A transport of Jeffrey model viscoelastic fluid by complex peristalsis motion of nonuniform curved channel's walls under resistance of magnetic field

The main aim of the present investigation is that the viscoelastic fluids, such as blood, can easily be manipulated due to their magnetic features with an electromagnetic field. These peristaltic pumps are new inventions in bio-engineering domains that provide more sustainable and sophisticated efficiencies as compared with unadventurous surgical pumps. Inspire by such uses, in the present study, a mathematical investigation into the peristaltic motion of viscoelastic fluid under the magnetic influence on a complex and curved nonuniform channel is considered. For the viscoelastic fluid, the Jeffrey model is used. The rheological equations are mathematically expressed in curvilinear coordinates and simplify by using the transformations. The transformed rheological equations are solved numerically by using the BVP4C method. The consequences of numerous flow feature such as axial velocity, pumping and trapping phenomena under the magnetic, radius of curvature, and viscoelastic parameters are calculated and displayed in graphical form for discussion. Additionally, an association with the curve and straight channels is deliberated with the help of graphs for both simple and complex peristaltic scenarios in MATLAB Software. The magnitude of pumping phenomena is enhanced by increasing magnetic parameter. The curved peristaltic pump has a larger magnitude of peristaltic pumping as compared with the straight peristaltic pump. The efficiency of complex pumps in the rheology of a viscoelastic fluid is much better than the simple peristaltic channel under both curvature and magnetic effects.