Mathematical study of peristaltic propulsion of solid-liquid multiphase flow with a biorheological fluid as the base fluid in a duct

Abstract In this paper, the peristaltic transport of a MHD dusty three-dimensional biorheological (Casson) fluid in a duct is investigated. The governing flow problem is based on the continuity and momentum equations. These equations are modeled for both the fluid phase and particle phase by means of a creeping flow regime and long wavelength assumption. The exact solution has been obtained for the resulting partial differential equation by means of the eigenfunction expansion method. Graphical results are discussed against all the emerging parameters such as the Hartmann number, particle volume fraction, Casson fluid parameter etc. Numerical integration has been used to determine the pumping characteristics. Trapping phenomena are also discussed and sketched by drawing streamlines for all the physical parameters. A graphical comparison is also presented with the previously published data and it is found that the present results are in excellent agreement, which assures that the current methodology and results are correct. It is observed that the velocity profile diminishes due to a greater influence of the particle volume fraction and Hartmann number. Moreover, it is found that the Casson fluid parameter enhances the fluid velocity near the walls of the duct and opposes the flow in the middle of the duct.

[1]  Mohsen Sheikholeslami,et al.  Magnetic field influence on nanofluid thermal radiation in a cavity with tilted elliptic inner cylinder , 2017 .

[2]  S. Sreenadh,et al.  Influence of lateral walls on peristaltic flow in a rectangular duct , 2005 .

[3]  Muhammad Mubashir Bhatti,et al.  Slip effects and endoscopy analysis on blood flow of particle-fluid suspension induced by peristaltic wave , 2016 .

[4]  M. M. Bhatti,et al.  Study of variable magnetic field and endoscope on peristaltic blood flow of particle-fluid suspension through an annulus , 2016 .

[5]  Mohsen Sheikholeslami,et al.  Active method for nanofluid heat transfer enhancement by means of EHD , 2017 .

[6]  Ahmed Zeeshan,et al.  Endoscope analysis on peristaltic blood flow of Sisko fluid with Titanium magneto-nanoparticles , 2016, Comput. Biol. Medicine.

[7]  M. Awais,et al.  Theoretical analysis of upper-convected Maxwell fluid flow with Cattaneo–Christov heat flux model , 2017 .

[8]  H. A. Attia,et al.  Unsteady Couette Flow of a Thermally Conducting Viscoelastic Fluid under Constant Pressure Gradient in a Porous Medium , 2014 .

[9]  Masami Nakagawa,et al.  Steady particulate flows in a horizontal rotating cylinder , 1998 .

[10]  Mohsen Sheikholeslami,et al.  Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles , 2017 .

[11]  Rahmat Ellahi,et al.  Numerical analysis of steady non‐Newtonian flows with heat transfer analysis, MHD and nonlinear slip effects , 2012 .

[12]  S. Mekheimer,et al.  NONLINEAR PERISTALTIC TRANSPORT OF MHD FLOW THROUGH A POROUS MEDIUM , 2003 .

[13]  J. C. Misra,et al.  Peristaltic transport of a particle-fluid suspension in a cylindrical tube , 1994 .

[14]  Rahmat Ellahi,et al.  Study of Heat Transfer with Nonlinear Thermal Radiation on Sinusoidal Motion of Magnetic Solid Particles in a Dusty Fluid , 2016 .

[15]  U. K. Singh,et al.  A Two-Layered Suspension Flow Induced by Peristaltic Waves , 2008 .

[16]  K. Ramesh,et al.  Effect of heat transfer on the peristaltic transport of a MHD second grade fluid through a porous medium in an inclined asymmetric channel , 2017 .

[17]  M. M. Bhatti,et al.  Heat transfer and inclined magnetic field analysis on peristaltically induced motion of small particles , 2017 .

[18]  Sohail Nadeem,et al.  Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium , 2012 .

[19]  Tasawar Hayat,et al.  Velocity and thermal slip effects on peristaltic motion of Walters-B fluid , 2016 .

[20]  Rahmat Ellahi,et al.  Heat and mass transfer of two-phase flow with Electric double layer effects induced due to peristaltic propulsion in the presence of transverse magnetic field , 2017 .

[21]  L M Srivastava,et al.  Peristaltic transport of a particle-fluid suspension. , 1989, Journal of biomechanical engineering.

[22]  S Nadeem,et al.  Peristaltic flow of a Jeffrey fluid in a rectangular duct , 2010 .

[23]  Arshad Riaz,et al.  EFFECTS OF MAGNETOHYDRODYNAMICS ON PERISTALTIC FLOW OF JEFFREY FLUID IN A RECTANGULAR DUCT THROUGH A POROUS MEDIUM , 2014 .

[24]  Dharmendra Tripathi,et al.  Mathematical model for ciliary-induced transport in MHD flow of Cu-H 2 O nanofluids with magnetic induction , 2017 .

[25]  M. M. Bhatti,et al.  Peristaltic propulsion of particulate non-Newtonian Ree-Eyring fluid in a duct through constant magnetic field , 2017, Alexandria Engineering Journal.

[26]  Rahmat Ellahi,et al.  Study of variable magnetic field on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls , 2016 .

[27]  L M Srivastava,et al.  Peristaltic transport of blood: Casson model--II. , 1984, Journal of biomechanics.

[28]  Ahmed Zeeshan,et al.  Heat transfer analysis on peristaltically induced motion of particle-fluid suspension with variable viscosity: Clot blood model , 2016, Comput. Methods Programs Biomed..

[29]  M. M. Bhatti,et al.  Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls , 2016 .

[30]  J. Prakash,et al.  Peristaltic transport of a MHD Carreau fluid in a tapered asymmetric channel with permeable walls , 2015 .