BDF‐Based Numerical Simulations Using ode15s Solver for Mucus Behavior Within an Amplitude‐Modulated Passage

This study explores a backward differentiation formula (BDF)‐based numerical approach using MATLAB's ode15s solver to simulate mucus flow through a gradually widening channel with amplitude‐modulated (AM) wavy walls. The wall motion is constructed using a modulated wave (the product of two cosine functions) to mimic the metachronal beating of cilia. The Johnson–Segalman (J–S) model describes the viscoelastic fluid behavior under wall slip and an inclined magnetic field. Results show how the Weissenberg number, viscosity ratio, magnetic force at a certain angle, and slip coefficients affect velocity profiles, streamlines, pressure distribution, and skin friction coefficient. The beat wave pattern significantly alters the flow structure compared to simple waves. These findings provide insights into mucus transport in physiological systems.