Numerical study of double-diffusive natural convection in a square cavity

doi:10.1016/0017-9310(92)90251-M

International Journal of Heat and Mass Transfer

Volume 35, Issue 4, April 1992, Pages 833-846

https://doi.org/10.1016/0017-9310(92)90251-M Get rights and content

Abstract

Steady-state thermosolutal convection in a square cavity filled with air, submitted to horizontal temperature and concentration gradients, is studied numerically. In the first series of numerical simulations, the influence of solutal buoyancy force on heat or mass transfer rate is investigated: Lewis and thermal Rayleigh numbers are kept constant (Le = 1, Ra_T = 10⁷), solutal Rayleigh number is varied (Ra_S = 10⁵−5 × 10⁷). The second series deals with the influence of Lewis number on fluid motion for heat transfer driven flow (Ra_T = 10⁷, Ra_S = 0) and mass transfer driven flow (Ra_T = 0, Ra_S = 10⁷) configurations. Lewis number is varied from 0.3 to 5. Correlations are obtained between heat and mass transfer rates and the non-dimensional numbers characterizing both phenomena.

Résumé

La convection thermosolutale, en régime stationnaire, dans une cavité carrée remplie d'air, soumise à des gradients horizontaux de température et de concentration, est étudiée numériquement. Dans la première série de simulations, on étudie l'influence de la force de poussée solutale sur les taux de transfert de chaleur ou de masse: les nombres de Lewis et de Rayleigh thermique sont constants (Le = 1, Ra_T = 10⁷), le nombre de Rayleigh solutal varie ( $Ra_{S} = 10^{5} a ̀ 5 × 10^{7}$ ). La deuxième série de simulations se rapporte à l'analyse de l'influence du nombre de Lewis sur le mouvement du fluide, dans les cas d'écoulements à force de poussée thermique dominante (Ra_T = 10⁷, Ra_S = 0) et à force de poussée solutale dominante (Ra_T = 0, Ra_S = 10⁷). Le nombre de Lewis varie de 0.3 à 5. Des corrélations sont obtenues entre les taux de transfert de chaleur et de masse et les nombres adimensionnels caractérisant les deux phénomènes.

Zusammenfassung

Es wird die stationäre doppelt-diffusive Konvektion in einem quadratischen luftge-füllten Hohlraum unter dem Einfluβ horizontaler Temperatur- und Konzentrations-Gradienten numerisch untersucht. Eine erste Reihe numerischer Simulationen befaβt sich mit dem Einfluβ der konzentrationsbedingten Auftriebskraft auf den Wärme- oder Stoffübergang: Die Lewis- und die thermische Rayleigh-Zahl werden konstant gehalten (Le = 1; Ra_T = 10⁷), die Konzentrations-Rayleigh-Zahl wird im Bereich 10⁵ ⩽ Ra_S ⩽ 5 × 10⁷ variiert. Eine zweite Reihe behandelt den Einfluβ der Lewis-Zahl auf die Fluidbewegung für thermisch getriebene (Ra_T = 10⁷; Ra_S = 0) und konzentrationsgetriebene Anordnungen (Ra_T = 0; Ra_S = 10⁷). Die Lewis-Zahl wird dabei im Bereich 0,3–5 variiert. Es ergeben sich Korrelationen zwischen den Wärme- und Stoffübergangskoeffizienten sowie für die dimensionslosen Kennzahlen, welche beide Phänomene charakterisieren.

Реферат

Чиcлeннo иccлeдyeтcя cтaциoнapный пepeнoc тeплa и мaccы в зaпoлнeннoй вoздyчoм квaдpaтнoй пoлocти пpи нaлoзeнии гpaдиeнтoв тeмпepaтyp и кoнцeнтpaций в гopизoнтaльнoм нaпpaвлeнии. B пepвoй cepии чиcлeнныч pacчeтoв иccлeдyeтcя влияниe пoдьeмнoй cилы зa cчeт pacтвopeннoгo вeщцecтвa нa cкopocть тeплoи мaccoпepeнoca. Пpи этoм чиcлo Льюиca и тeплoвoe чиcлo Pэлeя coчpaняютcя пocтoянными (Le = I, Ra_T = 10⁷), чиcлo Pэлeя для pacтвopeннoгo вeщecтвa измeняeтcя (Ra_S = 10⁵ − 5 × 10⁷). Bo втopoй cepии pacчeтoв ycтaнaвливaeтcя влияниe чиcлa Льюиca нa двизeниe зидкocти для тeчeний зa cчeт тeплoпepeнoca (Ra_T = 10⁷, Ra_S = 0) и мaccoпepeнoca (Ra_T = 0, Ra_S = 10⁷). Чиcлo Льюиca вapьиpyeтcя oт 0,3 дo 5. Пoлyчeны oбoбщaющиe cooтнoщeния для cкopocтeй тeплo- и мaccoпepeнoca, выpaзaeмыч чepeз бeзpaзмepныe кpитepии, чapaктepизyющиe эти явлeния.

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Abstract

Résumé

Zusammenfassung

Реферат

Int. J. Heat Mass Transfer

Int. J. Heat Fluid Flow

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Natural convection with combined driving forces

PhysicoChem. Hydrodyn.

Double-diffusive natural convection

Combined heat and mass transfer by natural convection in a vertical enclosure

ASME J. Heat Transfer