HOMOTOPY SEMI-NUMERICAL MODELLING OF NANOFLUID CONVECTION BOUNDARY LAYERS FROM AN ISOTHERMAL SPHERICAL BODY IN A PERMEABLE REGIME

摘要

Nanofluids hold significant promise in enhancing transport phenomena in chemical engineering and energy storage systems. Key mechanisms via which thermal conductivity is elevated are Brownian motion and thermophoretic diffusion effects. In this study we examine with a powerful semi-numerical technique, the Homotopy Analysis Method (HAM), the steady laminar free convection heat and mass transfer in incompressible nanofluid boundary layer flow from a spherical geometry embedded in an isotropic, homogenous porous material. Employing the classical Darcy model, the boundary layer equations are formulated with a porosity function (ε). These nonlinear parabolic partial differential equations are normalized from an (x,y) coordinate system to a (ξ,η) coordinate system, with appropriate boundary conditions. Detailed computations are performed with HAM to elucidate the effects of Brownian motion number (Nb), Lewis number (Le), buoyancy parameter (Nr) and thermophoresis parameter (Nt) on the key transport variables: re-scaled nanoparticle volume fraction (f), dimensionless velocity (S/) and dimensionless temperature (Θ). The solutions are benchmarked with a robust shooting quadrature, demonstrating excellent correlation. The significant potential of HAM in analyzing strongly coupled, nonlinear nanofluid flows is demonstrated. The study finds applications in packed bed reactor simulations in chemical engineering and also near-field thermal contamination processes from containers buried in soil.