Abstract
The Soret and Dufour effects on the peristaltic transport of a conducting Casson nanofluid in a flexible channel are studied. The influence of dissipation and Joule heating are also discussed. The governing equations are simplified by using a long wave length and small Reynolds number approximations. The analytical solutions for stream function and axial velocity are obtained. Moreover, the Runge–Kutte-based shooting method is utilized to solve the coupled energy and concentration equations. The impact of important parameters on the flow is explained using graphs for both Newtonian and Casson fluid cases. It is observed that the Casson fluid has more velocity than the Newtonian fluid in the middle of the channel and the situation is reversed at the channel walls. Further, a higher temperature is noted for Casson fluid than for Newtonian fluid throughout the channel, whereas concentration shows the opposite behavior.
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Latham, T.W.: Fluid motions in a peristaltic pump. M.S. Thesis, Massachusetts Institute of Technology, Cambridge (1966)
Fung, Y.C., Yih, C.S.: Peristaltic transport. Trans. ASME, J. Appl. Mech. 35, 669–675 (1968)
Shapiro, A.H., Jaffrin, M.Y., Weinberg, S.L.: Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech. 37 (4), 799–825 (1969)
Usha, S., Ramachandra Rao, A.: Peristaltic transport of two-layered power-law fluids. J. Biomech. Eng. 119, 483–488 (1997)
Srinivas, S., Kothandapani, M.: The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls. Appl. Math. Comput. 213, 197–208 (2009)
Lakshminarayana, P., Sreenadh, S., Sucharitha, G., Nandagopal, K.: Effect of slip and heat transfer on peristaltic transport of a Jeffrey fluid in a vertical asymmetric porous channel. Adv. Appl. Sci. Res. 6 (2), 107–118 (2015)
Vajravelu, K., Sreenadh, S., Lakshminarayana, P., Sucharitha, G., Rashidi, M. M.: Peristaltic flow of Phan-Thien-Tanner fluid in an asymmetric channel with porous medium. J. Appl. Fluid Mech. 9 (4), 1615–1625 (2016)
Vajravelu, K., Sreenadh, S., Lakshminarayana, P., Sucharitha, G.: The effect of heat transfer on the nonlinear peristaltic transport of a Jeffrey fluid through a finite vertical porous channel. Int. J. Biomath. 9 (2) 1650023 (25 pages) (2016)
Vajravelu, K., Sreenadh, S., Dhananjaya, S., Lakshminarayana, P.: Peristaltic flow and heat transfer of a conducting Phan-Thien-Tanner fluid in an asymmetric channel - application to chyme movement in small intestine. Int. J. of Appl. Mech. Eng. 21 (3), 713–736 (2016)
Akbar, N. S.: Influence of magnetic field on peristaltic flow of a Casson fluid in an asymmetric channel: Application in crude oil refinement. J. Magn. Magn. Mater. 378, 463–468 (2015)
Nadeem, S., Ul Haq, R., Akbar, N. S., Khan, Z. H.: MHD three dimensional flow of Casson fluid past a porous linearly stretching sheet. Alex. Eng. J. 52, 577–582 (2013)
Raju, C. S. K., Sandeep, N., Saleem, S.: Effects of induced magnetic field and homogeneous-heterogeneous reactions on stagnation flow of a Casson fluid. Eng. Sci. Technol. Int. J. 19 (2), 875–887 (2016)
Hayat, T. Ali Bhatti, Z., Ahmad, B., Alsadi, A.: Effects of variable viscosity and inclined magnetic field on peristaltic motion of fourth-grade fluid with heat transfer. Heat Trans. Res. 47 (5), 489–503 (2016)
Saleem, S., Awais, M., Nadeem, S., Sandeep, N., Mustafa, M. T.: Theoretical analysis of upper-convected Maxwell fluid flow with Cattaneo-Christov heat flux model. Chin. J. Phys. (2017) doi:org/10.1016/j.cjph.2017.04.005
Satyanarayana, K.V.V., Sreenadh, S., Sucharitha, G., Lakshminarayana, P.: The effect of wall properties on the convective peristaltic transport of a conducting Bingham fluid through porous medium. Ind. J. Sci. Tech. 9 (42), 1–9 (2016)
Sucharitha, G., Lakshminarayana, P., Sandeep, N.: Joule heating and wall flexibility effects on the peristaltic flow of magnetohydrodynamic nanofluid. Int. J. Mech. Sci. 131–132, 52–62 (2017)
Lakshminarayansa, P., Sreenadh, S., Sucharitha, G.: The influence of slip, wall properties on the peristaltic transport of a conducting Bingham fluid with heat transfer. Proc. Eng. 127, 1087–1094 (2015)
Sucharitha, G., Lakshminarayana, P., Sandeep, N.: Dual solutions of cross diffusion effects on MHD Peristaltic flow in a conduit. IOP Conference series, Material Science and Engineering 263, 062026 (2017)
Hayat, T., Abbasi, F. M., Maryem, A., Monaquel, S.: Slip and Joule heating effects in mixed convection peristaltic transport of nanofluid with Soret and Dufour effects. J. Mol. Liq. 194, 93–99 (2014)
Mehmood, R., Nadeem, S., Saleem, S., Akbar, N. S.: Flow and heat transfer analysis of a Jeffery nano fluid impinging obliquely over a stretched plate. J. Taiwan Inst. Chem. Eng. 74, 49–58 (2017)
Nadeem, S., Khan, S., A. U., Saleem, S.: A comparative analysis on different nanofluid models for the oscillatory stagnation point flow. Eur. Phys. J. Plus 131, 261 (2016)
Nadeem, S., Ahmed, Z., Saleem, S.: The effect of variable viscosities on micro-polar flow of two nanofluid. Z. Naturforsch A 71 (12), 1121–1129 (2016)
Lakshminarayana, P., Vajravelu, K., Sucharitha, G., Sreenadh, S.: Peristaltic slip flow of a Bingham fluid in an inclined porous conduit with Joule heating. Appl. Math. Nonlinear Sci. 3 (1), 41–54 (2018)
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Sucharitha, G., Lakshminarayana, P., Sandeep, N. (2019). MHD and Cross Diffusion Effects on Peristaltic Flow of a Casson Nanofluid in a Duct. In: Rushi Kumar, B., Sivaraj, R., Prasad, B., Nalliah, M., Reddy, A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01123-9_20
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DOI: https://doi.org/10.1007/978-3-030-01123-9_20
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