Inspired by the prevalence of non-Newtonian liquids in biological flows, our aim in this article is to elaborate on the flow of Carreau-Yasuda fluid generated by wavy cilia inside the micro-channel. The impact of complex wave and magnetic field (magnetohydrodynamics) are also taken into account. The low Reynolds number and large wavelength approximation are employed to simplify the problem. The finite-difference approach (finite-difference method) is utilized to get the convergent solution to the problem in MATLAB (2022b). The impact of emerging parameters on the axial velocity and streamlines is examined through various graphs. Moreover, a comparison among the Carreau-Yasuda fluid, Carreau fluid, and Newtonian fluid is also expounded.
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