of a couple stress fluid”, Meccanica, Vol. 46, No. 6, pp. 1319 – 1330 (2011).

[9] D. Tripathi, “A mathematical model for the peristaltic flow of chyme movement in small intestine”, Mathematical Bio Sciences, Vol. 233, pp. 90 – 97(2011).

[10] Kh. S. Mekheimer, and A.N. Abdel-Wahab, “Net annulus flow of a compressible viscous liquid with peristalsis”, Journal of Aerospace Engineering, Vol. 25, No. 4, pp. 660 – 669 (2012).

[11] P. Lakshminarayana, S. Sreenadh, and G. Sucharitha, “Peristaltic pumping of a conducting fluid in a channel with a porous peripheral layer”, Advances in Applied Science Research, Vol. 3, No. 6, 2890 – 2899 (2012).

[12] S. Maiti, and J.C. Misra, “Non-Newtonian characteristics of peristaltic flow of blood in micro vessels”, Communications in Nonlinear Science and Numerical Simulation, Vol. 18, No. 8, pp. 1970 – 1988 (2013).

[13] R.E. Powell, and H. Eyring, “Mechanisms for the relaxation theory of viscosity”, Nature,Vol. 154, No. 3909, pp. 427 – 428 (1944).

[14] H.K. Yoon, and A.J. OhaJar, “A note on the Powell Eyring fluid model”, International Communicationsin Heat Mass transfer, Vol. 14, No. 4, pp. 381 – 390 (1987).

[15] N.S. Akbar, and S. Nadeem, “Characteristics of heating scheme and mass transfer on the peristaltic flow for an Eyring–Powell fluid in an endoscope”, International Journal of Heat Mass Transfer, Vol. 55, pp. 375 – 383 (2012).

[16] T. Hayat, S.I. Shah, B. Ahmad, M. Mustafa,” Effect of slip on peristaltic flow of Powell–Eyring fluid in asymmetric channel”, Applied Bionics and Biomechanics., Vol. 11, No. 1-2, pp. 69 –79 (2014).

[17] F. Abbasi, A. Alsaedi, and T. Hayat, “Peristaltic transport of Eyring–Powell fluid in a curved channel”, Journal of Aerospace Engineering, Vol. 27, No. 6, 04014037 (2014).

[18] T. Hayat, A. Tanveer, H. Yasmin, and A. Alsaedi,” Effects of convective conditions and chemical reaction on peristaltic flow of Eyring–Powell fluid”, Applied Bionics and Biomechanics, Vol. 11, No. 4, pp. 221 – 233 (2014).

[19] N.T.M. Eldabe, M.F. El-Sayed, A.Y. Ghaly, and H.M. Sayed, “Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity”, Archive of Applied Mechanics, Vol. 78, pp. 599 – 624 (2008).

[20] S. Srinivas, and M. Kothandapani, “The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls”, Applied Mathematics and Computation, Vol. 213, No. 1, pp. 197 – 208 (2009).

[21] S. Srinivas, and M. Kothandapani, “Peristaltic transport in an asymmetric channel with heat transfer—a note”, International Communications in Heat and Mass Transfer, Vol. 35, No. 4, pp. 514 – 522 (2008).

[22] T.A. Ogulu, “Effect of heat generation on low Reynolds number fluid and mass transport in a single lymphatic blood vessel with uniform magnetic field”, International Communications in Heat and Mass Transfer , Vol. 33, No. 6, pp. 790 – 799 (2006).

[23] M. Gnaneswara Reddy, “Thermal radiation and chemical reaction effects on MHD mixed convective boundary layer slip flow in a porous medium with heat source and Ohmic heating”, Europian Physical Journal Plus, Vol. 129, No. 41, pp. 1-17 (2014) .

[24] M. Gnaneswara Reddy, “Unsteady radiative convective boundary layer flow of a casson fluid with variable thermal conductivity”, Journal of Engineering Physics and Thermophysics, Vol. 88, No. 1, pp. 240 – 251(2015).

[25] F.M. Abbasi, T. Hayat, B. Ahmad, and B. Chen, “Peristaltic flow with convective mass condition and thermal radiation”, Journal of Central South University of Technology, Vol. 22, No. 6, pp. 2369 – 2375(2015).

[26] M. Kothandapani and J. Prakash, “Effects of thermal radiation parameter and magnetic field on the peristaltic motion of Williamson nanofluids in a tapered asymmetric channel”, International Journal of Heat and Mass Transfer, Vol. 81, pp. 234 – 245(2015).

[27] M. Gnaneswara Reddy, and K. Venugopal Reddy,” Influence of Joule heating on MHD peristaltic flow of a Nanofluid with compliant walls”, Procedia Engineering Vol. 127, pp. 1002 – 1009 (2015).

[28] M. Gnaneswara Reddy and K. Venugopal Reddy, “Impact of velocity slip and joule heating on MHD peristaltic flow through a porous medium with chemical reaction”, Journal of the Nigerian Mathematical society, Vol. 35, No. 4, pp. 227-244 (2016).

[29] S. Hina, “MHD peristaltic transport of Eyring-Powell fluid with heat and mass transfer, wall properties and slip conditions”, Journal of Magnetism and Magnetic Materials, Vol. 404, pp. 148 – 158 (2016).

[30] M. Gnaneswara Reddy, K. Venugopal Reddy, and O.D. Makinde, “Hydromagnetic peristaltic motion of a reacting and radiating couple Stress fluid in an inclined asymmetric channel filled with a porous medium”, Alexandria Engineering Journal, Vol. 55, No. 2, pp. 1841 – 1853 (2016).