Numerical study of heat transfer by natural convection in a large-scale cavity heated from below

Abstract

In the present work we uses the lattice Boltzmann method (LBM) to simulate the heat transfer by natural convection in a square cavity filled by air and heated locally from below θ = 1 by a heated portion of length ℓ = H/4 placed in the center of the wall. One of the vertical walls has a cold portion θ = 0, while the other walls are adiabatic. This cavity simulates a living space with under floor heating and fitted with a glass door (single glass). Computations were made in two dimensions for different values of Rayleigh number in the range 5 × 106 to 108. The model uses the double populations approach to simulate hydrodynamic and thermal fields. The results are presented in terms of streamlines and isotherms, temperature profile in the middle of the cavity are, also, shown and discussed in this work. Heat transfer has been studied in terms of local Nusselt number on the walls and the average Nusselt number. This last later is correlated with Rayleigh number.