Mathematical modeling of bio-magnetic fluid bounded by ciliated walls of wavy channel incorporated with viscous dissipation: Discarding mucus from lungs and blood streams

Abstract Heat and mass transfer of non-Newtonian fluid is investigated in this article. Couples stress fluid has been treated as physiological fluid. The two-dimensional non-Newtonian flow is caused due to metachronal wave induced by the coincident oscillation of a tiny hair-like structure known as “Cilia” attached to opposite walls of the channel. A uniform magnetic field is also applied in the transverse direction, keeping the susceptibility of tiny size particles in view. A closed-form solution is obtained for the set of nonlinear differential equations, with the help of convective boundary conditions. The obtained results are also validated through graphs and tables, which reveal that a strong magnetic field badly effects the velocity of base fluid while it expedites as the length of tiny hair is prolonged. More energy is added to the system due to the Brinkman number, and the temperature profile depletes the Biot number. Finally, the Hartmann number allows the boluses to increase and expand in size, which acts as a resistive force across the channel.