Numerical simulation of the peristaltic motion of a viscous fluid through a complex wavy non-uniform channel with magnetohydrodynamic effects

The applications of the fluid flow generated via the peristaltic pumping mechanism are diverse. Motivated by this fact, we bring together the classical peristaltic flow problem with the complex wavy curved channel under the magnetic effects. The flow problem is first modeled by using the curvilinear coordinate system. Galilean transformations are used to transform the problem from the fixed frame to the moving frame. Since creeping flow is generated due to the complex wave in a narrow-gapped channel, this allows us to employ a low Reynolds number (dominant viscous forces) and lubrication assumption. Furthermore, the fourth-order equation is solved numerically with the MATLAB program bvp4c. Here, we examined an informative prospective, which is useful in manufacturing the magnetic pumping devices. One may control the fluid speed, flow rate and pressure by adjusting the magnetic strength and occlusions in complex wavy walls. This study is relevant to biomedical science for micro-scale devices, magnetic therapy, chemical engineering, biological drug delivery systems, blood pumping and micro devices used during surgery.