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The onset of bioconvection contains both nanoparticles and gyrotactic microorganisms confined within a Hele-Shaw cell is investigated by incorporating the effects of Brownian diffusion and thermophoresis by using the zero flux nanoparticle boundary conditions. The linear analysis is based on the normal mode technique and the resulting equations are solved numerically by the higher order Galerkin weighted Residual method. The critical Hele-Shaw Rayleigh number is presented in terms of bioconvection parameters, nanofluid parameters, and Hele-Shaw parameters. It is found that the highly promoted disturbance in the presence of gyrotactic microorganisms enhances heat transfer in nanofluids. Gyrotactic microorganisms enhance the bioconvection and this effect is larger if both the concentration and average speed of microorganisms have larger values. Wavenumber is the function of Hele-Shaw Rayleigh number, bioconvection Péclet number and Gyrotaxis number. A comparison is also made between the different bioconvection Péclet number and bioconvection Hele-Shaw number. The present study may found applications in bio-convection nanotechnological devices.
nanofluid, Hele-Shaw cell, thermophoresis, Brownian motion, bioconvection, gyrotactic microorganism
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