Natural convection near a vertical wall of constant mass flux and temperature situated in a mass stratified fluid
Abstract
This paper presents the analysis of the natural convection process that occurs near a vertical impermeable wall embedded in a fluid containing a certain constituent. The temperature of the wall is constant and the mass flux of the constituent is constant at the wall. At infinity, the fluid has a constant temperature and a linearly varying concentration of the constituent. The scale analysis of the governing equations reveals the succession of the heat (HDC) and/or mass (MDC) driven convection regime that attains the equilibrium state along the wall. Two possibilities are encountered: a heat driven convection (HDC) regime if Ra ṡ γ2 ṡ Le4 / 3 ṡ N-3 ≥ 1 and a HDC-VMDC regime succession if Ra ṡ γ2 ṡ Le4 / 3 ṡ N-3 ≈ 1, where Ra is the Rayleigh number, Sc is the mass dimensionless stratification parameter, N is the buoyancy ratio, Le is the Lewis number, γ = 1 - (1 + Pr1 / 2 ) -1 and Pr is the Prandtl number. These results are illustrated for two parameter sets by solving the conservation equations using the finite differences method.
- Publication:
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Materials Science and Engineering Conference Series
- Pub Date:
- November 2018
- DOI:
- 10.1088/1757-899X/444/8/082020
- Bibcode:
- 2018MS&E..444h2020N