Abstract In this paper, the effects of magnetic field, nonlinear thermal radiation and homogeneous-heterogeneous quartic autocatalysis chemical reaction on an electrically conducting (36 nm) alumina-water nanofluid containing gyrotactic-microorganism over an upper horizontal surface of a paraboloid of revolution is presented. The case of unequal diffusion coefficients of reactant A (bulk-fluid) and reactant B (catalyst at the surface) in the presence of bioconvection is presented. In this article, a new buoyancy induced model for nanofluid flow along an upper horizontal surface of a paraboloid of revolution is introduced. The viscosity and thermal conductivity are assumed to vary with volume fraction and suitable models for the case 0% ≤ ϕ ≤ 0.8% are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). 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. It is found that at any values of magnetic field parameter, the local skin friction coefficient is larger at high values of thickness parameter while local heat transfer rate is smaller at high values of temperature parameter.