Numerical study of axisymmetric magneto-gyrotactic bioconvection in non-Fourier tangent hyperbolic nano-functional reactive coating flow of a cylindrical body in porous media

Modern functional nanomaterials coating processes feature an increasing range of intelligent properties including rheology, biological (bio-inspired) modifications, elaborate thermophysical behaviour and complex chemical reactions which are needed for the precise synthesis of bespoke designs. Such manufacturing flow processes are extremely complex and involve both heat and multiple mass transfer (species diffusion) phenomena. Intelligent nano-coatings are particularly attractive since they exploit magnetic nanoparticles which can be manipulated by external magnetic fields. Recently, Boeing Aerospace have explored the use of micro-organisms for intelligent aircraft coatings. Mathematical models provide an excellent analysis for elucidating the response characteristics of such coating dynamics processes. With this motivation, the present analysis is indented to develop a new mathematical model to examine the axisymmetric, magnetohydrodynamic, chemically reactive, gyrotactic bioconvection flow of a tangent hyperbolic nanofluid past a cylinder saturated with Darcy porous medium, as a model of smart-coating enrobing flow. The influence of Cattaneo–Christov heat flux (non-Fourier thermal relaxation parameter), thermophoresis and Brownian motion are taken into consideration. The steady-state, boundary layer, partial differential conservation equations are rendered dimensionless via appropriate transformations, and the subsequent nonlinear, coupled, system of governing equations is numerically solved by employing implicit Keller box method. The impact of various factors such as Hartmann magnetic number, Weissenberg viscoelastic parameter, Prandtl number, non-Fourier thermal relaxation parameter, thermophoresis, Brownian motion, micro-organisms concentration difference variable, chemical reaction, bioconvection Peclet number, Schmidt number and bio-convection Schmidt number on the flow, heat transfer, mass transfer, motile density, local friction factor, local heat transfer rate, local mass transfer rate and local microorganism density number wall gradient is visualized graphically. Validation with earlier studies is included. Further validation with a finite element method (FEM) code (SMART-FEM) is presented. Results reveal that the heat transfer upsurges for amplifying the Weissenberg number and Hartmann magnetic number. Microorganism concentration distribution of the non-Newtonian nanofluid coating diminishes for amplifying the bioconvection Schmidt number and Peclet number. Magnifying the power law index parameter reduces the momentum boundary layer thickness of tangent hyperbolic nanofluid, while there is an acceleration in the fluid flow near the surface of the cylinder. Local Sherwood number rises with higher values of homogenous destructive chemical reaction parameter. The computations provide a solid benchmark for further CFD modelling.