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

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## 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.

## Keywords

Peristaltic waves Radial magnetic field Boundary layer phenomena Hartmann number## Notes

### Acknowledgements

We are thankful to the learned reviewers for their constructive and valuable suggestions. I (Khurram Javid), dedicated this research work to my daughter Onysa Khurram (1 *year old*). A special thanks to my supervisor Dr. Nasir Ali and my co author Dr. Zeeshan Asghar for their valuable contribution.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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