47nm alumina-water nanofluid flow within boundary layer formed on upper horizontal surface of paraboloid of revolution in the presence of quartic autocatalysis chemical reaction

In this article, a modified version of buoyancy-induced model is considered to investigate the flow of 47nm alumina-water nanofluid along an upper surface of horizontal paraboloid of revolution in the presence of nonlinear thermal radiation, Lorentz force and quartic autocatalysis kind of homogeneous heterogeneous chemical reaction. The case of unequal diffusion coefficients of reactant A (bulk fluid) and B (high concentration of catalyst at the surface) in the presence of bioconvection is considered. Governing equation suitable to unravel the thermophoresis which takes place within the boundary layer is presented. Since chemical reactant B is of higher concentration at the surface more than the concept described as cubic autocatalytic, the suitable schemes are herein described as isothermal quartic autocatalytic reaction and first order reaction. The viscosity and thermal conductivity are assumed to vary with volume fraction (ϕ) 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 some pertinent parameters on velocity, temperature, diffusion of motile microorganism, concentration of bulk fluid and catalyst is illustrated graphically and discussed.