Adomian decomposition solution for propulsion of dissipative magnetic Jeffrey biofluid in a ciliated channel containing a porous medium with forced convection heat transfer

Physiological transport phenomena often feature ciliated internal walls. Heat, momentum and multi-species mass transfer may arise and additionally non-Newtonian biofluid characteristics are common in smaller vessels. Blood (containing hemoglobin) or other physiological fluids containing ionic constituents in the human body respond to magnetic body forces when subjected to external (extra-corporeal) magnetic fields. Inspired by such applications, in the present work we consider the forced convective flow of an electrically-conducting viscoelastic physiological fluid through a ciliated channel under the action of a transverse magnetic field. The flow is generated by a metachronal wave formed by the tips of cilia which move to and fro in a synchronized fashion. The presence of deposits (fats, cholesterol etc) in the channel is mimicked with a Darcy porous medium drag force model. The two-dimensional unsteady momentum equation and energy equation are simplified with a stream function and small Reynolds' number approximation. The effect of energy loss is simulated via the inclusion of viscous dissipation in the energy conservation (heat) equation. The non-dimensional, transformed moving boundary value problem is solved with appropriate wall conditions via the semi-numerical Adomian decomposition method (ADM). The velocity, temperature and pressure distribution are computed in the form of infinite series constructed by ADM and numerically evaluated in a symbolic software (MATHEMATICA). Streamline distributions are also presented. The influence of Hartmann number (magnetic parameter), Jeffrey first and second viscoelastic parameters, permeability parameter (modified Darcy number), and Brinkman number (viscous heating parameter) on velocity, temperature, pressure gradient and bolus dynamics is visualized graphically. The flow is decelerated with increasing with increasing Hartmann number and Jeffery first parameter in the core flow whereas it is accelerated in the vicinity of the walls. Increasing permeability and Jeffery second parameter are observed to accelerate the core flow and decelerate the peripheral flow near the ciliated walls. Increasing Hartmann number elevates pressure gradient whereas it is reduced with permeability parameter. Temperatures are elevated with increasing magnetic parameter, Brinkman number and Jeffery second parameter. Increasing magnetic field is also observed to reduce the quantity of trapped boluses. Increasing permeability parameter suppresses streamline amplitudes. Both the magnitude and quantity of trapped boluses is elevated with an increase in both first and second Jeffery parameters.