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DOUBLE-DIFFUSIVE CONVECTION WITH FINE DUST

R. C. Sharma, Neeta Rani

Czech. J. Phys. B 39 (1989), No. 7, 710

Received 28 september 1990

1. In Abstract, second and third sentences (lines 2 - 4 ) should be replaced by "The solute gradient introduces oscillatory modes in the system in contrast to the validity of principle of exchange of stabilities in its absence".

2. In equations (12), (16) and (38); AZF should be multiplied by 1/2, where 2 = = k/k' , the ratio of thermal diffusivity and solute diffusivity.

3. In equations (28), (30), (40) and (41), N~ should be replaced by 2N~.

4. In equations (32) and (43), dNR/dN ~ should be +2 instead of 1.

5. Equations (17), (19), (22), (23), (39) and the text from eq. (24) onwards (upto end of section 3) should read as below:

(17) 8t 2 V2/ V2w

(19) (D2 - a2 - Hn) (D2 - ~2 -- 2Hn) [Lx - L2(D2 - ~2)] (D2 - o~2) W =

-- a2(~n + n ) [ S , ( D 2 - ~2 - ~ /~n) - ~N~(D ~ - ~2 - H , ) ] W .

(22) ( D 2 - ~2 - U n ) ( D ~ - ~ - 2 t ~ ) X = ~ ( ~ + H ) [ N , ( D ~ - ~ - 2 / ~ )

- ~N~(D ~ - ~ - H n ) ] W. (23) ~0 x X , ( D 2 _ ~2 _ H n ) ( D 2 - ~2 _ 2 H n ) X dz =

= ~2(zn + H) I~ X*[NR( D2 -- a2 _ 2Hn) W - 2N~(D 2 - o: z - Hn) W] dz,

(39) ( D 2 - ~ - H,,) ( D ~ - ~ - 2H.) [(L~ + L ~ ~ - L~ D~) ~ ( D ~ - ~ )

+ L~ T A D 2] W =

= ~.~(L, + L ~ ~ - L ~ D ~) (~,, + H )

• [NR(D 2 -- o~ z -- 2Hn) W - 2Ns(D 2 -- a2 _ Hn) W ] ,

(24) I~ + ( H + 2 ~ ) , ~ + 2 ~ . ~ I ~ =

-- ~2('cn + H ) [ ( N R - 2N~)(L*lI4 -4- L*I6)+ 2 H n ( N R - N~)(L*I5 + L*2I,,)],

58~ Czechoslovak Journal of Physics, Vol. 41 (1991), No. 6

where

Errata

I~ = In (ID~XI ~ + 2 ~ [ D X [ ~ + ~ ' lx l ~) d~ ,

1~ = In (IDXI ~ + =~lxI ~) dz,

z~ = ~o' lxl ~ d ~ , (25)

I4 = ~o t [(0 2 - c~ 2) WI 2 d z ,

I~ = j'g (IDw[ ~ + ~ l w / ~ ) dz ,

16 = ~o 1 (103W12 + 3~x2[D2W[2 + 3~x4[DW[ 2 + o~61W] 2) dz,

which are all positive definite. Putting n -- in o, where n o is real, into equation (24) and equating the imaginary parts, we obtain

(26)

H(1 + 2) I2 + ~2(NR -- 2N~) (FHNp 1I,, + zhI6) - ~2H22(NR - N~) I ,

o ~ 2 z 2 N p t ( N R - 2N~)I,, - o~2Hz2(NR - - N~) { N ; I ( F - H ) I s + zI4} n 2 = _

or

(27) n o = 0 .

In the absence of solute gradient, equation (26) yields n 2 to be negative, which is impossible as no is real, and so no = 0 meaning thereby that the principle of exchange of stabilities is valid (Scanlon and Segel [1]). The presence of solute gradient introduces oscillatory modes in the system, as n 2 may be positive.

References

[1] Scanlon J. W., Segel L. A.: Phys. Fluids 16 (1973) 1573.

Czech. J. Phys. 41 (1991) 589