Numerical Simulations of Bio-Convection in the Stream-Wise and Cross-Flow Directions Comprising Nanofluid Conveying Motile Microorganism: Analysis of Multiple Solutions

Abstract

This work tackles the phenomenon of motile microorganisms and nanoliquid flow in the esteem of cross-flow (CF) and stream-wise (SW) direction. The analysis exposed to viscous dissipation, Brownian motion, thermal radiation, magnetic function, and thermophoresis impacts is encountered. The mathematical model consists of the partial differential equations (PDEs) switched into nonlinear ordinary differential equations (ODEs) through proper transformations of new variables. The multiple outcomes of the flow problem are achieved through the Lobatto IIIA formula. The features of controlling constraints are sketched for the motile organism, temperature, velocities (CF and SW), and concentration fields. Also, the Sherwood and the Nusselt numbers along with motile density and friction factor are sketched. One imperative numerical outcome of this research is the existence of dual numerical solutions for the nanofluid flow. The upshots indicate that the profiles of microorganisms decelerate due to bio-convection Schmidt and Péclet numbers. The magnetic function decelerates the velocity in the directions of SW and CF in the branch of the first solution and upsurges in the branch of the second solution. The concentration profile uplifts due to [Formula: see text] in both solutions while the opposite behavior is observed for different values of [Formula: see text] in both solutions. The temperature uplifts due to magnetic and radiation effects in both solutions.