Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 21, Issue.: 3

Original Research Article

A NUMERICAL STUDY OF TURBULENT NATURAL CONVECTION IN A SQUARE ENCLOSURE USING A TWO EQUATION MODEL

 

MUTILI PETER MUTISYA1* AND AWUOR KENNEDY OTIENO1

1School of Pure and Applied Sciences, Kenyatta University, Box 43844 – 00100, Nairobi, Kenya.

Abstracts

In this study the performance of one numerical turbulence model, k − ε 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 k − ε  model known as the Low – Reynolds – number k − ε  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 k − ε 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.

Keywords :

Turbulent natural convection; heat transfer; square enclosure; Rayleigh number.