A theoretical study is presented for three-dimensional flow of bioconvection nanofluids containing gyrotactic microorganisms over a bi-axial stretching sheet. The effects of anisotropic slip, thermal jump and mass slip are considered in the mathematical model. Suitable similarity transformations are used to reduce the partial differential equation system into a nonlinear ordinary differential system. The transformed nonlinear ordinary differential equations with appropriate transformed boundary conditions are solved numerically with the bvp4c procedure in the symbolic software, MATLAB. The mathematical computations showed that an increase in Brownian motion parameter corresponds to a stronger thermophoretic force which encourages transport of nanoparticles from the hot bi-axial sheet to the quiescent fluid. This increases the nanoparticle volume fraction boundary layer. Fluid temperature and thermal boundary layer thickness are decreased with increasing stretching rate ratio of the bi-axial sheet. The present simulation is of relevance in the fabrication of bio-nanomaterials and thermally-enhanced media for bio-inspired fuel cells.

The purpose of the article is to present a transport model for magnetohydrodynamics‐forced convective non‐Newtonian boundary flow from a thin needle in a nanofluid in the presence of microorganisms and Stefan blowing. The governing equations are reduced to ordinary differential equations with the help of similarity transformations and then numerically solved by using the Matlab bvp4c function. The effect of various emerging parameters on the flow field, heat, mass, and density of motile microorganisms transfer was computed and studied. It was found that some of the parameters have an important effect on the boundary layer thickness. Justification with earlier simpler model in the absence of magnetic field is included. The model finds applications in various transdermal delivery system, biomedical electromagnetic treatments and to design new medical devices for cell delivery to the central nervous system.

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Transport phenomena with fluid flow, heat, mass, nanoparticle species and microorganism transfer external to a needle in a porous medium have many biomedical engineering applications (e. g. hypodermic needles used in hemotology). It is also used to design many biomedical engineering equipments and coating flows with bio-inspired nanomaterials. Coating flows featuring combinations of nanoparticles and motile micro-organisms also constitute an important application area. A mathematical model for convective external boundary layer flow of a power-law nanofluid containing gyrotactic micro-organisms past a needle immersed in a Darcy porous medium is developed. Multiple slips boundary conditions and Stefan blowing effects at the needle boundary are taken into account. The model features a reduced form of the conservation of mass, momentum, energy, nanoparticle species and motile micro-organism equations with appropriate coupled boundary conditions. The governing nonlinear partial differential equations (NPDEs) are converted to dimensionless form and appropriate invariant transformations are applied to obtain similarity ordinary differential equations (SODE). The transformed equations have been solved numerically using the in-built Matlab bvp4c function. The influence of the emerging parameters on the dimensionless velocity, temperature, nanoparticle concentration, motile micro-organism density functions, skin friction, heat, mass, and micro-organism transfers) are discussed in detail. It is found that velocity decreases whilst temperature, concentration, and density of motile microorganism increase with an increase in blowing parameter for shear thinning (pseudoplastic), Newtonian, and shear thickening (dilatant) fluids. It is also found that skin friction, Nusselt number (dimensionless heat transfer rate), Sherwood number (dimensionless nanoparticle mass transfer rate) and motile micro-organism wall density gradient decrease with increasing blowing, Darcy, power law and needle size parameters. Comparison with the earlier published results is also included and an excellent agreement is obtained.

This paper studies the combined effects of viscous dissipation, first and second-order slip and variable transport properties on phase-change hydromagnetic bio-nanofluid convection flow from a stretching sheet. Nanoscale materials possess a much larger surface to volume ratio than bulk materials, significantly modifying their thermodynamic and thermal properties and substantially lowering the melting point. Gyrotactic non-magnetic micro-organisms are present in the nanofluid. The transport properties are assumed to be dependent on concentration and temperature. Via appropriate similarity variables, the governing equation with boundary conditions are converted to nonlinear ordinary differential equations and are solved using the BVP4C subroutine in the symbolic software MATLAB. The non-dimensional boundary value features a melting (phase change) parameter, temperature-dependent thermal conductive parameter, first as well as second-order slip parameters, mass diffusivity parameter, Schmidt number, microorganism diffusivity parameter, bioconvection Schmidt number, magnetic body force parameter, Brownian motion and thermophoresis parameters. Extensive computations are visualized for the influence of these parameters. The present simulation is of relevance in the fabrication of bio-nanomaterials for bio-inspired fuel cells.