MHD dissipative flow and heat transfer of Casson fluids due to metachronal wave propulsion of beating cilia with thermal and velocity slip effects under an oblique magnetic field

• Effects of heat transfer on MHD flow induced by cilia beating of Casson fluids are studied.
• The magnitude of velocity for Casson fluids is more as compared with Newtonian fluids.
• Pressure rise reduces with increasing the effects of magnetic field.
• Temperature field rises with increasing the thermal slip effects.
• Size of trapping boluses enhances with increasing the viscoplastic nature of fluids.

A theoretical investigation of magnetohydrodynamic (MHD) flow and heat transfer of electrically-conducting viscoplastic fluids through a channel is conducted. The robust Casson model is implemented to simulate viscoplastic behavior of fluids. The external magnetic field is oblique to the fluid flow direction. Viscous dissipation effects are included. The flow is controlled by the metachronal wave propagation generated by cilia beating on the inner walls of the channel. The mathematical formulation is based on deformation in longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The model also features velocity and thermal slip boundary conditions. Closed-form solutions to the non-dimensional boundary value problem are obtained under physiological limitations of low Reynolds number and large wavelength. The influence of key hydrodynamic and thermo-physical parameters i.e. Hartmann (magnetic) number, Casson (viscoplastic) fluid parameter, thermal slip parameter and velocity slip parameter on flow characteristics are investigated. A comparative study is also made with Newtonian fluids (corresponding to massive values of plastic viscosity). Stream lines are plotted to visualize trapping phenomenon. The computations reveal that velocity increases with increasing the magnitude of Hartmann number near the channel walls whereas in the core flow region (center of the channel) significant deceleration is observed. Temperature is elevated with greater Casson parameter, Hartmann number, velocity slip, eccentricity parameter, thermal slip and also Brinkmann (dissipation) number. Furthermore greater Casson parameter is found to elevate the quantity and size of the trapped bolus. In the pumping region, the pressure rise is reduced with greater Hartmann number, velocity slip, and wave number whereas it is enhanced with greater cilia length.