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.

Purpose This study aims to carry out an analysis for flow and heat transfer of a new hybrid nanofluid over a vertical flat surface embedded in a saturated porous medium with anisotropic permeability at high Rayleigh number. Here the hybrid nanofluid is considered as the working fluid, with different kinds of small particles in nanoscale being suspended. Design/methodology/approach The generalized homogenous model is introduced to describe the behaviors of hybrid nanofluid. Within the framework of the boundary layer approximations, the governing equations embodying the conservation equations of total mass, momentum and thermal energy are reduced to a set of fully coupled ordinary differential equations via relevant scaling transformations. A flow stability analysis is performed to examine the behavior of convective heat energy. Accurate solutions are obtained by means of a very efficient homotopy-based package BVPh 2.0. Findings Results show that the linear correlations of physical quantities among the base fluid and its suspended nanoparticles are adequate to give accurate results for simulation of behaviors of hybrid nanofluids. Heat enhancement can be also fulfilled by hybrid nanofluids. A flow stability analysis suggests the heat-related power index m > −1/3 for satisfying the increasing behavior of convective heat energy. Originality/value Free convection of a hybrid nanofluid near a vertical flat surface embedded in a saturated porous medium with anisotropic permeability is investigated for the first time. The simplified hybrid nanofluid model is proposed for describing nanofluid behaviors. The results of this proposed approach agree well with those given by the traditional hybrid nanofluid model and experiment. It is expected that, by using different combinations of various kinds of nanoparticles, the new generation of heat transfer fluids can be fabricated, which possess similar thermal-physical properties as regular nanofluids but with lower cost.

The time-dependent mixed bioconvection flow of an electrically conducting fluid between two infinite parallel plates in the presence of a magnetic field and a first-order chemical reaction is investigated. The fully coupled nonlinear systems describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms equations are reduced to a set of ordinary differential equations via a set of new similarity transformations. The detailed analysis illustrating the influences of various physical parameters such as the magnetic, squeezing, and chemical reaction parameters and the Schmidt and Prandtl numbers on the distributions of temperature and microorganisms as well as the skin friction and the Nusselt number is presented. The conclusion is drawn that the flow field, temperature, and chemical reaction profiles are significantly influenced by magnetic parameter, heat generation/absorption parameter, and chemical parameter. Some examples of potential applications of such bioconvection could be found in pharmaceutical industry, microfluidic devices, microbial enhanced oil recovery, modeling oil, and gas-bearing sedimentary basins.