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

Abstract

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 (centre 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.

Differential transform solution for Hall and ion‐slip effects on radiative‐convective Casson flow from a stretching sheet with convective heating

“…The rheological equation of state for an isotropic and incompressible Casson (viscoplastic) fluid is:…”

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

“…Here A x ( ) 11 , A x ( ) 12 ···B x ( ) 12 are given in the Appendix. The pressure gradient ∂ ∂ p x dp dx ( / , ie, / ) by using Equation (44) and Equation (44) in Equation (17)…”

“…Interesting studies in this regard include Siddiqui et al (who used the Ostwald‐de Waele power law model), Maqbool et al (who considered the fractional Burgers model for ciliated propulsion in a tilted vessel) and Siddiqui et al (who simulated the epididymal fluid through the ductus efferentes of the male reproductive track by considering the viscous fluid model and Carreau fluid model, respectively, in metachronal wave of cilia motion in an asymmetric tube). Akbar et al studied the hydromagnetic viscoplastic metachronal propulsion with multiple slip effects. Shaheen and Nadeem investigated viscoelastic Jeffrey six‐constant nanofluid ciliated flow in an annular conduit.…”

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

“…Vasu et al 7 implemented homotopy and generalized differential quadrature methods to simulate the impact of Casson viscoplasticity and bioconvection microorganism mass transfer in hydromagnetic rheological nanofluid flow from an extending sheet. Akbar et al 8 studied electromagnetic propulsion of Casson liquids in ciliated tubes with power series methods.…”