Thermophoresis and Brownian motion effects on MHD bioconvection of nanofluid with nonlinear thermal radiation and quartic chemical reaction past an upper horizontal surface of a paraboloid of revolution

In this paper, the combined effects of buoyancy force, Brownian motion, thermophoresis and quartic autocatalytic kind of chemical reaction on bioconvection of nanofluid containing gyrotactic microorganism over an upper horizontal surface of a paraboloid of revolution are analyzed. The case of unequal diffusion coefficients of reactant A (bulk-fluid) and reactant B (catalyst at the surface) in the presence of nonlinear thermal radiation is presented. The fluid under consideration contains random movement of microscopic nanoparticles (i.e. Brownian motion). Moreover, it is assumed that the thermo-physical of the nanofluid does not vary with volume fraction. The governing nonlinear partial differential equations are obtained and transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge-Kutta fourth order method with shooting technique. Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for a limiting case. The influence of pertinent parameters are illustrated graphically and discussed. The presence of Brownian motion and thermophoresis decreases and increases concentration of reactant B (heterogeneous) respectively. Brownian motion boosts concentration of bulk fluid while thermophoresis reduces it.