Mathematical modeling of <scp>bio‐magnetic</scp> fluid bounded within ciliated walls of wavy channel

Abstract Peristaltic transport of couple stress fluid with heat transfer is investigated through flexible walls of the channel furnished with hair‐like structures. Locomotion of biological fluid is the result of the simultaneous propagation of metachronal waves (MCWs) and peristaltic waves. MCW emerges due to multi‐movement of cilia, while the elastic‐walls of the channel are responsible for the peristaltic wave. The two‐dimensional rheological flow experiences the resistive behavior of applied magnetic fields, besides, the role of viscous dissipation and entropy generation. A closed‐form solution is achieved for the nonlinear coupled differential equation, which is vetted through graphs. Finally, the theoretical analysis introduces the manufacture of a ciliate bronchial tube that can efficiently; remove mucus out of the lungs and bloodstream.

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