Mixed convection flow over a solid sphere embedded in a porous medium filled by a nanofluid containing gyrotactic microorganisms

In this paper, the steady mixed convection boundary layer flow about a solid sphere with a constant surface temperature embedded in a porous medium saturated by a nanofluid containing gyrotactic microorganisms in a stream flowing vertically upwards for both cases of a heated and cooled sphere, is studied numerically. One such characteristic of nanofluid is the anomalous high thermal conductivity at very low concentration of nanoparticles and the considerable enhancement of convective heat transfer. However, without external factor introduced, instability occurs and causing the nanoparticles to aggregate and agglomerate. The microorganisms are imposed into the nanofluid to stabilize the nanoparticles to suspend due to a phenomenon called bioconvection. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme known as the Keller box method. By considering the governing and bioconvection parameters, the numerical results are obtained and discussed for the skin friction coefficient, the local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and density motile microorganisms profiles. It is found that the bioconvection parameters have strong influence towards the velocity and density of motile microorganisms transport rates.