Md.S. Ansari - Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, India
O. Otegbeye - School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, South Africa
M. Trivedi - Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, India
S.P. Goqo - School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, South Africa

A study on the effects of gyrotactic microorganism and nanoparticles in the bio-convection magnetohydrodynamic flow of Casson fluid at the nonlinear stretching boundary is investigated. Irregular heat source/sink, Joule and viscous dissipations, Brownian motion, and thermophoresis are included in the energy equation. The model outlining the flow system is non-dimensionalised and retained in the same form. The equations are worked out by pairing, i.e. first pair momentum and gyrotactic micro-organism density equation and second pair energy and nanoparticle concentration equation. This technique is termed as a paired quasilinearisation method (PQLM). Convergence and accuracy of PQLM are shown. Obtained numerical results are depicted in graphs in order to observe further insight into the flow pattern. Interesting aspects of various controlling parameters in flow, heat, nanoparticle concentration and microorganism density are discussed.

Casson Nanofluid, Magnetic field, Nonlinear stretching sheet, Gyrotactic microorganism, Paired quasi-linearisation method