Finite element modeling of conjugate mixed convection flow of Al₂O₃–water nanofluid from an inclined slender hollow cylinder

Abstract

Steady laminar mixed convection flow and heat transfer characteristics of Al 2 O 3 -water nanofluid about a vertical slender hollow cylinder are investigated numerically, under the effect of wall conduction. The transformed, non-dimensional, nonlinear governing equations (obtained with the Boussinesq approximation) are solved, using a robust, extensively validated, Galerkin finite element method for spherical-shaped nanoparticles with volume fraction ranging up to 4%, with associated boundary conditions. Nine-node quadrilateral finite elements are employed. Experimental models for thermal conductivity and viscosity incorporating Brownian motion terms have been taken into consideration. The influence of physical parameters, namely wall conduction parameter, Richardson number (buoyancy parameter) and nanoparticle volume fraction, on velocity profile, temperature profile and on Nusselt number is shown graphically. Excellent validation of the present numerical results has been achieved with earlier published results. Both skin friction coefficient and Nusselt number are enhanced with increasing Richardson number. With increasing inclination angle there is a decrease in average Nusselt number. Furthermore, average Nusselt number and interfacial temperature are both reduced with nanoparticle diameter. The flow is accelerated with increasing Richardson number whereas the bulk temperature is found to be suppressed. The study has important applications in thermal enhancement of solar energy systems.

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