Metachronal propulsion of a magnetised particle-fluid suspension in a ciliated channel with heat and mass transfer

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Biologically-inspired pumping systems are of great interest in modern engineering since they achieve enhanced efficiency and circumvent the need for moving parts and maintenance. Industrial applications also often feature two-phase flows. In this article, motivated by these applications, the pumping of an electrically-conducting particle-fluid suspension due to metachronal wave propulsion of beating cilia in a two-dimensional channel with heat and mass transfer under a transverse magnetic field is investigated theoretically. The governing equations for mass and momentum conservation for fluid- and particle-phases are formulated by ignoring the inertial forces and invoking the long wavelength approximation. The Jeffrey viscoelastic model is employed to simulate non-Newtonian characteristics. The normalised resulting differential equations are solved analytically. Symbolic software is employed to evaluate the results and simulate the influence of different parameters on flow characteristics. Results are visualised graphically with carefully selected and viable data. With increasing wave number (β) fluid velocity is accelerated in the core region whereas it is decelerated near the channel wall, for the Newtonian case. With increasing eccentricity of cilia elliptic path (α), a similar response is computed as for the wave number. The size of the bolus is enhanced (and quantity of boluses is reduced) with increasing eccentricity of the cilia elliptic path (α) and Hartmann (magnetic) number (M) whereas bolus size is decreased (and quantity of boluses is increased) with increasing wave number (β) and particle volume fraction (C). It is also noted that increasing Schmidt number (Sc) and Soret number (Sr) diminish the concentration magnitudes. Furthermore, Brinkman number (which represents viscous heating effects) significantly boosts the temperature magnitudes. The current analysis provides a useful benchmark for more general computational simulations.