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An investigation is made for a three-dimensional unsteady mixed nano-bioconvection flow between two contracting or expanding rotating discs. The passively controlled nanofluid model in which Brownian diffusion and thermophoresis are considered as the two dominant factors for nanoparticle/base-fluid slip mechanisms is introduced for description of this flow problem. A novel similarity transformation is introduced so that the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticle volume fraction, and microorganisms are reduced to a set of five fully coupled ordinary differential equations. Exact solutions are then obtained analytically for this complex nonlinear system. Besides, the influences of various physical parameters on distributions of velocity, temperature, nanoparticle volume fraction, and the density of motile microorganisms, along with the local Nusselt number and the local wall motile microorganisms flux, are presented and discussed. It is expected that this study can provide a theoretical base for understanding the transport mechanisms of unsteady bioconvection in nanofluids. [ABSTRACT FROM AUTHOR]