Natural convection near a vertical wall of constant mass flux and temperature situated in a mass stratified fluid

• Published in: IOP conference series. Materials Science and Engineering 2018-11, Vol.444 (8), p.82020
• Main Author: Neagu, M
• Format: Article
• Language: English
• Subjects: Conservation equations; Constituents; Free convection; Mathematical analysis; Parameters; Prandtl number
• ISSN: 1757-8981; 1757-899X; 1757-899X
• DOI: 10.1088/1757-899X/444/8/082020

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 ⋅ γ2 ⋅ Le4 / 3 ⋅ N−3 ≥ 1 and a HDC-VMDC regime succession if Ra ⋅ γ2 ⋅ Le4 / 3 ⋅ 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.