Numerical prediction of natural convection in vented cavities using restricted domain approach

Abstract

The present study reports the numerical simulation of natural convection heat transfer from an open square cavity with two side vents provided symmetrically on the side walls. The top wall which is maintained at a constant temperature ( T w), is the heat source for the cavity and the side walls are adiabatic. A restricted domain approach that predicts the regions of inflow, outflow and velocity distributions is employed. The applicability of two types of pressure boundary conditions at entry and exit regions are studied and compared. Non-linear coupled partial differential equations governing natural convection are solved on a structured non-uniform staggered grid using a second-order accurate upwind least square scheme for discretising the convection terms, central difference scheme for diffusion terms and SIMPLER algorithm for pressure–velocity decoupling. An in-house code is developed and is validated with the results of three classical natural convection problems. Simulations have been carried out for a wide range of thermal parameter, Rayleigh numbers (10 4 ⩽ Ra ⩽ 10 8), orientation of the cavity about horizontal (0 ⩽ δ ⩽ 180) and geometrical parameter, vent ratio ( 0.05 ⩽ D L ⩽ 0.25 ) . The numerical simulation predicts the dimensionless mass flow rate through the cavity and variation of local Nusselt number over the hot wall. A correlation for average Nusselt number is developed in terms of Rayleigh number and angle of tilt of the cavity for D L ⩾ 0.1 .