Research Article
Effect of Rayleigh Number on Double-Diffusive Natural Convection Flow in a Rectangular Enclosure
Peninnah Ngina Musili*
,
Mark Okongo,
Alice Lunani Mulama Murwayi
Issue:
Volume 12, Issue 3, September 2026
Pages:
51-61
Received:
6 June 2026
Accepted:
18 June 2026
Published:
4 September 2026
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 = 104, 5×104, 105, and 106, 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 104 to 105 leads to a clear transition from conduction-dominated to convection-dominated heat and mass transfer. At Ra = 104, profiles are smooth, and gradients are weak; at Ra = 105, 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 = 105, 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.
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 studi...
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Research Article
Effect of Buoyancy Ratio on Double-Diffusive Natural Convection Flow in a Rectangular Enclosure
Peninnah Ngina Musili*,
Mark Okongo,
Alice Lunani Mulama Murwayi
Issue:
Volume 12, Issue 3, September 2026
Pages:
62-75
Received:
4 June 2026
Accepted:
23 June 2026
Published:
9 September 2026
DOI:
10.11648/j.ijfmts.20261203.12
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Abstract: Double diffusive natural convection driven by Simultaneous temperature and concentration gradients are fundamental to many engineering and environmental processes. The buoyancy ratio N, defined as the ratio of solutal to thermal buoyancy forces, critically determines whether thermal or solutal effects dominate the flow structure, heat transfer, and species transport. While most existing studies rely on two-dimensional simplifications and alternative numerical methods, this paper presents a three-dimensional numerical investigation of the effect of the buoyancy ratio on steady, laminar double-diffusive natural convection in a rectangular enclosure with an aspect ratio of 0.5. The continuity, momentum, energy, and concentration equations governing the flow are solved using the finite-volume method with the SIMPLE algorithm on a staggered grid. Parametric simulations are performed for buoyancy ratios N = 1.0, 2.5, 5.0, and 10.0, with fixed Prandtl number Pr = 7.0, Lewis number Le = 2.5, and Rayleigh number Ra = 50000. Results show that increasing the buoyancy ratio from 1.0 to 10.0 significantly enhances the uniformity of the temperature field and enhances vertical heat transfer. Concentration profiles become sharper and more localized as the buoyancy ratio is increased. At a high buoyancy ratio, solutal buoyancy dominates, producing a thin solutal boundary layer and strong stratification, thereby promoting salt fingering. Velocity profiles become stronger, more organized, and more stable as the buoyancy ratio increases. The 3-dimensional nature of the flow reveals that the effect of the buoyancy ratio in the enclosure is isotropic; the primary circulation plane along the z-y plane shows the greatest changes, while the secondary planes (x-y and x-z) show only a significant change. The finite volume method proves to be an effective tool for 3-dimensional parametric studies. The results provide a valuable benchmark for engineering applications where controlling the balance between thermal and solutal buoyancy is crucial, such as chemical reactors, drying systems, and thermal management devices.
Abstract: Double diffusive natural convection driven by Simultaneous temperature and concentration gradients are fundamental to many engineering and environmental processes. The buoyancy ratio N, defined as the ratio of solutal to thermal buoyancy forces, critically determines whether thermal or solutal effects dominate the flow structure, heat transfer, and...
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