Tangent hyperbolic non-Newtonian radiative bioconvection nanofluid flow from a bi-directional stretching surface with electro-magneto-hydrodynamic, Joule heating and modified diffusion effects

Motivated by bio-inspired nano-technological functional coating flows, in the current paper a theoretical study of laminar, steady, incompressible bioconvection flow of a tangential hyperbolic (non-Newtonian) nanofluid from a bi-directional stretching surface under mutually orthogonal electrical and magnetic fields is presented. Nonlinear thermal radiation, Joule heating and heat source/sink effects are included. Non-Fourier and non-Fickian models are also implemented which feature thermal and solutal relaxation. Buongiorno’s nanoscale model is adopted which features thermophoresis and Brownian motion effects. Rosseland’s model is employed for thermal radiation. The electro-viscous effects arising from the distortions of the double-capacitance electric flow field are addressed with a modified formulation of the Poisson–Boltzmann equation. Via appropriate similarity transformations, the coupled, nonlinear partial differential conservation boundary layer equations and wall and freestream boundary conditions are rendered into a nonlinear ordinary differential boundary value problem which is solved numerically with an efficient numerical Lobatto—IIIa collocation method available in the MATLAB bvp4c shooting solver. Validation with previous studies is included. Velocity is strongly damped with increasing buoyancy ratio and bioconvection Rayleigh number is generally greater with positive rather than negative electrical field parameter. Increasing the Eckert number reduces the density of motile microorganisms while raising the temperature. An increment in Brownian motion and radiative parameters strongly accentuates temperatures.