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Turbulent natural convection of air is studied, by the elliptic-relaxation model − , in a tall vertical cavity whose hot and cold walls are maintained at linear temperatures of slopes and , respectively. The average temperatures of the active walls are located at mid-height of the cavity. Four situations are analyzed, corresponding to = = (case I ), = − = (case II ), = 0 and = (case III ), = and = 0 (case IV). These boundary conditions may be more representative or used to control heat transfer for certain systems. The effects of the slope (−1 ≤ ≤ 1), the aspect ratio of the cavity (10 ≤ ≤ 80) and the average Rayleigh number (5 × 10 ≤ ≤ 10 ) on the streamlines, isotherms, contours of the turbulent kinetic energy, heatlines, local and average Nusselt numbers are investigated. It is shown that the local and average heat transfers of cases III and IV can be deducted from those of cases I and II. The obtained dynamic and thermal fields as well as local and average heat transfers of the studied cases are quite different of those of the classical case corresponding to = 0. A simplified procedure for calculating the average Nusselt number is also developed for each case.

Analysis of Turbulent Natural Convection by an Elliptic Relaxation Model in Tall Vertical Cavities with Linear Temperatures on Sidewalls