Influence of heat transfer on MHD Carreau fluid flow due to motile cilia in a channel

Mucus transport mediated by motile cilia in the airway is an important defense mechanism for prevention of respiratory infections. Cilia motility can be affected by temperature difference and magnetic field. In this research, we investigate the combined effects of magnetic field and buoyancy force due to temperature difference. In the present study, mixed convective flow of a Carreau fluid model through a ciliated channel is modeled and analyzed by a symplectic metachoronal wave. The momentum and energy equations for the Carreau fluid are modeled and simplified by the stream function and small Reynold's number approximation. The influence of magnetic parameter, Carreau fluid parameter, Brinkmann number and Weissenberg number on velocity, temperature and pressure gradient are presented via graphs. It is observed that Hartmann number helps to decelerate the flow, whereas Weissenberg number, Grashof number and Carreau fluid parameter are responsible for the accelerated flow. The heat transfer rate rises by increasing the values of Hartmann number, Weissenberg number, Carreau fluid parameter and Brinkmann number.