Magnetic field and viscous dissipation effect on bioconvection in a permeable sphere embedded in a porous medium with a nanofluid containing gyrotactic micro-organisms

Micro-organisms play a vital role to understand the ecological system and therefore it is very important to understand the behavior of micro-organism due to different parameters. In the present paper, we investigated the bioconvection about a permeable sphere with constant surface temperature embedded in a porous medium filled with a water-based nanofluid containing gyrotactic micro-organisms. The convection and movement of the micro-organisms are constrained or assisted by thermophoresis, viscous dissipation effects, and an applied magnetic field. First, we have used the similarity transformation to simplify the governing equations. Then, we have solved the governing nonlinear partial differential equations numerically using a recent spectral relaxation method. The effects of the significant parameters on the local density of the gyrotactic micro-organisms have been determined and discussed. It is observed that by introducing the magnetic field in the system, the skin friction, local nanoparticle Sherwood number, and the local density of the micro-organism decrease, while the last two governing parameters show a positive response with increase in the viscous dissipation.