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December 31, 1967
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Investigation of a Non-steady Flow of a Conducting S/05T/60/030/05/01/014 Liquid in a Plane Channel With Mobile Borders B012/BO56 boundary problems obtained will be discrete, which simplifies the solution considerably. There are 1 figure and 5 referenoi~s' 4 Soviet and 1 English. ASSOCIATIONt Fiziko-tekhnioheskiy institut AN SSSR Leningrad (Institute f Physics and Teohnolozy of the AS USSR, Loningrad) SUBMITTED: December 14, 1959 Card 2/2 ,.-UPLAND, Ta.S. Some cases of irregmlai motion of a conducting liq~ati in an annular pipee Zhure tekhe fiz. 30 n7o.7-.799-802 ii '6109 (MBU 13:8) 1. Fiziko-tekhnicheskiy institut AM SSSR, Leningrad. (Fluid dynamics) 8036 I 0-~,000 01, 2-"A 1 3/057/60/030/010/018/019 41 / t1 10 0 !r-111 B013/B063 ATJTHORa Ufliand, Ya. S, 01 TITLE- Steady Flux of a Conducting Fluid in a Right-angled Channel in the Presence of a Transverse Magnetic Field PERIODICAL.- Zhurnal tekhnicheskoy fiziki, 1960~ Vol~ 30, Yo., 10, pp, 1256 - 1258 TEXT: The rutior describes the plane.-parallel motion of all incompressible, viscous, rinducting fluid in a homogeneous magnetic field which is perpend'-',;ular to the motion-of the flu:id- An exact solution of this problem for the case of non-conducting channel walls was given in Ref.. I, The present paper gives an exact solution for another limiting case, i,e,, for ideally conducting~ right-,angled channel walls, The definite solution has the form of (17). (R - Reynolds number; M - Hartmann number'.. Since- m r the trigonometric series contained in (17) tend to zero for b--_~,co , the V first summands constitute a one-dimensional condition corresponding to the flow between two parallel walls of perfect conduction, From this it may Card 1/2 Steady Flux of a Conducting Fluid in a Right-angled Channel in the Presence of a Transverse Magnetic Field 847736 S/057/60/0--0/010/oia/oig BO-13IB06-i be that, contrary to Hartmann's well-known solution for the case of zion. z~:-ting walls (Ref. 2), such a one-dimensional condit*ion may hold ~u, walls have an arbitrary and infinite condu even - ction Ref., Contiary to th~! results of Ref. 1, the solution in the form of (17) is particularly convenient for calculations involving high values of the parameter k ~ b/a. i.e.,, for determining such corrections of the one- dimensional condition as take account of the effect of wide channels, y . 1 b. Therq. are 3 referencest 2 Soviet, ASSOCIATIONt Fiziko-tekhnicheskiy institut AN SSSR; Leningrad (Institute of Physics and Technology AS USSR, Leningrad) SUBMITTEI)a May 27, !960 Card 2/2 8037 S/05 60/030/010/019/019 Boi3 o63 7 1 -all YB /0 POOO f,-1,? AUTHORi Uflyand, Ya., S, .W=:= - --- TITLEi The Hartmann Problem for a Circular Tube PERIODICLLx Zhurnal tekhnicheakoy fiziki, 1960,, Vol~ 30, No, 10, pp, 1256 - 1260 TEXT3 From Refs, 1-3 it is known that for a viscous, incompressible, conducting fluid moving perpendicular to a homogeneous magnetic field (H.), the equations of magnetohydrodynamics read as follows,~ Ah + -au - 0, AU + M2 ah (1) , where a characteristic velocity. a a haracteriat Amension, R - Reynolds number, M - Hartmann number, m coeffir~ient of viscosity, P - gradient in the direction of motion. By meana of substitutions the set of equations (I) can be transformej into two sepaTate equations of the following form (4): &F -41 2F . 0, J~'f ~~L2'f - o; P. h112, The present paper deals with a circular cross Card 1/2 80P The Hartmann Problem for a Circular Tube S/057/60/030/010/019/019 BO!3/BO63 section of radius a. Such problems may be considered to be a generaliza- tion of the well-known one-dimensional Hartmann problem. The solution of equations (1) on the axis of the tube is given by trigonometric series, where Q , r/A; r and 0 are polar coordinates Q Cos 0),' I.(x) are n modified cylindric-al functions., The final soluiion of the problem is also_ given,, An exact solution to the corresponding problem for a ring-shaped crcas aection, for a flow around a cylinder, etc, may be obtained ~ Y\ similarly. This is illustrated by formula ( '10) for the velocity distribJ1 tion in a flow around a non-conductive cylinder which moves at a constant Velocl-ty v0 (Kn (Y.) - McDonald function)., It is noted that in ordinary hydroiynamics, such a problam has only a trivial solution v~.r of whereae in magnetohydrodynamie.9, velority tends to zero for r---,%oo . There are 4 referencrasi I Soviet ASSOCIATIONt Fiziko-tekhnicheskiy institut AN SSSR, Leningrad (Institute of Physics and Technology AS USSR, Leningrad) SUBMITTEDi July 11, 1960 Card 2/~? AUTHORS: TITLE: 30998 - 4011241611000100910221,058 ID234/D303 Lebedov, N.N. and Uflyand, Ya.G. 3-dimensional problem of the theory of elasticity for an infinite body weakened by two plane round holes PERIODICi-E: Referativayy zhurnal. Melchanika, no. 91 1961, 11 abstract 9 V6 (Tr. Leniagrr. politelchn. in-ta, 1960, no. ::~10, 39-49) TEXT: Th4authors concider the =ially symmetrical problem of th6 theory of elasticity for an infinite space containing two plane round holes (irith the centers on one straight line) of the same radius' situated on parallel pla-acs z - 0, z = -2h. On the surfaces of a hole, equal axially syrmnetrical distributions of nor- mal ((rz) and tangential ('d ) stresses are given and it is suppozeo''; zr that at the points of a,hole belonging to its different sides the stresses are equal in magnitude and opposite in direction. Wing 0*' " OOC/009/022/058 S/12~61_/ 303 3-dimensio-nal problem... D234 to the syminctry with respect to the plane:-z . --h the problem is reduced to co-nsidcring, an elastic half-bpacc z > It with the / boundary conditions L 0 of (Vrz)z--h . z--h and the appropriate conditions at inf inity. The solution in the regions - h z < 0 and 0 ,;~ z < oo is expressed in texTiis of harmonic Papkovichwileuber functions, Phonse deteimciination is reduced to two systems of even integral equations. These systems are reduced to ai system of Fredholm integral equAtions witin regular kernels. Unknown functions in the latter -we detennined and -in terms cf these, the quantities which are essential for the applications can be axprcooed in closed and comparatively simple form (a formulafor'~ (7, at z - 0, r > a is given). Mmerical results are given for the * 0). i case of uniform dilatation at inAnity (cr(r) q, V(r) = Z-,,\bstracter's note: Complete translation-7 .-Card 2/2, ------ UPLYAND, Ya. S. The second basic problem in the theory of elasticity for a wedge. Trudy LPr no*210:6?-94 160. (MIRA 13:11) .(Wedges) ,01713J90 AUTHORt Uflyand, Ya. S. (Leningrad) 89399 S10401611025100110201022 B125/B204 TITLE: The torsion oscillations of a semispace PERIODICAL: Prikladnaya matematika i mekhanika, v. 25, no. 1, 1961, 159-162 TEXTz The present paper deals with the torsional vibrations of a semi- bounded elastic bcxly, which are produced by the rotation of a rigid cylinder connected with the semispace on a circular surface. An exact solution of this problem was given by H. F. Sagoci (Ref. 1), using wave- like spheroid functions. The problemt To a rigid stamp connected witi. the semispace (z> 0) on a circle having the radius a, the torsional moment M = M Ree'(V t + 0~) is applied, where V is the frequency of the oscilla- 0 f tions. All equations of the elasticity theory may be satisfied, even i only one component of the displacement vector on -the -j-axis (r,q,z are the cylindrical coordinates) is assumed to be non-vanishings uy-Re(ue i(Vt +d,) where the function u(r,z) must satisfy the equation Card 1/6 89399 S104 61/025/001/020/022 The torsion oscillations of-e B125YB204 32u + .1 ju _ R_ + _a2u +k2u = 0 k -V (1.3). Here f is the density 2 r -br r2 3 z2 fl' and G the shearing modulus. On the boundary of the semispace the condi- tions uI Z-0---Er, r< a, A-u 0, r >a (1-4) must be satisfied. Here OZ Z=o E is the'complex amplitude of the angle of rotation of the stamp, which is considered to be given when solving the problem. The tangential stress 11 T G duq vanishes on the surface of the body outside the stamp. If the jz 1z solution of (1.3) (which tends towards zero at z--l-co), is represented CD in he form u e-Z J1(Ar)A(%)dX, one obtains the integral OD co equa!,tions A(A)Jj(~r)dA - er, ra (1-7) 0 0 Card';,'2/6 r:, 89399 3/040/61/025/001/020/022 The torsion oscillations of... B125/B204 for the unknown function A(;\) froni the boundary conditions (1-4). Using a method given by N. N. Lebedev, it is possible to reduce the problem under investigation to solving the regular Fred-holm integral equation a T(X) fq (t)[V(t-x) g(t+x)jdt - 4' x, 0