Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model

Abstract

In this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two-phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman-Forchheimer equation was used to formulate the porous layer. The enclosure has a low temperature, while the cylinder is maintained at a high temperature. The governing equations are expressed in PDEs and converted into weak formulations (Galerkin FEM). In numerical simulations, the average concentration, the amplitude of undulated cylinder, the number of undulated, and the Rayleigh number are investigated. It is observed that the homogeneous nanofluid model could be valid for low heating intensity with higher waviness frequency and/or higher amplitude. The higher the alumina concentration, the higher the heat transfer rate. The heat transfer rate can be boosted by up to 13% by suspending 1% alumina particles. The heat transfer enhancement decreases with increasing the amplitude and/or increasing the waviness number.