Rheological and magnetic effects on a fluid flow in a curved channel with different peristaltic wave profiles

Abstract

Peristalsis is one of the most dynamic phenomena that is significantly applicable to biomedical engineering. Motivated by such fact, the current article deals with the numerical simulation of magnetically induced fluid flow bounded within two curved peristaltic walls. Fluid rheology is approximated by linearly viscoelastic Jeffrey fluid, while five different wave profiles are utilized to capture the peristaltic effects. A constant magnetic field is also applied in the radial direction. The constitutive equations in curvilinear coordinates are reduced under the lubrication theory. The reduced boundary value problem is further solved by MATLAB built-in routine BVP6C. The axial velocity, pressure rise and stream function are numerically obtained in the wave frame. The impacts of different peristaltic wave profiles and several embedded parameters, for example, the dimensionless radius of curvature, magnetic parameter (Hartmann number) and viscoelastic parameter, respectively, on the flow characteristics are shown through graphs and discussed in detail. Boundary layer phenomena are also highlighted for large values of the Hartmann number and the ratio of relaxation to retardation time parameter for different peristaltic waves. A special case of the straight channel is also retrieved from a large curvature parameter. This study provides fruitful information to understand the flow phenomena of blood, foods, nutrients and liquids that pass through non-uniform veins or arteries.