Investigation of natural convection in convergent vertical channels

Using air as the working fluid, natural convection heat transfer in a uniform wall temperature convergent vertical channel has been investigated numerically. The investigation encompassed half angles of convergence between 0° (parallel-walled channel) and 10° and the solutions were performed for (S/L) Ra_s range of 1 to 2 × 10⁴. In order to find a correlation format which will merge the convergent channel results for low Rayleigh number ranges (Ra′ < 10²) with those for the parallel-walled channel ones, the minimum (S_min), mean (S_avg), and maximum (S_max) interval spacing between channel walls were used as characteristic dimensions. It was found that merging was best achieved by the use of maximum interval spacing (S_max) as the characteristic dimension. These numerical findings agree with those for high Rayleigh number ranges (Ra′ > 10²) reported in the literature.