SCIENTIFIC ABSTRACT ZHUKHOVITSKIY, B.YA. - ZHUKHOVITSKIY, YE.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R002064920004-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 19, 2001
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

MALOV, Vladimir Sergeyevich; ZfIUKJiOVIT-SKq,.B.Ya.j red.
[Romoto controll Tolemokhanika. lzd.2., dop. I paror.
Moskva, Fmorglia, 1965. 94 P. (Bibllotolca po avtorn-
tike, no.123) (MIRA 18;6)

ZHUKHOVITSKIY, Boris Yakovlevich; nEWEVITSM, losif Borisovich;
'K.M.'., prof., red.
(Theoretical principles of electrical engineering in
three parts) Teoreticheskis asnovy elektratokhnikl~v
trekh,chastiakh. Moakvaj Energila. Pt,2."-,1965. 238 P.
(mikk 19:1)

ZEMOVITalY. I.M. (Z#%gorod* lr#okva oblast')
Detection-of oxacer among patients with gastrointentinal diseaseso
Klin. nod. 32 nloR8:37-42 Ag 154. (HLRA 7:10)
(GASTROIMSTIVAL DISUMIS, complications,
canc6r, Incidence)
(GASTROl.M3TIVAL SYSTZH, neoplasms,
incidence in ocher gastrointestinal die,)

ZH=ITSKIT, I.M. (Belgoroct)
Inzng cancer & smoking; a ijurvov of recent literatum 111n.
med. 37 no.4:26-29 Ap 139. (Hm i2iQ
(IJMG IMOPJASKS, otiol. thogen.
smoking, review (Runr)
(S40KING, lnj,. offo
cancer of lung, review (Rue))
-7 TAT

ZMOVITsxly, I.M. (Belgorod)
-23
cancer arA its prevention* Yel'd. L akunbo 23 no#2:20
'58- WM 11--3)

ZHUKMVITSKIY, L.
Beyond the Arctic Circle. 11TO no-7:56-58 Jy(~59-
RA. 12: 11
1. Zamestitell predeedatelya Norillskogo pravloniya nauchno-
tokhnicheek-ogo obahchestva tayetuoy mstallurgii.
(Norillsk--Research, Industrial)

zhulmov, 1 11 L. F. (Noril Ink Directorate)
"Me Work of the Nor1l'sk Directorate of the Society.
report presented at the F:Uth Fall Assembly of the Central Admin. of the
Non-FmTous Metallurgical Sci.-Teoh. Society, Moscow 21-22 Fab 58,

ZHMOVITSKIT, K. S.
[Work of surass at the V.K.Molotov sanatorium for childrea afflictod.
with tubercUtsis of the baze] Opyt raboty meditelaskikh tooter
detskoge kestnetubarkulessegs ssx&t*ril4.lmeai V.R.Xolotsv&.Msgkra
Mod it, 1955. 86 p., (nn 9
(PRDIATRIC NWIRg)

ACC NRa Ap60j1$W SOURCZ omt URM67/65/
AUTHOR: Dzhelepov. B. So Zhvikovskiy. No No -Zhuk k
Malayan,_A. G.
ORG: none
TIM: GjMa222.ctrunj of EU sup 152* with a 9.2-hour half-live
SOURCE: Yadernaya f4fka, v. lp no. 6p 1965, 941-947
TOPIC TAGS: europiumi, gamma spectrum, samarium, spectrometer
~1 ~)J
ABSTRACT: rom 511520
The re ative Intensities of 13 -f-lines f are'
determined with the aid of magnetic photoritron and elotron
spectrometers (the error In the basic 11ne Intensities does not
exceed 6%). Four new E%1152* Y-lines which must be added to the
decay scheme are found. now excitation level with an energy of
168o KEV Is found In SmiA. A deviation from the Alaga (ate)
rales Is noted when the 1511 KEV (I-) level degenerQtes to the
2 " or ')+ rotation bands of the ground state. 71i-~ authors thank Ye. A. Khol. Rovaya
fDr the calorijaetrif, measurements of the preparations AuI90 and Sc4ls; Tu.-
.Knoltnov for making possible the research of gamma-spectrum ',;ul52-* -)n phCtOT
E--i-, _~K~iyun -iremonts and vl,*~h the proceising cf th(i
t __yan for help with the measi
txperimeents on photoritron; A. G.,_Dmitr~yev, V. 1. P-Ainnov, and 'I.
J'or assistance in measuring the elotron. has. 1 tal)"e.
I.Based on authors' Eng. abst.) [JMS) 7_1
31UB CODE: 20 / SUBM DATE: 3INov64 / OIRIG JTF: !W: X)16,
Card _1~ - '~: -,-;, _* -.-- - _ I

TITLE: Abram Ekvisovich Chernin
-SOURCE: Elektricheskiyet stantsii, no. 5. 1965, 93
'S" Y. Mi A Maio A. N.z-*
THOR: arkis 3 99koty_aj3, So S.; uat)onnkly.
Zhulln, 1. V,; VedosMa A. 9 1 el2ko, V. H.;
gle-Y aMe A.; KL-YfAto Yermb
S. Ya.; ~zar'Ze,, -111ko
Petrov, D. I.: Krikunchik,. A,J,; P9,L -M. I, P,; 3azorloy, V.
nskaya, Z. G.; Kartsev, V, L.;
jyj, n, -y rA.
Losev, S. B.; Dorodnova T. N.; Lutinch1k. V. A.; 1"u A.
i ORG: none
TOPIC TAGS: electric engineering, electric engineerinjg personnel
IT
ABSTRACT: An engineer since 1929, A. B. Chernin h", worked for years in developing
now techniques and equilxnent for relay protection9f electric power system. In
this 60th birthday tribute, he is credited with leading the group which produced
the directives on relay protection, contributing to the development of a method for
calculating transient processes in long diotance 400-500 kv paaer transmission lines
and with aiding in plamiing of the electric portions of power stations, substations
and power systems. The results of his engineering and scientific work have been
published 46 tims, he is a doctor of technical sciences (since 1963), and has
taught for 30 years at the Hosccw Power Insritute. Orig. art. has-. I figure. ZTPR
SUB CODE: 09 SUM DATE: none
HO
Card, 1A

ZHUMOVITSKIY, S.Yu.; RYABCHZM* V-I-
It is necessary to replace #,.he M-5 visconimeter by,the
SPV-4 viscosimeter: a topic for discussion. Neft. khoz. 38
no.9:47-52 S 160,. (MIRA 13:9)
(Viscosimeter)

ZHMOVITSKLY,,S.Yu~
Rating the coagula Ion degree of drilling fluids. Neft.khoz- 33 Z002:18-
7 1570- (MIRA 10:3)
(Oil well drillb%fluids)

ZHMOVITSKIY, S.Yu.
Sfficient principle for contrblllng the viscosity wieL static
pressure of dislocation of drilling mids. Neft.khoz. 37
no.2:38-43 7 '59. (MIR& 12:4)
(Oil well drilling fluids)

A"A
IJ A-'YO V
Mme: ZIMX(IVMKIY, S. Yu.
Dissertation: Thickening of drilling muds and a method for determining
cauues
Degree: Cand. Tech Sci
&- 0A -1
AZS&kjativv: Kin Higher Education USSR, Moscow Order of labor Red Banner
Petroleum List imeni Academician I. M. Gubkin
k' C' 0C'V -
D Place: 1956., Krasnodar
source: Knizhnaya. letopial, No 41 1957

ASO-NUI, A.0., red.,-, ZHUKHOTITSKIY, S.Tu., red.; KARAS". A. ,,'red.;
KOVTUNOV, G.A;;-,-WtffY9-Uf -nau`d1dy-jF sotradnik, reA,;
S.Is, red.; 13AYRVA, V.V., vedushchiy red.; POLOSINA, A.S.,
tekhn.red,
[Perfecting oil and gas drilling practices] Bovershonstvovani6
tekhaiki I tekhnologii bureniia na neft' I gaz; materialy.
-achno-tekhnizd-vo-nsft. I gorno-toplivnoi lit-ry,,
.,"_.Koskva., Gosna
1960. 347 pe (MIRA 13:9)
1. Vaeroosiyakoye soveshchaniyez4atnikov bureniya, trasnodar,
1958., -2w Rukovoditell iaboratori`i'promyvoc1mykh zhidkostey Xrasno-
derskogo filisla, Vassoyuznogo nauchno-issledovat skogo-instru-
mental' ovitakiy),. 3. KrazinodarskiyAlial
nogo institute (for Mmkh
Vsssojvuznogo nauchno-issladovatellskogo instrumentallnogo' Institute
(for Novtunov).
(Oil well. drilling)

5~
AUTHOR: Zhukhovitskiy,, S. Yu.
TITLE: Measuring the Static Shear
staticheskogo napryazheniya
93-6-5/20
Stress of Clay Solutions (Ob izmerenii
sdviga glinistykh rastvorov)
PERIODICAL: Neftyanoye khi)zyaystvo, 1957, Nr 6, pp. 17-19 (USSR)
ABSTRACT:
Card 1/2
In order to characterize the mechanical properties of clay solutidns
~L great number of constants must first be determined. These constants
fal.1 within five main groups, namely., elasticity, viscosity' boundary
stress, yield pointsp and strength of structure. Yost of these
constants must be taken into consideration in determining static
shear stress. The questions raised in,A.A. Linevskiy's article
(N&ftyanoye khozyaystvo, Wr 4, 1954) can*be Answeted only after
a.detailed analysis of processes taking place in rotational in-
struments with coaxial cylinders or with a tangentially moving
disc (Rebinder-'Veyler instrument). - After the outer cylinder of
the former irfstrument, has begu'n~ to move, or after the table of the
latter instrument has been lowered, the rotation of the cylinders
and the shift of the table and disc coincide. This takes place
within the limits of elastic deformation of the clay solution. As
the rotation of the outer cylinder or lowering of the table continues,
the acting strdsaes exceed the flow (creep) of the clay solution in
the area of intact structure. The plastic deformation taking place,
as correctl3Pted by Kister, E.G., and'Zlotnik, D.Ye, (Neftyanoye'
khozyaystvo, Nr 4, 1955) is considerable and can be easily observed.

93-6-5/20
Measuring the Static Shear Stress of Clay Solutions (cont)
A*.'A. Linevskiy erroneously erroneously took it to be the consequence of over-
coming the static shear Stress. As the rotation of the outer cylinder or the
lowering of the table continues, the stress reaches its maximum, above which a
quickly spreading rupture of structure occurs. The maximum stress causing
this rupture of structure is defined as.the static shear streas. The U-shaped
tube instrument recommended by Linevskiy cannot be used for measuring the
ultati~ shear stress. The determination of the static nhear stress of clay
solution is of considerable importance in selecting oil well drilling fluids
which must.possess a consistency capable of holding in suspension and bringing
the cuttings from the bottom,of the bore hole to the surface. In conclusion
it is stated that the static shear stress of clay solutions is measured by the
maximum torque angle of the suspended cylinder in rotational instruments
(CHC-12 CHC-2) and by the maximum elongation of the spring in Rebinder-Veyler
type of instrument. The instrument with a U-shaped tube, recommended by
A&A. Linevskiy, is not based on the right principles and for that reason it
is unsuitable for measuring,static shear stress of structural systems. There
,ar6 eight Slavic references.
AVAILABLE: Library of Congress
Card 2/2

ZHMOTITSKIT, S.Tu.
Measuring static pressure oflishoention of drilling muds.
Neft.khoz- 35 no 6:17-19 Je 157. (M1RA 10:7)
(Oil well drilling fluids) (Strains nnd stresses)

nT-17--
664.4
. Z61
Glinistyye raetvory v burenii (Olay mortar In drilling) Moskva,
Gostoptekhizdat, 1955.
170 p. Diagra., tables.
Literatura: p. (169)
1.

MIUMVITSM', 3,,Yu,; VDVAWA, A.A., redaktor; TROYMOV, A.V., redaktor
[Drilling fluids) Glinistve rastvory v burenii. Mookya, Gas. natchno-
tekhn. iod-vo neftlanol i g=otoplivnot lit-ry, 1955. 170 p.
(Oil-vell drilling fluids) (MLRA 8: 10)

ZHUXHOVITMaY, S#TU,
Method for distermining the degree of coagulation of drilling
MAR. Trudy VNII no.17:lo6-i22 '58 (KEU 12: 1)
(Oil well drilling fluids)

ZHUMOVITSKIE., S.Yu.; TOVAROVAs tLL.
Effect of drilled, clay on clay- muds. Trudy KF VNII no.5:169-173
161. (MERA 14:10)
(Oil well drilling fluids)
F1

KOBMLIDI ~.;ZHMOVITSKIT. Yo.
Measurement of the elasticity modulus of substances with high-dogres
sound absorption. Zhur.tekh.fiz.25 no.11:1998-2007 0 '55. (KLRA 9:1)
1,Xasticity-Keasurement)

GERSHUNIO G.ZA ZHMCVITSKIY, Ye.M.
Conveotive instability spectrum oF, a conducting medium in
,field. Zhur.eksp.i teor.fiz. 4~2 no-4:1122-1125 Ap 162
(P
1. Parmskijv gosudarstvenW univeWzW,,-;jt, i Permskiy gosudar
pedagogicheakiy inatitut.
(MagnaMTA
fi Ai
:t jf~~71 III M 1 , 1 1,
. "ii~,7-"11lriili

%WWOROYeathility of convection FD-Y5
Card 1/1 Pub.. 65 - 10/20
Author Zbukhovintl3kiy, Ye. M. (Molotov),

Title Applicatian of the Galerkin method to the problem of the sta
bility of a nonuniformally heated liquid
Periodical : Prikl. mat. I mckh.) 18P 205-211, Mar/Apr 1951,
Abstract : Develops a
method for solving approximately the problem of the
-
conditions for.the occurrence of thermal convection in liquid
heated frcm below. Presents examples of the application of this
method to cases of vertical and horizontal cylindrical zones. Seven
references, including V. S. Sorokin, "Variational method in the
theory of convection~" PMM, 17, No 1, 1953-
Institution Molotov State Pedagogic Institute
Submitted January 27, 1953

UT/py C-8 ;~'Lon
Car~ 1 1
Author : ZhukbIovitakiy, Ye. M. (Molotov)
Title : Stability of nonuniformly heated fluid in a vertical elliptical
cylinder
Periodical : Pril-~L. mat. J. mekh., 19, Nov-Dee 1955, 751-755
Abstract : Theauthor considers the problem of the conditions governing the
occurrence of thermal convection in a vertical elliptical cylinder
heated from below. He solves the problem approximately by the
Galerkin method (S. G. Mikhlin, Pryamyye metody v matenaticheskoy
fizl.ke (Direct methods in mathematical physical, State Technical
PresB, 1950), after deriving the principal equations (cf. author's
"Application of Galerkin to problem of stability of nonunifornLly
heated fluid," ibid., _18, No 2, 1954). The author notes that his
calclilated results are in agreement with the experimental results
ofV. V. Slavnov (Dissertation, Molotov University, 1952). Five
references: e.g. V. S. Sorokin, "Variational method in theory of
convection," ibid., 17, No 1, 1953.
Institution
Submitted November 29, 1954

AUTHOR: zhukavitskiy, Ya ;'011/126-6-3-1/32
TITILE: On the Stability of a Non-Uniformly Heated Electrically
Conductin- Liquid in a Magnetic Field (Ob ust-oychivosti
C;
neravnomerno nagretoy elektroprovodyashchey zhid-Icosti v
magnit-nom pole)
PERIODICAL: Fizika Metallov i 1.1etallovedenlye, 195.8, Vol 6, Nr 3,
PP 385-394 (USSR)
ABSTRACT: Sorokin has shown (Ref.1) that a liquid heated from under-
neath in such a way that a. constant uniform vertical -tempera-
ture gradient appears in it may be in equilibriwii. This
equilibrium will be stable only if the temperature gradients
are small. If the temperature gradient reaclies a certain
critical value definite motion will occur in the liquid,
There exists an increasing sequence of cricital gradients
which is sucla that, when the liquid passes -through each of
them, its eq:ailibrium becomes unatable with respect to the
correspondiAg perturbations. If the liquid is electrically
conducting a-ad is placed in the magnetic field, then when
motion occurs, electrical currents will be induced in the
liquid and the interaction of these currents with the field
will have an effect on the motion. The conditions under
Card 1/7 which convective motion will occur in an electrically

SOV/126-6-3-1/32
On the Stability of a Non-Uniformly Heated Electrically Conducting
Liquid in a Magnetic Field
conducting liquid may also depend on the magnetic field and,
in part, the presence of a magnetic field may alter the
magnitude of the critical gradionto and the form of critical
motion. It has been shown (Refs.2 and ') that the presence
of a magnetic field improves the stability of equilibrium:
convection will occur at higher temperature gradients-than
in the absence of the field. In the present paper a study
is made of the occurrence of convectivemotion in an electri-
cally conducting liquid in the presence of an e-xternal mag-
netic field. The particular problem considered is that of
an infinite vertical cylinder (the corresponding problem for
the case when. the field is absent vias solved by Ostroumov
(Ref-7)). The equations describing convective motion of an
incompressible electrically conducting 11 uld in the magnetic
field are written down in the usual form ~Eqs.l, 2 and 3).
These equations are completed by the addition of Maxwell's
equations (Eqs.4, 5 and 6) and the equation describing Ohm's
Card 2/7

SOV/126-6-3-1/32
On the Stabilit:7 of a Kon-UniforMly HeatOd Conducting
Liquid in a Magnetic Field
law in a moving liquid It io assumed that displace-
ment currents may be nc-Slected in comparison Nvith conduct-
ion currents and furthermore. in the heat conduntion equation
viscous dissipation and Joul~ heat may also be ex,.luded. The
equations are then re-expressed in a non-dimensional form:
9k
IV(p + hlait) + At., 111a yT + ft(aVP)T1 (13)
P Yv +.AT (14)
(aV )v +. 401 (15)
Pn*l Ft
Here, is the intensity of the magnetic field$ is the
velocity of the liquid, p is the pressure, M is the so-
called Hartman number:
Card 3/7

SOV/126-6-3-1/32
On the Stability of a Non-Uniformly Heated Electrically Conducting
Liquid in a MagneticTield
ILRH 11
M go is the constant internal
c
magnetic fiel&. Ra is the Rayleigh number, Y is a unit
vector in the vertical direction. T is t.be teninerature and
I'm where ji a are the magnetic permeability,
electrical conductivity and ki%ematic viscosity respectively.
the liquid.
The parameter.~. ~m characteri,jes the proporties of
For mez cury this parameter is approximately equal to 10
Eqs (1~i) and (15) are linear and should therefore contain a
tim;,fELCtOr 0'%-pk-Wt) where in general, w is complex so
that o) - w "~_ -i-w2 . The equilibrium of the liquid will.be
stable if w -.>O and in this oaoe the perturbations are
Card 4/7

SOV/126-6-3-1/32
On the Stability of a Non-Uniformly Heated U"lo,_,tricaily Conducting
Liquid in a Magnetic Field
damped out. I If w14-105: following a transition stage, stationary oscillations are set up for which
the stream function and t'he temperature as well as all piarameters of the solution-
temperature.gradient in the nucleus, Nusselt number, etc.-fluctuate around certain
average values, tho frequency of these fluctuations increasing with Gr. These oscil-
lations may possMLy be due to the development of small-scale motions, although it is
also possible that they have a physical basis in the formation of traveling waves in
the boundary layer,which have been experimentally observed. Orig, art. has: 8
,figures, 11 formulix.
~Sp~_~-'COM 20/ BULM DATE.:' 'o4Apr661 oRia Rw: 010/ OTH MW s 009
Card 2/2

ACC NRt
AP7001575 SOURCE CODS, UR10421166100010061WJ310099:
AWHORS: Gershuni, G. Z. (Perm'); ZhukhovitakiYt Ya, H. (Perm'); Tarunin, To, L.
(Perml')
ORGt none
TITLE'; Numerical fitudy of the convection of a liquid heated from below
SOT.CB: AN SSSR. Izventiya. Mekhani":zhidkosti i gazat no. 6, 1966t 93-99
TOPIC TAGS: digit&l computerg heat convection, NuBeelt number, Reynolda number,
Prandtl number, boundary value Iwobleml mathematic determinant/ Aragato digital
computer
ABSTRACT: This -paper presents a numerical sjudy of the plane convective moticn of a
liquid in a closed.square caviti (Bee Fig. I
x
Fig. 1.
Car 1/3

Sam
ACC NRt AnOO1575
'The convection equations for the flow function and temperature T in dimenoionleac
form are:
Aip + AAV or
OY Ox Or 8V 004,
r a,# or
-rt+ 7VTy-) -r, AT (P
where G and P are the Grashof' and Prandtl numbers., The units of distance, timet the
flow function, and temperatw7e are ap S21V 9 Vj and e, respectively. The method of
nets is used to,oolve the initial system of equational and the critical motiona
corresponding to the first four levels o tho spectrum.are shown (see Fig. 2).
00
Fig .. 2. 00 J.
All
The lower critical value of the Reynolds number R is the boundary of equilibrium
stability, I ound that at as of G below a certain critical value G all
t wao'f valu I
.initial perturbations are attenuated and equilibrium is the limiting stationax7
regime. Stationary oscillations exist only in the'range of Gra8hof numbers of
Card 213

ACC NRs AP7001575
5090 < G 4 62 000. Calculations with a 25 x 25 not showed that the frequency and
-do
form of these osoillatione tire' tersined onV by the parameter 0, Ifetaotablo
motions are discussed brief1q, -Orig. art* hast 13 formulas, 6 diagramep and 4 graphs.
SUB CODE: Z01 SUBII D&M I8Jun66/ ORIG REFt 0061 OTH RM 001

BIRIKH., R.V. (Perml)j GERSHUNI, G.Z. (Form'); ZHUKHOVITSKIY, Ye.M, (Perml)
Spectrum of pgrturbationB of plane-parallel flows at small
Reynolds n=bsro. Prikl. mat. i-makh. 29 no.D88-98 J&-F
165. (MIRA 1884)

GMSHUNIF PiGHOVITSKIX, Ye.M.:- 7,AYTS:,,V, V.M.
Electronic e.truature of thp inthane iroleculle. Zhur. strukt.
khiia. 5 ro.Lg598-603 Ag 164. (11:RA 1813)
1. Permskly gosudarstvannyy unlvers!tet I Pemsk~y gosudarst-vannY7
pedagoglehe.skiy inall-itut.

GERSHUNI, G.Z.; ZHIJKHOVITSKIY, Ya M.
Rotation of a sphere in a vincous conducting liquid in a
magnetic field at high Reynolds numbers. Zhur.tekh. fiz.
34 no. 2:336-339 F 164. (MIRA 1716)
1. Permskly gosudarstvennyy universitat i Permskiy
gosudarstvennyy pedagogicheskly institut.

4ACCESSION M AP4015965. 9/0040/63/qZ7/00 79JO7e3
IAUTHORS- Gershuni, G. Z. (Peirm!); Mukh"i (Porm,
'ITITLE: ~arametric e0iditlation -of convective instability
miatewl'i mekhan.1-vo-27t n
SOURCE I o. 5p 1963, 779-783
iTOPIC TAGS: parametric excitationt-convective insta.bilityt temperature gradientt:
I a paxametrio resonance, heat equationp
~nonstaticnflrV. equilibriixi, auto o cillation,
ABSTRACT*., Conveotiva'Atability,.of a.fluid in a gravity field is generally studied
:*under' ent'does not depend on
the assumption that: the equilibrium. temperature gradi
time. 1(onstationary.- e4~%ilibrium, of~ fluid As:als.o. possible 0 where the equilibrium-.
temperature dhanges.,with~_ time 4, a law determined by nonstatioT=7, heating concli-
tions. Apparently 0 -.,-stability ofsuch nonstationary equilibrium has not yet been
studied The authors'l'ar'kl' Interested particularly in the case where the equilibrium~
a eri. ically with time. The fluid is represented as
'temperature.gradient chartge p od
~anauto-6scillating system with-p9riodidally,obanging parameter. Under such condi-.
itionsVifiteresting phenomena of-the parametric resonance type are to be expected.
'The authors investigate stability,6f equilibrium of,&.plane horizontal fluid layer
Card

ACCESSION NH: AP4013424 S/00157/64/034/002/0336/0339
AUTHOR:,. Gershuni G.Z.; 2huWiovitskiy, Yo.M.
TITLE: Rotation of a sphere'.,ina viscous conductive liquid in a magnetic field'af
large Reynolds numbers
SOLMCE: Zhurnal tekhn.2iz*,v.34,* no.2, x 1064, 336-339
:,,,.TOPXC TAGS: magnotohydrodynainics, turbulent magnotohyd rod ynamics , turbulence, boun-
dary layer, magnotohydrodynaiaic boundary layer
:-ABSTRACT: The rotation of a non-condubting sphere in a viscous conducting liquid in
the presence of a tMilorm. magnetic field parallel to'the axis of rotation. is dis-
cussed.' The hydrodynamic Reynolds nwaber is assumed to * be large, so that a bounda-
ry layer is tormed7-the magniatic Reynolds number,is assumed to be smallo so t
hat
!~tho induced liald is small compared with the applied field. Th
a velocity of the
liquid in the boundary layer of uniform thicimess d is assumed to be given by
v,, toR zY ain 0-* vo=au)Rz(1-z)2sin20
where r, 0, (P are the usual rdinates, R is.the radius-of.t
aphericAl coo he sphere,
a is'a constant'Vo be detemined with d and-
card

-ACC -0 NR: AP4013424

z .(r-R)/d.
Express ions- are derived-for the-com nents of.-the current induced in the liquid.The
PO
currents are siall outside the b~6undary layer. Th% parameters a and d describing
the boundary layer are evaluated by integrating the Stokes-Xavier equations (includ-
ing the electromagnetic forces) across the boundary layer, employing the equation of
continuity to eliminate the radial component of the velocity. Finally, an exorqssio 'n
is derived for the braking (retarding) torque on the rotating sphere. For small ap-
plied fields, the braking torque is a linear function of the square of the applied
fir-ld strength; for large applied fields, the torque is proportional to the field
strength. The torque obtained, here~for large fields agreas within 2% with that pro-
viously calculated (O.Z.Gershuni and Yeoll.Zhukhovitakiy,ZhTF,30,1067.,1960) for
small Reynolds numbezs. Orig.art.has: 26 formulas.
ASSCCIATIOAN: Permskly~-, gosudar'stvo.nny*y universitet (.Pe=l Staie Univer -sity)j
Permskiy gosudarstvenny*V pedagogLcheskiy institut ( Pe=l Pedagogeal lutitute)

SUBMITTED:' 24Jan63 ENCL:
DATE.AC:Q,26Feb64 '00
SM COVE PH
In REF GOVI 001 (MER* 002.
Card

B/056/62/042/004/033/03T
13125/BI02
AUTHORS: Gershunil G. Z., Zhukhovi*vnki
TITLE: Convective instability spectrum of a conducting medium in a
magnetic field
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, V. 42p
no. 4, 1962f 1122-1125
TEXT: The conditions for oscillatory convective instability of a
conducting medium in a magnetic field are determined. A vertical plane
layer of a conducting medium is heated from below in a magnetic field.
The equilibrium is disturbed so that the velocity ; and the perturbation
~of the field 9 are vertical. The temperature perturbation is T w T(x,t),
where x is the coordinate taken from the center of the layer in a
transverse direction.. The pressure gradient is zero, and all quantities
depend on the time t .as ext . Then, the equations derived from the ordinary
equations of magnetohydrodynamica
%v'= tf +,RT + MIH',
).Pr v + 7, lPjnff - v' +
Card 1/3

8/056162/042/004/033/037
Convective instability spectrum ... B125/B102
(R : Rayleigh number, 11 w Hartmann number, P Frandtl numbery
P. OdVlc~~), have the solution v - v 0sinnx, T - TosiAnxt H Ho coanx (2)i
if v - 0, T 0 holds for the ideally conducting boundaries x +1 of the',
layer. The equations for the eigenvalues X of the perturbation~-(2) give
the equati6ne R x4 2M2
(P + PI) (I + P111) P PI
iR, PI + I + P-P2 M'V (8) and
b-=.--L(L-P-- P (9)
PM a3 I+P
for the bradches of the stability curves for monotonic and oscillatory
perturbatio 2
ns'. (7) end (a) are straight lines in the plane (RjM )* As
V. S. Sorokin pointed.'out that oscillatory instability occurs with certain~
properties of.the medium (064102> 1) and sufficiently strong fields
2
.7
(Y, >R). The critical field strength W . x (1 + P)(Pm - P) follows from
the condition R1 0 R2# This 'condition is evidently fulfilled for cavities,
of any shape. The necessary condition for the existence of an oscillatory
Card 2/3

S/05 62/042/004/033/037
Convective instability spectrum B125YB102
instability reads
Pmlp>~lTlsdV~irotHIldVI~IHI'dV~IVTIS(iv (14)t
the right-hand side being of the order of 1. There is I figure. The
English-language reference reads as follows: S. Chandrasekhar. Phil.
Mag -41, 501 , 1952.
ASSOCIATION: Permskiy gosudarstvennyy universitet (Perm state University)
Permskiy gosudarstvennyy pedagogicheekiy institut (Perm
State Pedagogical Institute)
SUBMITTED: No:vember 22, ig6i
Caid 3/3

S/05Y60/030/008/007/019
B019 13 060
AUTHORSs 'Gershuni, G. Z., Zhukhovitakiy, Ye. M.-
TITLE: The Flow of a Conductive Liqui Aroundra Sphere in a Strong
Magnetic Field
PERIODICAL: Zhurnal t-ekhnicheskoy fiziki, 1960, Vol. 30, No. 8,
926
pp. 925
TEXTt The authors considerthe flow around a sphere of a conductive
liquid1with a low Reynolds number in a magnetic field. The field direction
is as umea to lie in the direction of flow. They proceed from the steady-
state equations (2) and (3) in nondimensional quantitiest and obtain
solutions (4) which, for.weak magnetic fields, correspond to the results
obtained by Cheater (Ref. 1). The calculation of the coefficients is dea2L
with, and it is finally stated that with large field strengths resisting
power grows proportionally with the field. There are 4 references:
3 Soviet and 1 American.
Card 1/2

The Flow of a Conductive Liquid Around a Sphere 8/05 60/030/008/007/019
in a Strong Magnetic Field B019YBo6o
ASSOCIATION: Pormakiy gosudarstvennyy universitet (Perm-1 State University).
Permskiy yedagogicheskiy institut (Perm' Pedagogical
Institute)
SUBMITTEDs February 22, 1960
..Card 2/2

r
ZHUKWVIMKIY, K.., GEmmio (Perm)
"On the Motion of an Electrically Conducting Fluid Surrounding a Rotating
Sphere in the Presence of a Magnetic Field."
report presented at the F:Lrst All-Union Congress on Theoretical and Applidd
Mechanics, Moscow, 27 Jan 3 Feb 1960.

.*AUTHOR: ZBIXHOVITSKIYI Ye.M. (Perm') 40-5-10/20
TITLEt On the Stability of a Nonuniformly Heated Liquid in a
Spherical Cavity (Ob uBtoichivosti neravnomerno nagretoy
zhidkosti v aharovoy polosti)
PERIODICAL: Prikladnaya Mat. i 1[ekh.s1957,Vol.21#Nr 5 pp,689-693 (USSR)
ABSTRAM In the pa-per the problem of the stability of a heated Liquid in
a spherical cavity is investigated# Thm medium in which the oa-
vity is epared is assumed to be infinitely extended. The system
is to be heated from below. The task of the paper is the calcu-
lation of the critical vertical temperature gradients for which
the liquid lamination begins to become unstable. It is well-
known that this temperature gradient depends on the Ralei(yh-
numbers Under the boundary conditions valid for the sphere the
critical Raleigh-numbers are calculated for different cases
vith the aid of Galerkin's method. For the calculation accord-
ing to Galerkin a series expansion set up with at first unknown
functions is chosen for the velocity of the flow in the liquid,
the functions are of ouch form that the bdundary conditions are
satisfied. A recurrent system of defining equations is given
for the approximation functions which are set up as polynomials
Card 1/2 of throe variables. The solution itself than can be obtained in

On the Sta-bility of a Yonuniformly Heated Liquid in a 40-5-10/20
Spherical Cavity
spherical coordinates by Legendre polynomials. For a series of
cri-tioal oases the critical Raleigh-numbers and the ratio of
the heat oonductivity coefficients of liquid and solid body
were calculated. Some typical flow patterns for the critical
cases are given.
There are 2 figures, no tables, and 2 Slavio references. The
author mentions V.S. Sorokin [Ref ell and I.G. Shaposbaikov
SUBMITTEN December !)y 1955
AVAILABLEs Library of Congress
Card 2/2

88010
S/170/60 03/012/007/015
0(9 B019/BO5~O
AUTHORS: Gershuni, Go Zop~z""Jgjk Ye. M.
TITLE: Heat Transfer Through a Vertical Gap With Rectangular Cross
Section in the Case of Strong Convection
PF2.IODICAL: '.Inzhenerno-fizioheskiy zhurnal, 1960, Vol. 3, No. 12t
;p. 63-67
TEXT: It is assumed that in the rectangular.gap investigated in the
present paper,.the temperatures of its vertical walls are constant and
amount to -9 an.d+G. In the horizontal oross sections the temperature
changes from -6i to +G. Firstp the flow function is derived, the boundary
layer being assumed.to be considerably thinner than the thickness d and
the height h of the gap. Next, the motion in the boundary layer is
investigated. A. system of equations for the velocity and the temperature
of a.liquid in the gapis given and approximate solutions are obtained.
As a condition for the applicability of the approximate solutions obtained
here, GrPr))50(,3/2, where Gr is the Grasshoff number, Pr the Prandtl
Card 1/3

88MO
Heat Transfer Through a Vertical Gap With B/170/60/003/012/007/015
Rectangular Cross Section in the Case of B019/BO56
Strong Convection
number, and h/d,'~1. Finally,a formula for the heat transfer through
the gap is obtained. System of equations for velocity and temperature of
the liquid: 2 2
vxavx/ax + vyavxl/ay = UdU/dx + a vx/ay Gr~(x)T (5)
vxaT/ax + v yaT/By - (I/Pr)a 2Tlay2 (6)
avx/ax + av ylay .. o (7)
The approximate solutions are:
= p (Z) + 1,'Z)U(X).+ p (z)co 2nx (8)
v
x 0 Pi 2 '1+1
T = ql(z)To(x) + q2(z)cosnx/('+') (9-)
~(x) is a function, which for the upper and the lower wall of the gap is
0, for the lateral walls -1 or +1. z = y/6, where 6 is the thickness of
the boundary layer, the coefficients P, and q i must be taken as polynomials
corresponding to the boundary conditions. For the heat transfer through
Card 2/3

88010
Hoat,Tranofer Through a Vertical Gap With S/17 60/003/012/007/015
Rectangular Cross Section in the Case of B019Y3056
Strong Convection
the gap the relation b
(aT/ay)0dx 0-739X~GrPr)1/419/8
a
was obtained. There aro I figure and 4 references; 3 Soviet.
ASSOCIATION: Gooudarstvennyy %;niversitetj Gosudaretvannyy pedagogioheakiy
institut, g. Perm' (State University, State Pedagogical
Instituto, Perm')
SUBMITTED: May 27, 196o
Card 3/3

GZRSMMI, G.,Z.; ZHUIEDVITBUT TO*N*
Rotation of a,sphers, In a viscous conducting liquid in a magnetic
field, Zhir. trikh,. fis. 30 no.9tlO67-1073 3 160. (MMA 13: 3-1)
1. Porrmakly gosudaretvennyy universitat I Permskiy gosudarotvenny7
Fedagogicheskiy institut.
(Nagnetohydrodynamice)

S/057/60/030/009/011/021
B019/B054
47
L// 0
AUTHORS: Gershuni, G. Z. and Zhukhovitakiy, Ye. M.
TITLE: Rotation of a Sphere in a Viscous Conducting Liquid in a
Magnetic Field
PERIODICAL: Zhurnal tekhnicheakoy fiziki, 1960, Vol- 30, No- 9,
pp. 1067-1073
TEXT: The authors study the motion of a viscous incompressible conducting__
1i uid,11;;ound a steadily rotating sphere in the presence of a magnetic
fie d in th~e'direction of the rotational axis. They assume the case of
slow rotation in which the inertial forces can be neglected as compared
with the viscous forceag'i &e.j they assume a low Reynoldenumber. The mag-
netic-Reynol ds numb 11 r is also assumed to be low. The authors obtain ex-
pressions for the distribution of the velocity and the induced field, as
well as formulas fox, the braking moment. In the case of weak fields, the
braking moment increases proportionally to the square field strength. In
the case of high field strengths, the dependence is linear. The problem
arising with slow rotation of the aphore in a conducting liquid in 'a
Card 1/2,

Rotation.of a Sphere in a Viscous Conducting 3/057/60/030/009/011/021
Liquid in a Magnetic Field B019/BO54
longitudinal magnetic field was solved in successive approximation by
Yu. K..Krumin' (Ref. 1). He found a solution of this problem for weak fields
in which the velocity~distribution differs only slightly from that with-
out a field. In the present paper, the authors obtain a gJneral solution
which also holds for strong fields. In this connection, the authors set
up, in the first part, a linearized equation of motion of a viscous in-
compressible oonduoting liquid in dimensionless parameters. They obtain
solutions for the velocity of the medium and the field strengths with the
aid of Legendre polynomials and Bessel functions after a projection of the
said equation-of motion on the Z-axis which aoincides with the rotational
axis and the magnetic field direction. These general solutions are dis-
cussed for week and strong fields. There are 3 Soviet references.
ASSOCIATION: Permskiy gosudarstvennyy universitet (Perm' State University).
Permskiy gosudarstvennyy pedagogicheakiy institut
(Perm.State Pedagogical Institutel
SUBMITTED: March 25, 1960
Card 2/2

all I
J4
JA
fit
Ail
js 4
JIM

GIRSHM G. Z. ZHUKHOVITSKIT, Ye.m.
Closod comedtion boundary layer. Dokl.AN SSSR 124 no.2:298-300
Ja 15 9. (MIRA 12:1)
1. Pormakik,g6ou daretvanM7, universitet imeni,A.M. Gor1kogo
i Permakly padagogicheskiy institut. Predstavlano akademikom
M.A. Leont'oOicbem.
(Heat--Convection)
IN, IRS
P-M m-F Snag mg p a it

K A/ e) V
:GJMSHUNI, G.Z~; ZHUNHOVITSICITkI. TeemO
Stationary convective motion of an electrically conducting liquid
between paraIlel planes in a magnetic field. Zhur,eksp. i teor. fit,
.34 noi3:670-674 Mr 158. (MIRL l114)
1,Permakiy gpeudarstvannyy universitet i Permakly pedagogicheWdy
institute
(TAquide-Blect-ric properties) (Magnetic fields)
LOW
M. MI LIU

e-,M,
GUSHnUN OOZ.1 2
Stability of, stationary convoctive.mDtion of an electrically con-
ducting liquid between parallel vertical planes in a magnetic field.
Zhur.eksp. i teor. fiz. 34 no.3:675-683 Mr 158. (MM ilt4)
1.Permskiy gosudaret-vannyr universitat i Permakiy gogudaretyanW
peaagogicheekiy, institut.
(Idquids--Electric properties)
(Magnetic fields)
7"
111.11111711 oil NJ PICIIIII 11-1111,110" sag

124-57-Z-Z032 D
Translation from~ Referativnyy zhurnal, Mekhanika, 1957, Nr 2, p 78 (USSR)
AUTHOR: 2hukhovitskiyl Ye.
TITLE- Methods for Solving Problems of the Theory of Free Thermal
Convection and Some of Their Applications (Metody resheniya
zadach teorii svobodnoy teplovoy konvektsii i nekotoryye ikh
F-rimeneniya)
ABSTRACT. Bibliographic entry on the author's dissertation for the degree
of Candidate-.of Physical Sciences, presented to the Molotovskiy
gos. un-t (Molotov State University), Molotov, 1954.
ASSOCIATION Molotovskiy gos un-t (Molotov State University), Molotov
:1, 11jeat excha-rige--Theory 2. Convection--Theory 3. Mathematics
Card 1/1

SOTI/126-6-2-22/34
AUTHORS: Gershunit G. Z. and Zhukhovitskly. Ye.
MA PWU
TITLE: Forced Vibrations in an Elasto-Plastic System
.(V*ynuzhdennyye kolebaniya v uprugo-plasticheskoy sisteme)
PERIODICAL: Fizika Metallov i Metallovedeni7e, 1958, Vol 6, Nr 2,
pp 339-346 (USSR)
ABSTRACT: Forced vibrations in an elasto-plastic system beyond
the elastic limit are considered. Friction and hysteresis
are taken into account, The resonance properties of such
a system are discussed and compared with the experimental
data given in Refs. 1 and 2. The equation of motion of a
point under the action of an elasto-plastic, force F(x)
and an external forcerG sin (wt + 9) is of the following
form
Mx + X~ + F(x) = G sin (wt + (p) (2)
where X is the coefficient of friction and F(x) is given
by:
I 2(x - :xm)
F kix, F, Fm + k
Card 1/4 FIII ki(x. Fv -FM + k2 (m + xM

SOV/126-6-2-22/34
Forced Vibrations in an Elasto-Plastic System
where the various constants have the meaning indicated
in Fig.l. The above equation is then re-written inthe
dimensionless form
x + Ox + f(%) = g sin (pt + ~o) (4)
where
P W/Woj g G/FM1 P = N/MWO, f + F/Fm
fl = X) f II + a (x
fIII x - -61 fIV 2 -1 + cc (x+ 6),
k
2
and a =
XM
The problem consists of finding periodic solutions of the
above eqaation which have a period 2Tr/p. i.e. equal to the
period of the forcer. The appropriate system of boundary
conditioas is given by Eq.(6). The equations are solved by
Card 2/4 azi approximation method suggested by B. G. Galerkin.

Forced Vibrations in an Elasto-Plastic System SOV/126-6-2-22/34
In the case 0 the resonance curves are as shown in
Figs. 2 and 3 (cc - k2/k - cf. Fig.1). The form of the
curves indicates the prislence of considerable absorption
due to hysteresis. The assymmetry of the curves
becomes more pronounced as cc decreases. The 10111
.frequency side of the resonance curve is steeper than
tho high frequency side. When the coefficient of
friction is not zero the resonance frequency beyond the
elastic limit increases as friction increases. In
general, the resonance frequency decreasee at larger
amplitud.es of vibration and the relation between the
amplitude of vibration and the amplitude of -the forcing
function is non-linear. The problem was suggested by
Professor M. Kornfelld. There are 7 figures and
4 references, 3 of which are Soviet, 1 English.
Card 3/4

Forced Vibrations in an Elasto-Plastic System SOV/126-6-2-22/34
ASSOCIATIONS: Permakiy gosudarotvennyy univorsitet
(Perin, State University) and
Perms~iy pedagogieheskiy institut
(Perm.' Pedagogical Institute)
SUBMITTED: June 7, 1956
Card 4/4 1. Vibration--Theory 2. Mathematics-Applicationa
11"Womfom

GERSHUNI, G.Z.;,ZHUI',HDVITSKIY, Ta.M.
Fore-ed oscillations in elastic-plaotic systems. 71z. met. i
metalloved. 6 no-2:339-346 '58. (MIR& 1119)
1. Pmrmskiy 1paudarstvannyy universitet i Permskiy pedagogicbeskiy
institut,
(Vibrations) (Mastic solids) (Plasticity)
pill

,-ZMWMVITSKIT, Te.M.
Stability of irregulary heated electric current conductor liquids
in nagnetic fields. Pis. mot. i metalloved. 6 40-3:385-394 158.
(WRA 11:10)
1. Fermakiy.gosudaratvannyy podagogichenkly inatitut.
(Blectrolites) Oiquid metals) (Ixductios heating)

80V/139-5~8-4-6/30
AUTHORS.: Gershil-ni, q. Z. and Zhukhovitskiy, Ye.
TITLE: Two Types; of Unstatle C0jjvetttvT-7rft-Re-tr~en Parallel
Vertical Planes (0 dvukh tipakh neUBtoychivosti
konvekti-4mogo dvizheniya mezhdu parallelInymi
vertikallnymi ploskostyami)
PERIODICAL: IzveBt;iya V-ysshikh Uchebnykh Zavedeniy, Fizika,
1958, Nr 14, pp 43-47 (USSR)
ABSTRACT: The stability of stationary convective flow between
parallel vertical planes.held at different temperatures
has already been investi ated by the first author, using
Galerkin's method (Ref.l~. In the present paper the
authors have used a more complicated form for the
approximating functions (see Eqs-5), and have so found a
more accurate approximate solution. This has allowed a
more accurate calculation of the earlier results and has
in addition uncovered a second type of instability, not
given in the earlier work at all, a type with null phase
velocity which the authors call a "standing disturbance"
as opposed to a "travelling disturbance". Taking the
planes to be x = + 1, the dimensionless equations for
Cardl/4 stationary convecTive flow are given by Eq.(l). The

SOV/139-58-4-6/30
Two Types of Unstable Convective Flow Between Parallel Vertical
Planes
stream and temperature functions (p and E) of plane.
harmonic disturbances are given by Eqs.(2) and (3) with
~boundary conditions as in Eq.(4). G and F are the Grasshof
and Prandtl numbers, k and w the wave number and complex.
frequency of the disturbance. These equations were derived
by the first author (Ref 1). The question of stability
has thus been reduced to that of finding the eigen-values
of equations (2) to (4). The authors find an approximate
solution to this problem b assuming forms for (p and
of the type given in Eq.(N. They then make plausible
guesses at Wl, (P27191, 021 see Eqs.(6) and (8). All
boundary conditions are now satisfied by the approximate
solution. This solution differs from the cruder approxi-
mation the first author used previously (Ref 1) in that the
stream function W is now the sum of two functions, with
two variable coefficients, and that the additional
boundary condition on E), Eq.(?), is taken into account.
Using Galerkin's method, the authors obtain Eq.(12) for
real eigen values of w, and Eq.(11) for the corresponding
Card2/4 relation. between G and k. Eliminating w between

SOV/139-58-4-6/30
Two Types of Unstable Convective Flow Between Parallel Vertical
Planes
E4.(11) and Eq.(12), a curve is obtained in the (G,k) plane
which the authors call a 'neutral curve' - i.e. one
corresponding to real values of w. From the position of
the minimum on this curve the critical values of the
Grasshof number G and the wave number k can be found.
w = 0 gives a sol~fion of Eq.(12), and the corresponding
curve of GM against log P is shown in Fig.l. In the
range shown was practically constant, increasing only
from 1.6 to This is the instability that was not
revealed in the earlier viork (Ref 1). Excluding w = 01
for P> 1.8 the authors obtain the second type of
instability - the "travelling" type. For this type log GM
is plotted against log P in Fig.2 (full line). Eq.(14) is
asymptotically true, and a-good approximation for P> 50.
For this type Irm increases from 0 to 1.6 at P> 50.
For this type of disturbance there is a good agreement
with the author's earlier work (Ref 1). Thus eq'.(14) was
also obtained, though with 224 instead of 214 in the
numeratom, and the asymptote was reached at F = 0.96.
Card,3/4 The main results can be summarised thus:

SOV/139-58-4-6/30
~Rwo Types.of Unstable Convective Flow Between Parallel Vertical
Planes
For convective flow between two parallel planes held at
different temperatures, instabilities appear if ther5 is a
lcrge temperature difference between the planes. "Standing"
disturbances correspond -to P4 1.8, both types are
1.8, though for P;~ 2.2 the "travelling"
pOssible for F *
disturbances are the more dangerous as they correspond to
a smalle:o Grasshof number.
There aria 2 figures and 1 Soviet reference.
ASSOCIATIONS: Perjaskiy gosuniversitet (Perm' State University) and
Permskiy edagogicheskiy institut (Perm' Pedagogic
InstitutI3
SUBMITTED: January 8, 1958
Card 4/4

Obral),
i6bil'ity a*,f'an irre
.gularly heated liquid In a spherical cavity
Prikl, mat,II makh. 21 no.5r689-693 &0 157. (Km 1611)
(Stability) (Heat-Oonvoction)

ORMUNI, 0..Z.;,.ZHUIMOVITBKIY# YOOKS
Two types of unateady convection motion between parallel vertical
surfaces* hVevyetuchebezav.; fiz. no.4:43-47 158.
(MIRA 1.1;11)
1. Permokly gosuniversiteti Permakly pedagogicheekly instituto
(Heat-Coi*eetion)

AUTHORSi
TITLE:
PERIODICAL:
ABSTRACT:
Card 1/3
Gershuni, G. Z., Zhukhovitakiy, Yo. M. SOVI 56-3,4,-3-20/55
The Stationary Convective Motion of an Electrically Conducting
Liquid Between Parallel Surfaces in a Magnetic Field (Statsion-
arnoye konvektivnoye dvizheniye elektroprovodyashchey zhid-
kosti mezhdu parallellnymi plookostymmi v magnitnom pole)
Zhurnal Eksperimentallnoy i Teoreticheskoy Fiziki, 1958,
Vol. 34, Nr 3, pp. 670-674 (USSR)
The two planes referrred to in the title may be heated to
yarious temperatures. First, the equations of the motion of the
medium (these are the equations of convection in the case in-
veatigated here) and the Maywell equations for the field in the
medium.are written down. In the equation for the curl of the
magnetic field, the displacement current is neglected and in
the equation of heat conduction - the tough dissipation and
Joule dissipation. The electric field strength and the current
density-are eliminated first from Maxwell's equation. The
above-mentioned equations are subsequently converted into di-
mensionless variables- 4 dimensionless parameters occur in
these equations. The authors investigate here the steady

SqV156-34-3-20155
The Stationary Convective Motion of an Electrically Conducting
Liquid Between Parallel Surfaces in a Magnetic Field
convection in the apace between vertical parallel surfaces
in the case of the presence of an exterior magnetic field
which is vertical to the surfaces. If the linear dimensions
of the surfaces are sufficiently great compared with the
distance between them, then an accurate solution of the above-
-mentioned dimensionless equations can be determined which
describes the steady solution in the part distanced from the
ends.of the gap formed by the surfaces. 4hia motion has the
following pecularitiea: 1) The velocity v is always parallel
~ly on x. 3
to the z-axis. 2) The temperature T depends on xz~ The
field-vectorl is situated everywhere in the surface
viz. it holds Hy a 0- 4) All values do not depend on y
(plane problem) and 'except pressure, neither on z. In this
case the z-axis is parallel to the surfaces and the x-axis is
vertical to them. The authors determine here the distribution
of temperature, velocity and field strength on the cross
section. First, T a -x is found. Also the terms for the
velocity distribution and the magnetic field strength are
given explicitely; all these formulae together represent the
solution of the problem discussed here. A diagram demonstrates
Card 2/3 the velocity-distributions for the Gartman numbers M - 0,51l0.

SOV/56-34-3-20/55
The Stationary Convective Motion of an Electrically Conducting
Liquid Between Farallel Surfaces in a Magnetic Field
The velocitydistribution v Gx(x2 - 1)/6 is obtained with
lacking field. The motion decreases rapidly with increasing
field strength. Moreover, a peculiar boundary layer occurs in
. the flow: A thin layer with an important -radient of velocity
is formed in the vicinity of the walls. Also the distribution
of the induced magnetic field on the cross section is demonstrat-
ed by a diagram. Concluding, a formula for the vertical con-
vective thermic flow is given. The solution found here de-
scribeo the motion in a vertical gap in the presence of a
transversal external field..It may, however, be readily
general.ized for,cases with inclined gap and with an external
field oriented at random. There are 2 figures and 3 references,
1 of which is Soviet.
ASSOCIATION: Permskiy go3udarstvennyy universitet (Perm State University),
Permskiy pedagogicheskiy institut (Perm Pedagogical Institute)
SUBMITTED: September 19, 1957
Card 3/3

ROZIN-A, Sof!ym Sinoyevna; ZHWOVITSK ~fpisqyaviqh,
[City ok-Mishin and Its health resort] Gorod Kashin i ago
kmrort.~,Kulininp Kalininakoe Imizhnoe izd-vo, 1957. 159 P-
(IaRk 13:3)
-Mahin-Desoript ion)

AUTHORS: Gershuni, G. Z., Zhukhovitakiy, Ye. M. =/56-34 -3-21/55
TITLE. On the Stability of Steady Convective Motion of an
Electrically Conducting Liquid Between Perallel Vartienj

Plan4s in a .1bgnatic Field
(0b liatoyohivosti .9tatq1o-v,,rnogo
konvektivnopo Avizhentya elpActroprovodyashchey zhidkosti
nezhau pars1lelInymi vertlkallnymL ploskontyami v mrgnitnom
Pole)
PERIODICAL: Zhurnal Eknperlmentallnoy I Tooretichealcoy Pi7illi_, 1958,
Vol. 3.1, !.Tr 3, -np. r,75-583 (USSR)
ABSTRACT: First the authors refer to earlier ,-;orks dealillf! with the
same subject amonp, them one published by themselves (Ref.1).
The generalization to the cane of rnnclom pos'tion of the
nlanes is more dlfficult than in the ense of the steady
problem 7rid it can be cprried out In the sede way as G.Z, bersbmi
in his study (Ref First the equn tions f or the
_4i;_turbWti_.is are put down, the author3 here inventi.gating
p
t,wo-dimensional perturbation3. Also a current function M d
Card 1/ 4

I a vector potential are introduced. The -sign of the impginary
7-7 -ZTT,
M "t

-- ------- - -
tIvL
On the Stability.of Steady Convoc ,'otion of an Electri. SOV/36-34-3-21/55
caUyConductLng Liquid Between Parallel Vertical Planes in a idav~jietic
Field
Card 2/ 4
part of the frequency w determines the behaviour of small
perturbations. The authors then inention the differenti,.ql
eque.tions for the amplitudes of the perturbations of velo-
city and temperature inuat disappear in the pnrallel boundary
planes bounding the liquId; the corrospon(linp bouniary
conditiona are put down. The p~)rturbrttion.,3 of the mrv-en.)tic
field need, in general, not dDiappear; as bounddry'~on -
ditions for the field serve the usUn3.mnndiffons on the ible
separating surfaces of the mOdi.1- rmtIeMOre, ' two Poss
orientations of the constant external field are investigatecl-
1.-The con st it homogenous external field is situated -at
I
.0
right angles -o the parallel planes and thus also to the*
vector of the -relocity of the steady motion of the liquid.
an ~a
2.-The externa~-field has tho same direction as the velo-
city. With lonrAtu4inal and also with tranaverse fields the
amplitude of thq vector potential of the perturbation of
the field can b,"i-elininated from the equations. The problela
then reduces to he finding of the amplitudes of zhe current
function and of emperature from th'i given equations of the
b,
problem. an-I the) unlary conditions pertaining to it.

On the Stabl,lity of 15-teady Convective 121otion of an
Electrically Conducting Liquid Between Pnrallel Vertical Planes In a
Magnetic Field
This problem will have a solution only for certain values
of the complex number W In the aecond chapter of this
work the problem formed is nolved by approxi;aation according
to the method by Galerkin, the course of computation
being followed st-ap by step. The results obtained are
discus-~3ed separately for the case of a longitudinal and
a transverse field. In the transverse case the critical
wave number kM decreases monotonously with increasing M
..i.e. with the magnetic field becoming stronger the wnve
'length of the steady perturbations increases, Besides,
the investigated steady motion is unstable also with
regard to nonsteady perturbations when a transverse field
is present. Such a instability appears at sufficiently
great field strengths. A diagram shoIV3 the dependence of
the critical wave number on the field strength. In the
case of a lonmitudinal field the atability can be
compensatedonly by steady perturbations withW - 0 . A
Card 3/4 longitudinal field increases the stability of motion

Oithe Stability .of Steady Convective Motion of an BOV/ 56-34 -3-21/55
ElectrIcally Conducting Liquid Between Parallel Vartteal Plaaaa in a
,Magnetic Field
much less than a transverse fiold. In a lon.Tituelinnl
field1the critical wave number decreases monotonously
with incrapining fteld strength. The a.u8.1itative results
obtained can be made more- precise by their
appro cimstion method used. There arn 2 figuree, i table
and 9 referencest 4 of which are Soviet,
ASSOCIATIOIN Permakiy gosudaratvenny universitat (Stato -Univarsity
Perin) .,Pornskiy gosudarstvannyy padagogichoskiy Institut
(Perm.State Podagpgic Institute)
SUBMITTEDi Sept-enber 19, 1957
Card 4/4

240)
,.AUTHORS: Gershunip G. Z., Zhukhovitskiy, Ye. M. SOY/20-124-2-15/71
TITLE: A Closed Convective Boundary Layer
(ZaMknU16
yy konvektivnyy pogranichnyy sloy)
PERIODICAL: Doklady Akademii nauk7SSSRj f959, Vol 124, Nr 2, pp 298-300
(USSR)'
ABSTRACT: 'The present paper solves the problem of the closed conveotive
boundary layer in a horizontal circular cylinder. The surface
of the csylinder with a radius R is kept at the temperature
To M 0 vin x, where x denotes the coordinate along the circle and
(Da time-constaftt amplitude* The temperature assumed to be
homogeneous in the core is considered to be the temperature of
reference. The core is assumed to rotate as a solid at the rate
0)r, where the angular velocity co is required. The
boundary- layer equations (in disregard of the curvature of the
layer and with introduction of dimensionless variables) are.,
2
VX Vx vx
V + v 2 + G sin x T
x
Card 1/3

A Closed Convective Boundary Layer SOV/20-124-2-15/7~
2
-ZT- aT 1 T X
4- 0
VX BX. VY -a y Pr ~Y2 -6'-x -a Y
IHere G g 6.0 R3/V 2 denotes the Grasakhof number and
Pr the Prandtl number. The velocity layer and the
temperaAre layerare assumed to have the same thickness
6(6