Nanofluid bio-thermal convection: simultaneous effects of gyrotactic and oxytactic micro-organisms

This paper investigates the onset of nanofluid bio-thermal convection in a horizontal layer of finite depth for the case when the suspension contains two species of motile micro-organisms exhibiting different taxes, gyrotactic and oxytactic micro-organisms. The obtained instability problem is controlled by four agencies, namely by distributions of nanoparticles, gyrotactic and oxytactic micro-organisms and by the vertical temperature variation. The utilization of the linear instability theory makes it possible to decouple the effects of these agencies and obtain an eigenvalue equation that involves four Rayleigh numbers: the nanoparticle Rayleigh number, the bioconvection gyrotactic and oxytactic Rayleigh numbers, and the traditional thermal Rayleigh number. Each Rayleigh number represents the effect of one of the four aforementioned agencies. Previously obtained results are recovered for limiting cases. The effects of different agencies on the boundary of marginal non-oscillatory instability are investigated.