### Entropy Generation for Peristaltic Blood Flow with Casson Model and Consideration of Magnetohydrodynamics Effects

#### Abstract

In this article, entropy generation on peristaltic blood flow of the Casson fluid model is investigated under the influence of magnetohydrodynamics. The present mathematical analysis consists of continuity equations, momentum, and energy equations, which are simplified using the approximation of long wavelength and creeping flow regime. The reduced coupled differential equations are solved analytically, and a closed form of solution is presented. The impact of all the physical parameters of interest, such as the Brinkmann number, Hartmann number, and Casson fluid parameter, are taken into account. Trapping phenomena is also discussed with the help of contours. It is observed that the Casson fluid parameter and magnetic parameter show similar effects on velocity. Further, it is also observed that entropy profile behaves as an increasing function for all the pertinent parameters.

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N Casson. A Flow Equation for Pigment-Oil Suspensions of the Printing Ink Type. Pergamon Press, Oxford 1959, p. 84-104.

JC Misra and SK Pandey. Peristaltic transport of blood in small vessels: Study of a mathematical model. Comput. Math. Appl. 2002; 43, 1183-93.

S Akram and S Nadeem. Analytical analysis of peristaltic flow of a 6 constant Jeffreys model of fluid in an inclined planar channel. Walailak J. Sci. & Tech. 2014; 11, 129-48.

S Nadeem, RU Haq, NS Akbar and ZH Khan. MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. Alexandria Eng. J. 2013; 52, 577-82.

S Pramanik. Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation. Ain Shams Eng. J. 2014; 5, 205-12.

NS Akbar. Influence of magnetic field on peristaltic flow of a Casson fluid in an asymmetric channel: Application in crude oil refinement. J. Magn. Magn. Mater. 2015; 378, 463-8.

M Sheikh and Z Abbas. Homogeneous-heterogeneous reactions in stagnation point flow of Casson fluid due to a stretching/shrinking sheet with uniform suction and slip effects. Ain Shams Eng. J. 2017, DOI: 10.1016/j.asej.2015.09.010.

KS Mekheimer. Peristaltic flow of blood under effect of a magnetic field in a non-uniform channels. Appl. Math. Comput. 2004; 153, 763-77.

KS Mekheimer and MAE Kot. The micropolar fluid model for blood flow through a tapered artery with a stenosis. Acta Mech. Sinica 2008; 24, 637-44.

KS Mekheimer and MAE Kot. Suspension model for blood flow through arterial catheterization. Chem. Eng. Commun. 2010; 197, 1195-214.

KS Mekheimer, MH Haroun and MAE Kot. Influence of heat and chemical reactions on blood flow through an anisotropically tapered elastic arteries with overlapping stenosis. Appl. Math. 2012; 6, 281-92.

SK Pandey and D Tripathi. Peristaltic transport of a Casson fluid in a finite channel: Application to flows of concentrated fluids in oesophagus. Int. J. Biomath. 2010; 3, 453-72.

D Pinho, RO Rodrigues, V Faustino, T Yaginuma, J Exposto and R Lima. Red blood cells radial dispersion in blood flowing through microchannels: The role of temperature. J. Biomech. 2015; 49, 2293-8.

TW Latham. Fluid Motions in a Peristaltic Pump. Ph.D. Dissertation, Massachusetts Institute of Technology, USA, 1966.

EO Carew and TJ Pedley. An active membrane model for peristaltic pumping: Part I-Periodic activation waves in an infinite tube. J. Biomech. Eng. 1997; 119, 66-76.

R Ellahi, MM Bhatti and K Vafai. Effects of heat and mass transfer on peristaltic flow in a non-uniform rectangular duct. Int. J. Heat Mass Trans. 2014; 71, 706-19.

R Ellahi, MM Bhatti, C Fetecau and K Vafai. Peristaltic flow of couple stress fluid in a non-uniform rectangular duct having compliant walls. Commun. Theor. Phys. 2016; 65, 66-72.

S Nadeem and S Akram. Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun. Nonlinear Sci. 2010; 15, 1705-16.

MA Abbas, YQ Bai, MM Rashidi and MM Bhatti. Application of drug delivery in Magnetohydrodynamics peristaltic blood flow of nanofluid in a non-uniform channel. J. Mech. Med. Biol. 2016; 16, 1650052.

A Sinha, GC Shit and NK Ranjit. Peristaltic transport of MHD flow and heat transfer in an asymmetric channel: Effects of variable viscosity, velocity-slip and temperature jump. Alexandria Eng. J. 2015; 54, 691-704.

A Ebaid. A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method. Phys. Lett. A 2008; 372, 5321-8.

S Ibsen, A Sonnenberg, C Schutt, R Mukthavaram, Y Yeh, I Ortac and MJ Heller. Recovery of drug delivery nanoparticles from human plasma using an electrokinetic platform technology. Small 2015; 11, 5088-96.

MM Bhatti, MA Abbas and MM Rashidi. Combine effects of Magnetohydrodynamics (MHD) and partial slip on peristaltic blood flow of Ree-Eyring fluid with wall properties. Eng. Sci. Tech. Int. J. 2016; 19, 1497-502.

MM Rashidi, MM Bhatti, MA Abbas and MES Ali. Entropy generation on MHD blood flow of nanofluid due to peristaltic waves. Entropy 2016; 18, 117.

MM Bhatti, R Ellahi and A Zeeshan. Study of variable magnetic field on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls. J. Mol. Liq. 2016; 222, 101-8.

MA Abbas, YQ Bai, MM Bhatti and MM Rashidi. Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls. Alexandria Eng. J. 2016, 55, 653-62.

S Akram, S Nadeem and A Hussain. Partial slip consequences on peristaltic transport of Williamson fluid in an asymmetric channel. Walailak J. Sci. & Tech. 2015; 12, 885-908.

NS Akbar, M Raza and R Ellahi. Peristaltic flow with thermal conductivity of H2O+ Cu nanofluid and entropy generation. Results Phys. 2015; 5, 115-24.

NS Akbar. Entropy generation analysis for a CNT suspension nanofluid in plumb ducts with peristalsis. Entropy 2015; 17, 1411-24.

MM Rashidi, S Bagheri, E Momoniat and N Freidoonimehr. Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Eng. J. 2017, 8, 77-85.

MM Rashidi, S Abelman and NF Mehr. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int. J. Heat Mass Trans. 2013; 62, 515-25.

OA Bég, MM Rashidi, N Kavyani and MN Islam. Entropy generation in hydromagnetic convective Von-Kármán swirling flow: Homotopy analysis. Int. J. Appl. Math. Mech. 2013; 9, 37-65.

MM Rashidi, L Shamekhi and S Kumar. Parametric analysis of entropy generation in off-centered stagnation flow towards a rotating disc. Nonlinear Eng. 2014; 3, 27-41.

R Ellahi, M Hassan, A Zeeshan and AA Khan. The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection. Appl. Nanosci. 2016; 6, 641-51

S Nadeem, A Riaz, R Ellahi, NS Akbar and A Zeeshan. Heat and mass transfer analysis of peristaltic flow of nanofluid in a vertical rectangular duct by using the optimized series solution and genetic algorithm. J. Comput. Theor. Nanosci. 2014; 11, 1133-49.

A Riaz, S Nadeem, R Ellahi and A Zeeshan. Exact solution for peristaltic flow of Jeffrey fluid model in a three dimensional rectangular duct having slip at the walls. Appl. Bio. Biomech. 2014; 11, 81-90.

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