In this present work, we study heat transfer in a confined environment. We have to determine the thermal and dynamics fields of the cavity while observing the effect of the Rayleigh number which depends on the characteristics of the fluid and the temperatures imposed. The behavior of boundary layers in natural convection is analyzed along this square cavity. The central halves of its vertical walls are heated at different temperatures. The left active part is at a higher temperature than the one on the right wall. The remaining inactive parts and the horizontal walls (upper and lower) are adiabatic. The thermal and dynamic modeling of two-dimensional problem was done using a calculation code Fortran 90 and a visualization software ParaView based on the finite volume method. The equations governing this phenomenon of unsteady flow have thus been solved. This allows the modeling of both air flow and heat transfer with a numerical stabilization of the solution. So, we have presented our results of numerical simulations using a visualization tool. The results show the different velocity and temperature curves, velocity vectors and isotherms in laminar flow regime.

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.