Effects of thermal and concentration convection and induced magnetic field on peristaltic flow of Williamson nanofluid i

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Effects of thermal and concentration convection and induced magnetic field on peristaltic flow of Williamson nanofluid in inclined uniform channel Safia Akram1,a

, Qamar Afzal2

1 MCS, National University of Sciences and Technology, Islamabad, Pakistan 2 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

Received: 17 June 2020 / Accepted: 19 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract Noteworthiness of double-diffusive convection with nanofluids by induced magnetic field and diverse wave shapes for peristaltic stream of Williamson fluid in a uniform channel has been theoretically examined. Mathematical formulation of two-directional and two-dimensional flow of a Williamson fluid model is explained in detail. The exact solutions of nanoparticles are described. Perturbation solutions of nonlinear PDEs are also calculated. Numerical and graphical results are displaced to see the conduct of temperature, concentration, nanoparticle volume fraction, pressure rise, pressure gradient, magnetic force function and stream functions. It is concluded that the profile of temperature increases and profile of concentration decreases by increasing values of Brownian motion parameter Nb , thermophoresis parameter Nt , Dufour parameter N T C and Soret parameter NC T .

1 Introduction Recently, phenomenon of peristaltic has become a subject of extraordinary great importance for the analysts due to its widespread applications in medical, physiological and industrial processes. A few applications of peristalsis consist of transport of urine through kidney to bladder, transport of lymph in lymphatic vessels, bile transport in bile duct, pumping of blood in heart lung machines and transport of sanitary fluid. Peristaltic flow problem was first evolved by Latham [1]. The observable fact of peristaltic transport using long wavelength and low Reynolds number has been evaluated by Shapiro et al. [2]. Later on, due to numerous applications of peristalsis, many investigators study the concept of peristalsis with various flow geometries [3–10]. Magnetohydrodynamics deals with the cram of magnetic properties and behaviour of electrically conducting fluids. The examples of magnetofluids are plasmas, salt water, liquid metals and electrolytes. The study of magnetohydrodynamics on peristaltic flow has fascinated the attention of many researchers because of its spacious range of applications such as blood pump machines, reduction of bleeding during surgeries, designing of MHD power generators, magnetic wound or treatment of cancer tumour resulting hyperthermia and tar-

a emails: [email protected]; [email protected] (corresponding author)

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geting transport of drug utilizing magnetic particles as drug carries. A wide-ranging literature of magnetohydrodynamics on peristaltic flow is given by the studies [11–15]. The study of nanofluids on peristaltic flo

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