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A mathematical model has been developed for steady-state boundary layer flow of a nanofluid past an impermeable vertical flat wall in a porous medium saturated with a water-based dilute nanofluid containing oxytactic microorganisms. The nanoparticles were distributed sufficiently to permit bioconvection. The product of chemotaxis constant and maximum cell swimming speed was assumed invariant. Using appropriate transformations, the partial differential conservation equations were non-dimensionalised to yield a quartet of coupled, non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with appropriate boundary conditions. The dominant parameters emerging in the normalised model included the bioconvection Lewis number, bioconvection Peclet number, Lewis number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, local Darcy-Rayleigh number and the local Peclet number. An implicit numerical solution to the well-posed two-point non-linear boundary value problem is developed using the well-tested and highly efficient Keller box method. Computations are validated with the Nakamura tridiagonal implicit finite difference method, demonstrating excellent agreement. Nanoparticle concentration and temperature were found to be generally enhanced through the boundary layer with increasing bioconvection Lewis number, whereas dimensionless motile microorganism density was only increased closer to the wall. Temperature, nanoparticle concentration and dimensionless motile microorganism density were all greatly increased with a rise in Peclet number. Temperature and dimensionless motile microorganism density were reduced with increasing buoyancy parameter, whereas nanoparticle concentration was increased. The present study found applications in the fluid mechanical design of microbial fuel cell and bioconvection nanotechnological devices.

Closed-form solutions are presented for the transient hydromagnetic flow in a rotating channel with inclined applied magnetic field under the influence of a forced oscillation. Magnetic Reynolds number is large enough to permit the inclusion of magnetic induction effects. The Maxwell displacement current effect is also included and simulated via a dielectric strength parameter. The governing momentum and magnetic induction conservation equations are normalized with appropriate transformations and the resulting quartet of partial differential equations are solved exactly. A parametric study is performed of the influence of oscillation frequency parameter (ω), time (T ), inverse Ekman number, i.e. rotation parameter (K 2 ), square of the Hartmann magnetohydrodynamic (MHD) parameter (M 2 ), and magnetic field inclination (θ) on the primary and secondary induced magnetic field components (bx, by) and velocity components (u, v) across the channel. Network solutions are also obtained to validate the exact solutions and shown to be in excellent agreement. Applications of the study arise in planetary plasma physics and rotating MHD induction power generators and also astronautical flows. Mathematics Subject Classification (2000). 76W05 · 76X05 · 65Z05.

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Buoyancy-driven laminar free-convection flow, heat, and mass of a non-Newtonian nanofluid from a horizontal circular cylinder to a micropolar fluid have been investigated numerically using an implicit finite difference scheme. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A nonsimilarity solution is presented that depends on the Prandtl number Pr, Schmidt number Sc, Brownian motion parameter Nb, thermophoresis parameter Nt, material parameter K, and buoyancy ratio parameter N. It is observed that increasing the Brownian motion parameter increases the temperature, Sherwood number, and wall couple stress but decreases the velocity, concentration, angular velocity, skin friction, and Nusselt number. An increase in the thermophoresis parameter is observed to accelerate the velocity, concentration, angular velocity, skin friction, and Nusselt number, whereas it decreases the temperature, the reduced Sherwood number, and wall couple stress. The velocity, angular velocity, Nusselt number, and wall couple stress are reduced with increasing material parameters, whereas the temperature, concentration, skin friction, and Sherwood number are enhanced. It is also observed that increasing material parameters increases velocity, angular velocity, skin friction, Nusselt number, and Sherwood number but decreases temperature, concentration, and wall couple stress. The model finds applications in energy systems and the thermal enhancement of industrial flow processes.

White (1974) and Chamkha and Issa (2000). The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and nuclear hazards.

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