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

Ambethkar Vusala

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 4

5--20

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 ≫1), liquid metals (Pr≪1) and gases (Pr < 1) for different Rayleigh numbers in the range of 3x105 ≤ RaL ≤ 7x10 9 from relevant empirical correlations existing in the literature. Accordingly, the thermal diffusion effects within the horizontal rectangle are analyzed.

Effect of inclination on free convective heat transfer during melting of a phase change material in a rectangular enclosure

Devahastin S., Siow S. L., Mujumdar A. S.

Applied Mechanics and Engineering

1998

Vol. 3, no 3

491-515

Determination of heat transfer during melting in enclosures is important in the design of heat exchangers using phase change material (PCM) for thermal energy storage. Melting of the PCM generally invokes free convection currents in the melt phase depending on the orientation and geometry of the heat transfer surfaces. This paper deals with a computational investigation of the flow patterns and heat transfer rates which develop during the melting of a PCM contained in a rectangular chamber. Effects of heating both the vertical and horizontal faces as well as orientation of the cavity to the gravitational vector are examined. The shapes of the solid-liquid interface demonstrate clearly the generation of the cellular structure in the melt phase when the bottom horizontal face is heated. The cellular structure results in an undulating pattern for the heat transfer distribution on the bottom surface. The number of peaks and valleys in the Nusselt number distribution depends on the thickness of the melt layer.