A Numerical Study of Turbulent Natural Convection in a Square Enclosure Using a Two Equation Model

In this study the performance of one numerical turbulence model, is accessed. In predicting heat transfer
due to natural convection inside an air-filled square cavity. Turbulent natural convection in an enclosure plays
an important role in the field of heat transfer and buildings environment. Natural turbulent convection is square
air cavities having isothermal vertical and highly heat – conducting horizontal walls are compared with the
experimental data obtained for these cavities at a varying Rayleigh numbers, 1.8 x 109, 1.44 x 1010 and 1.15 x
1011. In carrying out numerical investigations, a two – dimensional, low turbulence, two – parameter
model known as the Low – Reynolds – number turbulence model was used. The vorticity – vector
potential formulation was used to eliminate the need to solve the pressure terms. The vorticity, vector potential
energy and two – equation model with their boundary conditions were solved using finite difference
approximations. The results of the investigation are presented for the distribution of the velocity and
temperature components. The non – linear terms and in the averaged momentum and energy equations
respectively are modelled using the model to close the governing equations. The cavity is maintained at
313K on the hot wall and 293K on the opposite cold wall. The horizontal walls are adiabatic. The results
obtained show that as the Rayleigh number increases, the values of the stream function increases. As the
Rayleigh number increases, uniform distribution of heat inside the cavity is achieved.