Analysis of thermal radiation in magneto-hydrodynamic motile gyrotactic micro-organisms flow comprising tiny nanoparticle towards a nonlinear surface with velocity slip

This study investigates 2D bioconvection magneto-hydrodynamic (MHD) flow and heat transfer of the non-Newtonian (Casson) nanofluid model. The phenomenon of Brownian motion and thermophoresis containing gyrotactic microorganisms over a nonlinear surface is demonstrated pictorially under the simultaneous impact of thermal radiation and velocity slip. Herein, the flow is electrically conducting where different cases and the effect of convergence parameters such as chemical reactions and heat generation/absorption are studied. The transformed ODEs are tackled numerically by employing the Bvp4c scheme. This method contains three-stage Lobatto IIIa collocation formula that provides continuous solutions up to fifth-order accuracy. The salient features of relevant flow parameters are illustrated through tables and graphs, and the current results are compared with the previous ones, which claim considerable agreement. The main finding reveals an increase in the thermophoresis parameter (Nt) and radiation (R) parameters, uprising the temperature profile which leads to enhancement in the thermal boundary layer. Also, the impact of the magnetic parameter (M) shows decrement in the velocity profile because there exists a Lorentz force that suppresses fluid motion. The friction factor and local Nusselt number decrease for higher values of the Casson parameter (β), whereas increment is illustrated for the suction parameter (S).