Control Volume Based Finite Element Method Study of Nano-fluid Natural Convection Heat Transfer in an Enclosure Between a Circular and a Sinusoidal Cylinder

Abstract

Abstract In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). The fluid in the enclosure is Cu-water nanofluid. Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results show that for all Rayleigh number, increasing number of undulations causes the average Nusselt number to augment except that the average Nusselt number for N = 4 is greater than N = 5.