New Nu-Ra correlations are proposed to evaluate the steady-state natural convection heat transfer taking place in air-filled enclosures of parallelogrammic section. The thermal conditions and dimensions of the cavities treated in the present work lead to high values of the Rayleigh number, reaching 3 x 10(9). The cavities considered are formed by two vertical active walls connected by a closing adiabatic channel. The cold wall is maintained isotherm at temperature T-c while the hot one consists of 5 bands, alternately isotherm at temperature T-h and adiabatic. The upper and lower walls of the channel are inclined at an angle a with respect to the horizontal. This angle is either positive (hot wall below the level of the cold one) or negative, giving rise respectively to a conducting or insulating cavity in the convective sense of the term. A detailed steady-state 2D numerical study is carried out with the finite volume method and is accompanied with surface temperature experimental measurements. A good agreement between the experimental and numerical results is found in terms of the global heat exchanges and hence of the convective transfer. The dependence of the mean Nusselt number is presented as a function of the inclination angle alpha and of the Rayleigh number Ra and confirm the convective diode effect taking place. Correlations of the type (Nu) over bar (x) = k(alpha)Ra-n, suitable for -60 degrees <= alpha <= +60 degrees, are proposed for the range 5 x 10(3) <= Ra <= 3 x 10(9) corresponding to diverse engineering applications. (C) 2010 Elsevier Ltd. All rights reserved.