Buoyancy induced model for the flow of 36 nm alumina-water nanofluid along upper horizontal surface of a paraboloid of revolution with variable thermal conductivity and viscosity

Abstract

The motion of nanofluid (water and 36 nm alumina nanoparticles) along upper horizontal surface of a paraboloid of revolution in the presence of nonlinear thermal radiation, Lorentz force and space dependent internal heat source within thin boundary layer is investigated theoretically. It is assumed that buoyancy induces the flow over this kind of surface which is neither a horizontal/vertical nor cone/wedge, hence suitable buoyancy model for this case of fluid flow is presented. 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 limiting case. The influence of pertinent parameters are illustrated graphically and discussed. It is found that temperature and velocity functions are maximum at higher values of internal space dependent heat source. Local heat transfer rate is maximum at smaller values of internal space dependent heat source.