ABSTRACTS

A STUDY

OF

HEAT

TRANSFER

DURING

A FLUID

IN A H I G H - F R E Q U E N C Y

CONVECTION

OF

ELECTROMAGNETIC

FIELD

M. S . B a k i r o v , V. G. D ' y a k o n o v , a n d A. G. U s m a n o v

UDC 536.242:536.252

This is the f i r s t study concerning the effect of an e l e c t r o m a g n e t i c field at a 650 kHz frequency on the heat t r a n s f e r during natural convection of water, acetone, benzene, and t r a n s f o r m e r oil. Tests w e r e p e r f o r m e d in a vessel typically used for studying the heat t r a n s f e r during natural convection. The h e a t e r s w e r e copper, c h r o m e - p l a t e d copper, and b r a s s tubes 6 mm in d i a m e t e r and 260 mm long. A tube was energized with h i g h - f r e q u e n c y e l e c t r i c c u r r e n t so that an e l e c t r o m a g n e t i c field appeared around it. It has been established, as a r e s u l t , that the h e a t - t r a n s f e r rate i n c r e a s e s a p p r e c i a b l y in a h i g h - f r e quency field. F o r w a t e r at 17~ for example, the h e a t - t r a n s f e r coefficient is 2.2 times higher in an e l e c t r i c field (c~E) than without a field (so). As the heat load q is increased, both a E and c~0 i n c r e a s e , but their ratio a E / s 0 is a l m o s t independent of q. As the t e m p e r a t u r e of the fluid r i s e s , the ratio OZE/a 0 d e c r e a s e s for water, acetone, and benzene (Fig. 1). A s m a l l e r increase in the h e a t - t r a n s f e r rate was noted in t e s t s with the b r a s s tube. This could be explained by the lower intensities of the e l e c t r i c field E and the magnetic field H at the s u r f a c e of the b r a s s tube than at the s u r f a c e of the copper tube under equal heat loads. It is to be noted that a h i g h - f r e q u e n c y e l e c t r o m a g n e t i c field even of a moderate intensity (in this case E of the o r d e r of 5.103 V / m and H of the o r d e r of 5.103 A / m ) has a s t r o n g boosting effect on the heat t r a n s f e r during natural convection of a fluid. According to the data obtained by other a u t h o r s , app r o x i m a t e l y the s a m e i n c r e a s e in t o w - f r e q u e n c y e l e c t r i c fields r e q u i r e s an intensity E of the o r d e r of 5 9 10 5 V/m. The increased rate of heat transfer in a high-frequency field may be due to electromagnetic forces acting on the thermal boundary layer and due to changed thermophysical properties of the fluid when in a field.

I

", ~

i ~--t

o--zt

o

~

~

3

o

I a

-

3

b t

Fig. i. Ratio aE/C~0 as a function of the t e m p e r a t u r e for (a) a copper tube and (b) a b r a s s tube: 1) acetone; 2) benzene; 3) w a ter. T r a n s l a t e d f r o m I n z h e n e r n o - F i z i c h e s k i i Zhurnal, Vol. 24, No. 1, pp. 160-165, J a n u a r y , 1973. Original a r t i c l e submitted July 7, 1970; a b s t r a c t submitted June 23, 1972.

9 19 75 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, storgd in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

121

An e s t i m a t e of t h e s e f o r c e s has shown that they a r e s m a l l e r than the f o r c e s due to n a t u r a l g r a v i t y convection. Unlike the gravitational f o r c e s , h o w e v e r , t h e s e f o r c e s a l t e r n a t e at double the field frequency. The p o s s i b i l i t y that the t h e r m o p h y s i c a l p r o p e r t i e s of a fluid m a y change in a field has been hinted at in [1], w h e r e the authors speculated about a s t r u c t u r a l t r a n s f o r m a t i o n of w a t e r in a h i g h - f r e q u e n c y field. The effect of a field on the heat t r a n s f e r can be accounted for by introducing into the conventional c r i t e r i a l equation the effective t h e r m o p h y s i c a l coefficients for w a t e r in a field. An evaluation of t e s t data in these t e r m s has yielded a relation for the complex of effective t h e r m o p h y s i c a l p r o p e r t i e s of a fluid in a field, as functions of the heat load and of the potential difference b e tween tube and v e s s e l wall. LITERATURE .

CITED

S. A. B r u n s , V. A. Chanturiya, and R. Sh. Shafeev, Dold. Akad. N a u k SSSR, 168, 152 (1966).

MASS

TRANSFER

HIGH-VOLTAGE

IN A S O L I D St)ARK

G. A. Aksel'rud, I. N. Fiktistov,

LIQUID

DISCHARGES

SYSTEM THROUGH

UNDER A TUBE

A. D. M o l c h a n o v , a n d V . 1). K o s y k

UDC 621.9.044

The feasibility of a c c e l e r a t i n g the p r o c e s s of e x t e r n a l m a s s t r a n s f e r by means of s p a r k d i s c h a r g e s h a s been d e m o n s t r a t e d in [1]. I n a s m u c h as dissolution p r o c e s s e s on an industrial s c a l e a r e r e a l i z e d m o s t e c o n o m i c a l l y in tubular a p p a r a t u s [2], the kinetics of dissolution in a tubular a p p a r a t u s under s p a r k d i s c h a r g e s w e r e studied h e r e both t h e o r e t i c a l l y and e x p e r i m e n t a l l y . Solving the h y d r o d y n a m i c p r o b l e m of fluid flow oscillations excited by s p a r k d i s c h a r g e s through a tube leads to the following e x p r e s s ion for the c r i t i c a l Reynolds n u m b e r . Re~= Eo~do PoFv

(1)

The kinetics of dissolution of KNO 3 s a l t s p e c i m e n s held in p l a c e was studied in a tubular a p p a r a t u s 32 m m in d i a m e t e r , and the dissolution of g y p s u m powder was studied in a r e c t a n g u l a r a p p a r a t u s 40 • 40 ram in c r o s s section. The s c h e m a t i c d i a g r a m of the a p p a r a t u s and the t e s t p r o c e d u r e had been shown e a r l i e r [31. An evaluation of the t e s t data has yielded the following c r i t i c a l equations of dissolution kinetics under s p a r k d i s c h a r g e s : 1. With s p a r k d i s c h a r g e s in a s t a t i o n a r y fluid (W F = 0): NUD=3.4 V'R-~M~-219

(2)

This r e l a t i o n fits t e s t data within the r a n g e s 3600 < Re M < 67,600 and E / F = 6-23 J / c m 2, with F = 9.1 cm z, t) 0 = (0.5-3.65) .10 ~ N / m 2, and 1)r D = 720. 2. With s p a r k d i s c h a r g e s in a steady s t r e a m of fluid (W F ~ 0): /~o~ 1/ NUD-NU0~/1.02~-27.2 poFw F 9 This relation fits t e s t data within the r a n g e s 0.015 < Ew/1)0FW F < 0.26, 730 < Re 0 = W F d 0 / v < 12,500, and W F = 6.4-109 c m / s e c , with E = 55 J, P r D = 720, and 1)0 = 105 N / m 2. Original a r t i c l e s u b m i t t e d M a r c h 9, 1972; a b s t r a c t s u b m i t t e d May 25, 1972.

122

(3)

In the c a s e of g y p s u m powder dissolving in distilled w a t e r in a suspension bed inside a tubular a p p a r a t u s , the kinetics of the p r o c e s s is d e s c r i b e d by the relation /E~o NUD=NUo V 0 . 9 + 40 p~fWS ,

(4)

valid within the r a n g e s 0.02 < Ew/PoFW S < 0.017 and E = 20-50 J, with PG = 10s N/m2, WS = 7.5 c m / s e c , and d o = 1.0-1.5 ram.

NOTATION Nu D, Nu0 a r e the N u s s e l t diffusion n u m b e r s , under s p a r k d i s c h a r g e s and without s p a r k d i s c h a r g e s , r e spectively; ts the Prandtl diffusion n u m b e r ; Pr D ts the modified Reynolds n u m b e r ; Re M ts the e n e r g y of charged capacitor; E 02 ts the f r e q u e n c y of d i s c h a r g e s ; is the d i a m e t e r of solid p a r t i c l e s ; do is the external p r e s s u r e above the liquid; Po ts the c r o s s - s e c t i o n a r e a of the tube; F /J ~s the k i n e m a t i c viscosity; is the period of p l a s m a cavity pulsations; T is the velocity of s t e a d y fluid s t r e a m ; WF ts the v e l o c i t y of suspension. W8 L I T E R A T U R E CITED I, 2. 3.

A. D. Molchanov, G. A. A k s e l ' r u d , A. I. C h e r n y a v s k i i , I. N. Fiklistov, I n z h . - F i z . Zh., 18, No. 2, 293-298 (1970). N. S. Spirin, in: Technological P r o b l e m s in P r o c e s s i n g Halurgical Raw M a t e r i a l s [in Russian], T r u d y VNIIG, Khimiya, M o s c o w - L e n i n g r a d (1967). A. D. Molchanov, G. A. A k s e l ' r u d , and I. N. Fildistov, Vestnik L e n i n g r a d s k . Politekh. Inst., No. 36, 65-67 (1969).

EVAPORATION

OF

A LIQUID

IN A H I G H - T E M P E R A T U R E

GAS S T R E A M A.

L.

UDC 536.423.1

Suris

The equation of e v a p o r a t i o n for a single d r o p l e t in a h i g h - t e m p e r a t u r e gas s t r e a m can be written as follows:

dGd

d--; :-4

~" in[l-:-Cv(T--ts) p Cv

(1)

"

Retaining only the f i r s t t e r m of the s e r i e s expansion

, (x-ll

. . . .

]

(2)

Original a r t i c l e submitted M a r c h 2 4 , 1972; a b s t r a c t s u b m i t t e d July 10, 1972.

123

using the relation for a m o n o d i s p e r s e s y s t e m where the density of the solution varies with time "gL .+ GG T

R*

(~?s--Y L)

~ p /

R*

(2) 6G C~m..k C ~ r n

C~,~ g

GO

c~h

CT~

CT.

G~

~

we t r a n s f o r m (1) into dx,

-

-

(u -j, hg) ~ g+ YL

/

'

where

'

( 9

R,) 0o

Cr. ' Gm

C~n ] ' vm

R,

~_ ( ~ 1',~ "~o~L; ~= ~ ~-o- ~ - y = - , , -- \ ~ - ' ~ /

6~

R*

0o

6o

cr~ Gm

(cT

;

c~m~

~m + ~

Gin

C~rn h:--R. C~/m; R.=R*+C~/n-[s=R+CL(Zs--trr},

v = cg--~m+~,-U:-.-' '

Grn

Gm

H e r e G, GOa r e the weight r a t e s of liquid flow at any apparatus section and at the inlet, respectively; Gd, G~ a r e the instantaneous mass and the initial mass of a droplet, respeztively; T iS time; p, P0 a r e the r a d i i of a liquid droplet s u r f a c e at any instant and at the f i r s t instant of time; T, T Oa r e the instantaneous and the initial t e m p e r a t u r e of the v a p o r - g a s mixture; ts, t m a r e the s u r f a c e t e m p e r a t u r e and the mean t e m p e r a t u r e of a droplet; X is the t h e r m a l conductivity of the v a p o r - g a s mixture; C T Gm, C T~ CTm, C t m a r e the mean specific heat of the gas and of the vapor, r e s p e c t i v e l y , within t e m p e r a t u r e intervals f r o m stand a r d to T, TO, and t s, r e s p e c t i v e l y ; C L is the mean specific heat of the liquid within the t e m p e r a t u r e interval f r o m t m to ts; C V is the mean specific heat of the vapor within the t e m p e r a t u r e interval f r o m t s to T; R is the heat of evaporation; Ts, y a r e the initial and the instantaneous density of the solution; and 7 L is the density of the solvent. The solution to Eq. (3) with the initial condition g(0) -- 1 can be written as '

where

(o_

,

_~.

In

y:

) 1/3

F

1

1

2Ye

( n ' 1/3

- ,7)

YL 1/3

Differentiating (2) with r e s p e c t to ~, with (4) taken into account, we obtain the r a t e at which the gas s t r e a m is cooled (chilled) by the evaporating liquid. F o r the evaporation of pure liquids, Ts = YL in Eq. (4).

124

DISCHARGE A.

F.

OF

LIQUID

A BOILING

Babitskii

UDC 532.529.5

E x i s t i n g m e t h o d s of s o l v i n g the d i s c h a r g e p r o b l e m in the c a s e of boiling liquids can be c l a s s i f i e d a c c o r d i n g to how the s y s t e m of equations is c l o s e d : the i s e n t r o p i c - p r o c e s s s c h e m e [1], the c o u p l e d - p r o c e s s e s s c h e m e [2], and the h y d r a u l i c - p r o c e s s s c h e m e [3]. With the i n t e g r a t e d equation of motion f o r a t w o - p h a s e fluid [1], one obtains a new solution to this p r o b l e m u n d e r the following conditions: the flow is o n e - d i m e n s i o n a l , s t e a d y , and t h e r m o d y n a m i c a l l y at e q u i l i b r i u m ; the t e m p e r a t u r e s , the p r e s s u r e s , and the v e l o c i t i e s of both c o m p o n e n t s a r e , r e s p e c t i v e l y , equal; t h e r e a r e no m a s s f o r c e s p r e s e n t and no e x t e r n a l h e a t is supplied. The equations of continuity, motion [1], and e n e r g y b e c o m e then, a f t e r i n t e g r a t i o n , pv/= p,,v0f0 = const, U

(1)

UO

I

(2)

p + ~ - (~,,o ~ Vof,o) = Pc + ~ - - (~'0:- VoPo), U2

U2

~:il + ~2io.+ ~ - = ~01i01-" ~0J0~. : o --

CliO01 ~- C2,00,.,;

~ =.

c~O~Oo

pc =

; 80: :

col~)Ol + co2~Oo2; c 1

(3)

2 -- const --

c2

=

co: + %2 : 1;

co:Oo____:O ; o 61 -" 61 = ~o: = I~o~--l'..).

In the s p e c i a l c a s e v o = 0, it follows f r o m E q s . (2) and (3) that the quantity of g e n e r a t e d v a p o r is 1

f3oli~1 : ~o2io .,. - - i: - - - -

6~= ! --

6:==

:

i.2-- fl +

901902

(Pc--P)

Oo, (Pol-- Po~)(Pc -- P)

(4)

If tabulated d a t a a r e u s e d for d e t e r m i n i n g the t h e r m o d y n a m i c p r o p e r t i e s of the m i x t u r e c o m p o n e n t s (water and v a p o r ) , then the s y s t e m of equations (1)-(3) will be a c l o s e d one and the p r o b l e m of d i s c h a r g e will have a tmique solution. M o r e o v e r , the flow of an ideal m i x t u r e is a c c o m p a n i e d by an i n c r e a s e in e n t r o p y . The v e l o c i t y and t h e e n t r o p y of the m i x t u r e a r e defined by the following l i m i t s : V (S = corlst) ~ / v (S) ~ v (Smax) = O; S o..~. S C S (v - 0).

NOTATION p v p S cj pj hj f

is is is is is is is is

the the the the the the the the

p r e s s u r e o f the m i x t u r e ; v e l o c i t y of the m i x t u r e ; d e n s i t y of the m i x t u r e ; e n t r o p y of the m i x t u r e ; v o l u m e c o n c e n t r a t i o n of the j - t h c o m p o n e n t (j = 1, 2); d e n s i t y of the j - t h c o m p o n e n t (j = 1, 2); e n t h a l p y of the j - t h c o m p o n e n t (j = 1, 2); c r o s s - s e c t i o n a r e a of the s t r e a m .

Subscripts 1 2 0

d e n o t e s the liquid; d e n o t e s the v a p o r ; d e n o t e s the initial s t a t e . LITERATURE

!,

2, 3.

4,

A. N. M. G.

CITED

F. B a b i t s k i i , Dokl. Akad. N a u k UkrSSR, Ser. A, No. 7 (1971). N. Soldatov, T e p l o 6 n e r g e t i k a , No. 1 (1958). S t u a r t and R. J o r n e l l , E n g i n e e r i n g , No. 1 (1936). Z e u n e r , T e c h n i s c h e T h e r m o d y n a m i k , 1, No. 2 (1890).

Institute of H y d r o m e c h a n i c s , A c a d e m y of S c i e n c e s of the Ukrainian SSR, Kiev. m i t t e d N o v e m b e r 4, 1971; a b s t r a c t s u b m i t t e d J u l y 20, 1972.

Original article sub-

125

HIGH-TEMPERATURE OF NICKEL

THERMOPHYSICAL

MEASUREMENT

PROPERTIES

A. F. Zverev, A. I . K o v a l e v , and A. V. Logunov

UDC 5 3 6 . 2 1 2 : 5 3 7 . 3 1 1 . 3 3 1

Nickel is a m a t e r i a l widely used now as the b a s e in a l a r g e group of heat r e s i s t a n t alloys capable of withstanding high t e m p e r a t u r e . N e v e r t h e l e s s , its p r o p e r t i e s (for instance, its t h e r m o p h y s i c a l p r o p e r ties) have not been explored thoroughly enough - e s p e c i a l l y a t t e m p e r a t u r e s above 1000~ In this study the authors m e a s u r e d the t h e r m o p h y s i c a l p r o p e r t i e s of nickel, 99.81% p u r e s p e c i m e n s , o v e r the t e m p e r a t u r e r a n g e f r o m r o o m to 1400~C. The Rozhdestvenskii a p p a r a t u s with its t e m p e r a t u r e r a n g e extended to 1000~ was used for m e a s u r i n g X and p f r o m r o o m t e m p e r a t u r e to 950~C, k by the r e l a tive method [1] and p by the compensation method [2]. M e a s u r e m e n t s in the 1000-1400~ r a n g e w e r e made on the a p p a r a t u s for a c o m p o s i t e d e t e r m i n a t i o n of t h e r m o p h y s i c a l p r o p e r t i e s [3], w h e r e a s p e c i m e n was heated with e l e c t r i c c u r r e n t in vacuum so that the t e m p e r a t u r e profile in the center portion would b e c o m e p a r a b o l i c . The a g r e e m e n t between t h e r m a l conductivity values obtained by two different methods on d i f f e r e n t a p p a r a t u s within c o m p a r a b l e t e m p e r a t u r e r a n g e s p r o v i d e s an additional indicator as to the r e l i a b i l i t y of the r e s u l t s . The s p e c i m e n s for the m e a s u r e m e n t s on each a p p a r a t u s had been p r e p a r e d f r o m the s a m e s t o c k of p u r e nickel. Rounded off values f r o m t h e s e t e s t s a r e shown in Table 1. The m a x i m u m (corresponding to the 950/o confidence interval) m e a s u r e m e n t e r r o r (random plus s y s t e m a t i c ) is: 5.5% for k, 1.5% for p, and 10%0 for e in the 200-900~ t e m p e r a t u r e range, 9% for k, 2% f o r p, and 11% for e in the 1000-1400~ t e m p e r a t u r e range. TABLE 1. T h e r m o p h y s i c a l P r o p e r t i e s of P u r e Nickel (99.81%) ff

T, ~

),~W/cm 9 ~ p, pg~cm L.IOS,W. ~2/(~ 2 T, ~ ~., W/cm. ~ p, ~a.cm L. 108,w, ~l(~ 2

20 .

100

7,68

-1113

80O 0,69 45,8 2,94

900 0,72 48,4 2,97

--

8

--

e~, X = 0,65p

--

LITERATURE le

2. 3.

A. I. Kovalev and A. V. Logunov, Machine C o n s t r u c t i o n [in Russian], A. V. Logunov and A. F. Z v e r e v , A. I. Kovalev and A. V. Logunov, (1971).

200

300

] 400 /

500

600

700

0,68 t 0,64 0,63 0,64 0,66 25,2 ' 3 3 , 5 ~7,4 40,2 43,2 3,0 i 3,18= 3,05 2,95 2,93 2,83 1200 1300 t400 -1000 0,78 0,81 0,84 0,86 I -0,75 -i3,2 ]55,8 18,4 61,4 50,8 2,99 3,02 i3,07 3,t2 3,16 -0,191, 0,21 0,23 0,24 0,18 0,411 0,42 -0,385 o239~I, 0,77 17,4

1100

0,405}

--

CITED

in: Methods of Testing, Inspecting, and Studying M a t e r i a l s for Vol. 1, M a s h i n o s t r o e n i e (1971). I n z h . - F i z . Zh., 15, No. 6, 1114 (1968). in: T h e r m o p h y s i c a l P r o p e r t i e s of Solids [in Russian], Nauka

Original a r t i c l e submitted N o v e m b e r 29, 1971; a b s t r a c t Submitted June 16, 1972.

126

IRRADIATION

OF

CHARACTERISTICS S.

P.

BODIES OF

WITH

THE

SELECTIVE

ABSORPTION

MEDIUM

Detkov

UDC 536.3

Calculations of the radiative heat t r a n s f e r between bodies involve an i n t e r s p e r s i o n of problems concerning their g e o m e t r y and s p e c t r a . The f i r s t step is to integrate a flux element over the depth of the volume. The next steps depend l a r g e l y on the sequence of integrations: over the s p e c t r u m and with r e s p e c t to the sPace angle. The advisability of integrating over the s p e c t r u m last is shown h e r e on the example of two-dimensional s y s t e m s of bodies for which the irradiation coefficients a r e calculated. According to the method proposed in [1], however, as well as in this method one can use the directional radiation c h a r a c t e r i s t i c s for the final calculations. A combination sequence of integration is r e c o m m e n d e d for s y s t e m s with a complex g e o m e t r y : the s p e c t r u m is subdivided into r a n g e s . When the s p e c t r u m is continuous, then integration with r e s p e c t to the s p a c e angle is within each r a n g e p e r f o r m e d last. This sequence is p a r t i c u l a r l y convenient in the case of variable t e m p e r a t u r e , p r e s s u r e , and concentration fields. Consideration is given h e r e to a r a n g e of the s p e c t r u m sufficiently n a r r o w so that the optical p r o p e r t i e s of the d i s p e r s e phase and of the s u r f a c e may be a s s u m e d constant. At the s a m e time, such a range c o v e r s a multitude of s p e c t r a l lines of the gas - lines of different intensities but the s a m e contour. The lines or the bands either do not overlap at all o r overlap completely. The e x p r e s s i o n s for the irradiation coefficients are of four different kinds, depending on the combination of volume and s u r f a c e zones. The angular distribution of radiant flux impinging on a body is d e s c r i b e d by the Law of Cosines. The transition f r o m a s y s t e m with an a r b i t r a r y g e o m e t r y to a s y s t e m of two-dimensional bodies yields a class of special fmlctions. The following a r e examples of these new functions appearing in the exp r e s s i o n s for the irradiation coefficients:

Mm,n (c, ~) : v .l r"K~ (Ct + c) ~) av.

Here

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exp --

cosn-t adv,,

T:%l,

v =J o-~01/a~,

Kn =-- - - K i n (t) = ~n

0 c : k / a o, c~o = a d ( y ),

w is the wave n u m b e r , e m - t ; Aco is the width of a s p e c t r u m range; o~0 is the center of a s p e c t r u m range, c m - t ; f is the contour of the s p e c t r a l absorption coefficient a ; y is the n o r m a l i z i n g factor; l is the t h i c k n e s s of a body, m; k is the attenuation coefficient of the d i s p e r s e phase; m, n = 1, 2 . . . . . Other functions a r e a l r e a d y well known and found in the technical l i t e r a t u r e . The values of some of them have been tabulated for the s i m p l e s t contours f. A general s c h e m e is p r o p o s e d for calculating the matrix of irradiation coefficients, its p r o p e r t i e s and simplifications a r e analyzed, and a specific example is shown of a radiation band with a d i s p e r s i v e contour. LITERATURE 1,

S.P.

CITED

Detkov, I n z h . - F i z . - Z h . , 21, No. 2 (1971).

Original a r t i c l e submitted October 25, 1971; a b s t r a c t submitted June 19, 1972.

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