Influence of wall properties on the peristaltic flow of a dusty Walter’s B fluid

  • A. A. KhanEmail author
  • H. Tariq
Technical Paper


This paper explores the impact of wall properties on the Walter’s B fluid with fine solid particles in a uniform channel. Traveling sinusoidal wave is imposed on the channel walls which induces peristaltic motion in the fluid. A regular series is employed to obtain analytic solution by taking small wave number. The phenomenon is modeled in the form of stream function for both fluid and solid particles. Impact of pertinent parameters such as viscoelastic parameter \(\kappa\), wave number \(\delta\), the elastic tension, i.e., rigidity of the wall (E1), the mass characterizing parameter, i.e., stiffness of the wall (E2) and the damping nature of the wall (E3) are discussed through graphs for both fluid and dust particles. It is observed that the size of the trapped bolus increases on the right-hand side of the channel for both fluid and solid particles by increasing viscoelastic parameter. The flow rate of fluid particles increases by increasing viscoelastic parameter, while it decreases for solid particles.


Walter’s B fluid Dusty fluid Wall properties Peristaltic motion 

List of symbols


Isotropic pressure of the fluid


Fluid density


Extra stress tensor


The rate of the stress tensor

\(\frac{\delta e}{\delta t}\)

The rate of stress tensor to the material in motion


Limiting viscosity at small shear rate


Short memory coefficient


Resistance coefficient of the solid particles


Number density of the solid particles


Mass of the solid particles


Wave number


Viscoelastic parameter


Tension membrane parameter \(\left( {{\raise0.7ex\hbox{${Td^{4} }$} \!\mathord{\left/ {\vphantom {{Td^{4} } {\nu \rho }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\nu \rho }$}}} \right)\)


Mass characterizing parameter \(\left( {{\raise0.7ex\hbox{${m^{\prime}d^{2} }$} \!\mathord{\left/ {\vphantom {{m^{\prime}d^{2} } {\lambda^{3} \rho }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\lambda^{3} \rho }$}}} \right)\)


Damping parameter \(\left( {{\raise0.7ex\hbox{${cd^{3} }$} \!\mathord{\left/ {\vphantom {{cd^{3} } {\lambda^{2} \nu \rho }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\lambda^{2} \nu \rho }$}}} \right)\)


Half width of the passage




Amplitude of the wave




Velocity of the wave


Tension in the membrane


Coefficient of the viscous damping forces


Mass per unit area


Operator representing the motion of stretched membrane with damping forces


Pressure outside the wall


Non-dimensional parameter \(\left( {{\raise0.7ex\hbox{${kNd^{2} }$} \!\mathord{\left/ {\vphantom {{kNd^{2} } \mu }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\mu $}}} \right)\)


Non-dimensional parameter \(\left( {{\raise0.7ex\hbox{${kd^{2} }$} \!\mathord{\left/ {\vphantom {{kd^{2} } {m\nu }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${m\nu }$}}} \right)\)


Kinematic coefficient of viscosity of the fluid


Geometric parameter \(\left( {{\raise0.7ex\hbox{$a$} \!\mathord{\left/ {\vphantom {a d}}\right.\kern-0pt} \!\lower0.7ex\hbox{$d$}}} \right)\)


Velocity components of the fluid

\(\left( {u_{\text{s}} ,v_{\text{s}} } \right)\)

Velocity components of the dust particles


Velocity of the fluid

\(\psi ,\phi\)

Stream functions


Flow rate of the fluid


Flow rate of the solid dust particles


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan

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