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Research Papers: Heat and Mass Transfer

Stable/Unstable Stratification in Thermosolutal Convection in a Square Cavity

[+] Author and Article Information
D. K. Maiti1

Department of Mathematics, Birla Institute of Technology and Science, Pilani 333031, Indiaḏiitkgp@yahoo.com

A. S. Gupta, S. Bhattacharyya

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India

1

Corresponding author.

J. Heat Transfer 130(12), 122001 (Sep 19, 2008) (10 pages) doi:10.1115/1.2969757 History: Received July 04, 2007; Revised June 06, 2008; Published September 19, 2008

A numerical study is made of double-diffusive convection in a square cavity with a sliding top lid in the presence of combined vertical temperature and concentration gradients. The bottom lid and other two walls are kept fixed. The side walls are adiabatic and impermeable to solute while the top and bottom lids are kept at constant but distinct temperature and concentration. The governing unsteady Navier–Stokes equations combined with the heat and mass transport equations are solved numerically through a finite volume method on a staggered grid system using QUICK scheme for convective terms. The resulting equations are then solved by an implicit, time-marching, pressure correction-based algorithm. The flow configuration is classified into four cases depending on positive/negative values of thermal Grashof number and solutal Grashof number. A detailed comparison of the four flow configurations is made in this paper. In conclusion, these four flow configurations can be brought to either stably or unstably stratified field. Furthermore, the possibility of salt-fingering and double-diffusive instability in the absence of the top lid motion is explored and the effect of the lid motion is clearly exhibited. The dependence of the average rates of heat and mass transfer from the top and bottom lids on the flow parameters is also investigated in the presence of top lid motion.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 5

Contour plots for GrC=5×106 when GrT=−106(B=−5) at Re=700 (Case-IIA): (a) streamlines, (b) isotherms, and (c) isohalines

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Figure 6

Contour plots for B=−5 (GrT=−106 and GrC=5×106) (Case-IIA: in the absence of top lid motion): (a) streamlines, (b) isotherms, and (c) isohalines

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Figure 7

Contour plots for GrC=0 when GrT=106(B=0) at Re=700: (a) streamlines and (b) isotherms

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Figure 4

Contour plots for GrC=106 when GrT=−106(B=−1) at Re=700 (Case-IIA): (a) streamlines, (b) isotherms, and (c) isohalines

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Figure 3

Contour plots for GrC=−106 when GrT=−106(B=1) at Re=700 (Case-IA): (a) streamlines, (b) isotherms, and (c) isohalines

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Figure 2

Contour plots for GrC=0 when GrT=−106(B=0) at Re=700: (a) streamlines and (b) isotherms

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Figure 1

Schematic of the flow configuration of the cavity with boundary conditions

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Figure 8

Contour plots for GrC=5×106 when GrT=106(B=5) (Case-IB: in the absence of top lid motion): (a) streamlines, (b) isotherms, and (c) isohalines

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Figure 9

Contour plots for GrC=−106 when GrT=106(B=−1) at Re=700 (Case-IIB): (a) streamlines, (b) isotherms and (c) isohalines

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Figure 10

Contour plots for GrT=5×106 when GrC=−106(B=−0.2) (Case-IIB: in the absence of top lid motion): (a) streamlines, (b) isotherms, and (c) concentration

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Figure 11

Contour plots of streamlines for B=−1 (GrT=−106, GrC=106) at Re=1 with Le=1(Pr=Sc=0.72)

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Figure 12

The average Nusselt number (Nu¯) and Sherwood number (Sh¯) versus solutal Grashof number (GrC): (a) RiT=−106∕7002 and (b) RiT=106∕7002

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Figure 13

The average Nusselt number (Nu¯) and Sherwood number (Sh¯) versus thermal Grashof number (GrT): (a) RiC=−106∕7002 and (b) RiC=106∕7002

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Figure 14

The average Nusselt number (Nu¯) and Sherwood number (Sh¯) versus Reynolds number: (a) stable stratification (Case-IA (B=5, GrT=−106), Case-IIA (B=−0.2, GrT=−5×106) and Case-IIB (B=−5, GrT=106)) and (b) unstable stratification (Case-IB (B=5, GrT=106), Case-IIA (B=−5, GrT=−106) and Case-IIB (B=−0.2, GrT=5×106))

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