TITLE:
Numerical Simulation of Two-Dimensional Natural Convection in a Confined Environment with the Vorticity-Stream Function Formulation
AUTHORS:
Mame Khady Kane, Cheikh Mbow, Mamadou Lamine Sow, Joseph Sarr
KEYWORDS:
Numerical Study, Differentially Heated Cavity, Vorticity, Modeling
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.8 No.1,
March
29,
2018
ABSTRACT: A numerical study is presented on the problem of 2D natural convection in a differentially heated cavity. The equations governing this unsteady flow phenomenon were solved using the vorticity-stream function formulation of the Navier-Stokes equations and heat. The results obtained are compared with the results of the literature and make it possible to validate this approach. In this work, we studied the heat transfer in a cavity and we determined the variation of the local Nusselt number which allows obtaining the rate of thermal transfer by convection in an enclosure. We analyzed thermal fields for different Rayleigh numbers by selecting two points to visualize temperature fluctuations over time. Thus, the creation of the ascending and descending movements of the fluid inside the cavity was analyzed. We have also established temperature histograms for the graphical presentation of the temperature distribution. The modeling of the two-dimensional problem was established using a “Fortran 90” calculation code. The results also show the different vorticity contour maps in laminar flow regime. We have presented our results of numerical simulations using a visualization tool. The Rayleigh number varies in the range of 103 to 106 for a Prandtl number equal to 0.72 corresponding to air.