LAUSR

Abstract In the industry, the thickness of many surfaces can be described as non-uniform. To a reasonable extent, an upper half surface of a horizontal object with variable thickness can be described as a paraboloid of revolution. In this article, a modified version of a buoyancy-induced model is considered to account for the force which drives the flow of 29 nm CuO-water nanofluid along its upper horizontal surface in the presence of nonlinear thermal radiation. The case of unequal diffusion coefficients of reactant A (bulk fluid) and B (high concentration of catalyst at the surface) in the presence of a gyrotactic microorganism is considered. It is assumed that there exist a significant difference between nanoparticle mass density and base fluid density. 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 earlier described as cubic autocatalytic, hence the suitable schemes herein described as isothermal quartic autocatalytic reaction and first order reaction. The dynamic viscosity and thermal conductivity are assumed to vary with volume fraction (ϕ) and suitable models for the case 0 ≤ ϕ ≤ 0.9 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. Numerical analysis of many emerging parameters is illustrated graphically and discussed.