Effect of Rayleigh Number on Double-Diffusive Natural Convection Flow in a Rectangular Enclosure

Abstract

Double diffusive natural convection driven by simultaneous temperature and concentration gradients is governed by the Rayleigh number Ra , which represents the balance between buoyancy and viscous forces. The Rayleigh number determines the transition from conduction-dominated to convection-dominated heat and mass transfer. While most existing studies rely on two-dimensional simplifications, this paper presents a three-dimensional numerical investigation of the effect of the Rayleigh number Ra on steady, laminar double-diffusive natural convection in a rectangular enclosure with an aspect ratio Ar of 0.5. The governing equations are solved using the finite volume method with the SIMPLE algorithm on a staggered grid. Parametric simulations are performed for Ra = 10 4 , 5×10 4 , 10 5 , and 10 6 , with fixed Prandtl number Pr = 7.0, Lewis number Le = 2.5, and buoyancy ratio N = 10. The results reveal that increasing the Ra from 10 4 to 10 5 leads to a clear transition from conduction-dominated to convection-dominated heat and mass transfer. At Ra = 10 4 , profiles are smooth, and gradients are weak; at Ra = 10 5 , sharp boundary layers and strong circulation appear. Concentration profiles become sharper and more localized with increasing Ra . At high Ra , solutal stratification occurs, and solute remains confined near the source, indicating enhanced solutal buoyancy effects. Temperature profiles evolve from nearly parallel isotherms (conduction) to wavy, distorted patterns with thermal plumes (convection). Vertical heat transfer increases significantly with Ra . Velocity fields become stronger and more organized as Ra increases. At Ra = 10 5 , well-defined primary and secondary circulation cells produce intense upwelling and downwelling, with velocities an order of magnitude higher than at low Ra . The 3-dimensional nature of the flow reveals anisotropy: the primary circulation plane (z-y) shows the strongest response, but secondary planes (x-y, x-z) also exhibit significant changes with Ra . These results provide valuable benchmarks for engineering applications where controlling the strength of buoyancy-driven convection is crucial, such as in solar collectors, building ventilation, and drying systems. The finite volume method proves to be an effective tool for such 3-dimensional parametric studies.