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This paper focuses on analytical and numerical investigation of double-diffusive bioconvection in a porous media saturated by nanofluid using the modified mass flux condition. Normal mode technique is employed to solve the governing equations of the Brinkman-Darcy model. The Galerkin weighted residual method (singleterm and six-term) is used to obtain numerical solution of the mathematical model. It is found that due to the presence of gyrotactic microorganisms, Rayleigh number is decreased substantially which shows that convection sets in earlier as compared to nanofluid without microorganisms and this destabilizing effect is more predominant for faster swimming microorganisms. modified Darcy number number, Soret parameter, and porosity postpone the onset of the bioconvection, whereas nanoparticle Rayleigh number, bioconvection Rayleigh number, nanoparticle Lewis number, Dufour parameter, Péclet number, and Lewis number pre-pone the onset of bioconvection under certain conditions.

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The effect of vertical throughflow on the onset of bio-thermal convection in a water-based nanofluid containing gyrotactic microorganisms is investigated using more realistic boundary conditions. The Galerkin weighted residual method is used to obtain numerical solutions of the mathematical model. The effects of bioconvection Rayleigh number, gyrotaxis number, bioconvection Péclet number, Lewis number, Péclet number, particle density increment number, modified diffusitivity ratio, and nanoparticle Rayleigh number on thermal Rayleigh number are examined.The combined effect of Brownian motion and thermophoresis of nanoparticles, vertical throughflow, and gyrotactic microorganisms on the thermal Rayleigh number is found to be destabilizing and its value is decreased by first to third orders of magnitude as compared to regular fluids. Critical wave number is dependent on bioconvection parameters, nanofluid parameters as well as throughflow parameter. The results obtained using passive boundary conditions are compared with those of active boundary conditions. The present study may find applications in seawater convection at the ocean crust.