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Analogy between thermal and mass diffusion effects of a free convective flow in rectangular enclosure

. In this investigation, the analogy between thermal and mass diffusive effects of a free convective ﬂow in a rectangular enclosure is emphasized. The upwind ﬁnite volume method is used to discretize the governing equations of the continuity, momentum, energy and mass transfer. The novelty in this exploration is to appropriately modify the well-known Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm so that it suits to the present problem and thereby, the new ﬂow variables such as the temperature and the concentration are computed. An empirical correlation for the average Sherwood number ( Sh ) that does not exist in literature is suggested in this work. The average Sherwood numbers for distinct ﬂuids (gases and liquids) are calculated, and mass diffusion effects within the horizontal rectangle are analyzed. The average Nusselt numbers ( Nu ) are calculated for distinct ﬂuids such as liquids ( Pr (cid:29) 1), liquid metals ( Pr (cid:28) 1) and gases ( Pr < 1) for different Rayleigh numbers in the range of 3 × 10 5 ≤ Ra L ≤ 7 × 10 9 from relevant empirical correlations existing in the literature. Accordingly, the thermal diffusion effects within the horizontal rectangle are analyzed.