Insight in Thermally Radiative Cilia-Driven Flow of Electrically Conducting Non-Newtonian Jeffrey Fluid under the Influence of Induced Magnetic Field

Abstract

This paper investigates the mobility of cilia in a non-uniform tapered channel in the presence of an induced magnetic field and heat transfer. Thermal radiation effects are included in the heat transfer analysis. The Jeffrey model is a simpler linear model that uses time derivatives rather than convected derivatives as the Oldroyd-B model does; it depicts rheology other than Newtonian. The Jeffrey fluid model is used to investigate the rheology of a fluid with cilia motion. The proposed model examines the behavior of physiological fluids passing through non-uniform channels, which is responsible for symmetrical wave propagation and is commonly perceived between the contraction and expansion of concentric muscles. To formulate the mathematical modeling, the lubrication approach is used for momentum, energy, and magnetic field equations. The formulated linear but coupled differential equations have been solved analytically. Graphs for velocity profile, magnetic force function, induced magnetic field, current density, pressure rise, and heat profile are presented to describe the physical mechanisms of significant parameters. It is found that the eccentricity parameter of the cilia equations opposes the velocity and the magnetic force functions. The thermal radiation decreases the temperature profile while it increases for Prandtl and Eckert numbers. A promising impact of the magnetic Reynolds number and electric field on the current density profile is also observed.

Keywords

• heat transfer
• induced magnetic field
• cilia motion
• non-uniform tapered channel
• non-Newtonian fluid
• exact solutions