Purpose The purpose of this paper is to investigate the bioconvection flow in a porous square cavity saturated with both oxytactic microorganism and nanofluids. Design/methodology/approach The impacts of the effective parameters such as Rayleigh number, bioconvection number, Peclet number and thermophoretic force, Brownan motion and Lewis number reduces the flow strength in the cavity on the flow strength, oxygen density distribution, motile isoconcentrations and heat transfer performance are investigated using a finite volume approach. Findings The results obtained showed that the average Nusselt number is increased with Peclet number, Lewis number, Brownian motion and thermophoretic force. Also, the average Sherwood number increased with Brownian motion and Peclet number and decreased with thermophoretic force. It is concluded that the flow strength is pronounced with Rayleigh number, bioconvection number, Peclet number and thermophoretic force. Brownan motion and Lewis number reduce the flow strength in the cavity. Originality/value There is no published study in the literature about sensitivity analysis of Brownian motion and thermophoresis force effects on the bioconvection heat transfer in a square cavity filled by both nanofluid and oxytactic microorganisms.

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The present paper investigates the incompressible, laminar, natural convection flow in a porous square cavity filled with a nanofluid in the presence of magnetic field and viscous dissipation. The nanofluid mathematical model proposed by Buongiorno is considered. The left wall of the enclosure is heated, while the right wall is cooled and the bottom and upper walls are adiabatic. The analysis is formulated in terms of vorticity stream function procedure. The governing equations, which are continuity, momentum, and energy equations, are solved by finite element method based on Galerkin weighted residual approach. The relevant parameters considered for computations are magnetic field, Rayleigh number, thermophoresis, Brownian motion, buoyancy ratio, Lewis number, and Eckert number. The numerical results in terms of streamlines, isotherms, isoconcentrations, the average and local skin friction coefficient and Nusselt numbers are reported for various values of Nt, Nb, Ra, Le, M, and Ec. It is found that the magnetic field, Brownian motion, thermophoretic force, and viscous dissipation show significant effect on the velocity, temperature, and concentration distributions in the cavity.