
Archive issue  vol.5 No.2
No. 
Author(s)  Title 
Pages 
1. 
 70th Anniversary of Professor Stanis³aw Karol WROÑSKI 
299302 
2. 
Singh A.K., Chandran P. and Sacheti N.C.  On the thermal boundary layer of a moving flat plate thermometer in the presence of Ohmic heating 
303313 
3. 
Rudraiah N., Bhargava S. and Sridharan P.  RayleighTaylor instability in a finite thickness layer of a nonNewtonian fluid 
315327 
4. 
Takhar H.S., Slaouti A.S., Soundalgekar V.M. and Jaiswal B.S.  Combined convection of water at 4^{o}C past a semiinfinite vertical plate 
329336 
5. 
Mukhopadhyay M. and Sheikh A.H.  A new plate bending element for the analysis of thin plates of arbitrary shapes 
337354 
6. 
Sharma R.C. and Thakur K.D.  Hall effect on thermal instability of RivlinEricksen fluid in porous medium 
355366 
7. 
Liu R.H. and Li J.  On nonlinear stability of shallow conical sandwich shells 
367387 
8. 
Magnucki K. and Szyc W.  Stability of ellipsoidal heads of cylindrical pressure vessels 
389404 
9. 
Hirani H., Athre K. and Biswas S.  Transient trajectory of journal in hydrodynamic bearing 
405418 
10. 
Dolejs V., Siska B. and Doleèek P.  Pressure drop during the flow of viscoplastic fluids through ducts 
419433 
11. 
Arslantürk C., Özgüç A.F., Fakültesi M.  Hydrodynamic and thermal analysis of Fluidyne heat engine 
435449 
12. 
Scurtu N., Pop I. and Postelnicu A.  Free and forced convection from a vertical cylinder with constant surface heat flux.  Part I: An asymptotic solution 
451469 
13. 
Toften T.H., Holdo A.E. and Bullen P.R.  A simple trajectory model for the near and far field of a jet in a cross flow 
471483 
14. 
Brujan E.A.  Supression of chaotic oscillations of gas bubbles by polymer additives 
485498 

2.
ON THE THERMAL BOUNDARY LAYER OF A MOVING FLAT PLATE
THERMOMETER IN THE PRESENCE OF OHMIC HEATING
A.K. SINGH
Department of Mathematics, Banaras Hindu University,
Varanasi  221005, INDIA
P. CHANDRAN and N.C. SACHETI
Department of Mathematics and Statistics, College of Science,
Sultan Qaboos University, Al Khod, Postal Code 123, Muscat,
SULTANATE OF OMAN
The energy aspect of the boundary layer flow due to Ohmic heating and frictional forces at a moving flat plate has been analyzed based on similarity transformations. The flow is assumed to take place in the presence of an externally applied transverse magnetic field. The velocity and temperature profiles in the boundary layer have been shown by numerically integrating the governing nonlinear ordinary differential equations. Furthermore, the variations of temperature, both close to and away from the boundary plate, have been illustrated graphically as a function of the Prandtl number. The effects of the dissipative processes on the skin friction and plate temperature have been discussed. The magnetic field increases both the skin friction and the wall temperature, whereas, for a fixed magnetic field, the effect of boundary motion is to decrease them.

Key words: 
Ohmic heating, flat plate thermometer, skin friction, plate temperature. 
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3.
RAYLEIGHTAYLOR INSTABILITY IN A FINITE THICKNESS LAYER
OF A NONNEWTONIAN FLUID
N. RUDRAIAH and P. SRIDHARAN
UGCDSA Centre of Fluid Mechanics, Department of Mathematics,
Bangalore University, Bangalore  560 001, INDIA
and
National Research Institute for Applied Mathematics,
7th Cross, 7th Block, Jayanagar, Bangalore  560 082, INDIA
S. BHARGAVA
Department of Studies in Mathematics, University of Mysore,
Manasa Gangotri, Mysore  570 007, INDIA
A mechanism of surface instability in nonNewtonian fluid is described using RayleighTaylor instability as an example. The combined effects of nonNewtonian parameter n, normal stress 'delta', film thickness h, and surface tension 'gamma' on surface instability is studied using linear stability analysis. It is shown that stable, neutrally stable and unstable states are possible depending on the values of n, in contrast to the existence of only unstable state in Newtonian fluids. Further, the graph of dispersion curve reveals that both n and 'lambda'(='gamma'/'delta') control dispersion curve with the layer thickness just affecting the nature of growth rate of instability.

Key words: 
RayleighTaylor instability, finite thickness layer, nonNewtonian fluid. 
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4.
COMBINED CONVECTION OF WATER AT 4^{o}C PAST
A SEMIINFINITE VERTICAL PLATE
H.S. TAKHAR
Manchester School of Engineering, University of Manchester,
Manchester, M13 9PL, UNITED KINGDOM
A.S. SLAOUTI
Depatment of Mechanical Engineering, Manchester Metropolitan University,
Manchester, M1 6GD, UNITED KINGDOM
V.M. SOUNDALGEKAR
31A12, Brindavan Society, Thane (400 601), INDIA
B.S. JAISWAL
Birla College, Kalyan (421 304), INDIA
Combined free and forced convection flow of water at 4^{o}C has been studied when the freestream is of the form exp (mx/2) where m is a constant and x is the distance measured along the semiinfinite vertical plate from the leading edge. Similarity solutions are obtained and the velocity and temperature profiles are shown on graphs, whereas the numerical values of the skinfriction and the rate of heat transfer are listed in a table. The effects of the fall in the temperature of water from 20^{o}C to 4^{o}C are discussed. Also the effects of Gr/Re^{2} (Gr  the Grashof number and Re  the Reynolds number) on the skin friction and the heat transfer are discussed.

Key words: 
combined convection, water at 4^{o}C, semiinfinite plate. 
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5.
A NEW PLATE BENDING ELEMENT FOR THE ANALYSIS OF
THIN PLATESOF ARBITRARY SHAPES
M. MUKHOPADHYAY and A. H. SHEIKH
Department of Ocean Engineering and Naval Architecture
Indian Institute of Technology, Kharagpur 721302, INDIA
It is well known that the isoparametric element has certain drawbacks when applied to thin plates subjected to bending. The specific problem which creeps up for such cases is known as the shear locking phenomenon which becomes more and more pronounced as the thickness of the plate reduces. Though this can be taken care of by techniques such as the reduced integration, problems still linger for very thin plates which occur in many practical structures. The mapping concept used in the formulation of the isoparametric element has been utilised in developing a new fournoded plate bending element. The shear deformation which is not important for the analysis for thin plates has not been considered and thus the disturbing feature of shear locking does not creep into the analysis, yet like the isoparametric element the new element is able to analyse plates having arbitrary shapes.

Key words: 
analysis, finite element, plate, arbitrary shape. 
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6.
HALL EFFECT ON THERMAL INSTABILITY OF RIVLINERICKSEN
FLUID IN POROUS MEDIUM
R.C. SHARMA and K.D. THAKUR
Department of Mathematics, Himachal Pradesh University,
Summer Hill, Shimla  171 005, INDIA
The thermal instability of electrically conducting RivlinEricksen elasticoviscous fluid in porous medium is considered to include the Hall current in the presence of a vertical magnetic field. For the stationary convection, the RivlinEricksen elasticoviscous fluid behaves like a viscous (Newtonian) fluid. The Hall current and medium permeability are found to have destabilizing effect, whereas the magnetic field has a stabilizing effect on the thermal instability problem for stationary convection. A sufficient condition for the nonexistence of overstability is obtained.

Key words: 
Hall current, thermal instability, RivlinEricksen fluid, porous medium. 
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7.
ON NONLINEAR STABILITY OF SHALLOW CONICAL SANDWICH SHELLS
R.H. LIU
Institute of Applied Mechanics
Jinan University
Guangzhou, 510632, PEOPLE'S REPUBLIC OF CHINA
J. LI
Department of Engineering Mechanics
Tongji University
Shanghai, 200092, PEOPLE'S REPUBLIC OF CHINA
In this paper, a theory for nonlinear bending of shallow conical sandwich shells is established by means of the method of calculus of variations. Using the modified iteration method which was suggested by Yeh et al. (1965a, 1965b), analytic solutions of nonlinear stability for the shells with four types of boundary conditions under uniform pressure are obtained. The numerical discussions based on the analytic solutions have been given in detail, which indicate that our method is efficient for the analysis of shallow shells.

Key words: 
nonlinear stability, shallow conical sandwich shells, the modified iteration method. 
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8.
STABILITY OF ELLIPSOIDAL HEADS OF CYLINDRICAL
PRESSURE VESSELS
K. MAGNUCKI
Institute of Technology, Pedagogical University
al. Wojska Polskiego 69, 65625 Zielona Góra, POLAND
W. SZYC
Institute of Applied Mechanics, Poznañ University of Technology
ul. Piotrowo 3, 60965 Poznañ, POLAND
Cylindrical vessels with ellipsoidal heads are widely used in engineering. They are subject mainly to internal pressure, however in some cases external pressure may also be present. The paper presents linear and nonlinear analyses of stability of ellipsoidal heads subject to external or internal pressure. The calculations have been made by means of finite element methods, using the COSMOS/M system. The results have been compared with existing analytical solutions of ellipsoidal shells specified in literature.

Key words: 
stability, thinwalled shells, pressure vessels. 
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9.
TRANSIENT TRAJECTORY OF JOURNAL
IN HYDRODYNAMIC BEARING
H. HIRANI and K. ATHRE
Dept. of Mech. Eng., Indian Institute of Technology,
Hauz Khas, New Delhi  110 016, INDIA
S. BISWAS
ITMMEC, Indian Institute of Technology,
Hauz Khas, New Delhi  110 016, INDIA
A simple methodology to trace journal orbit under dynamic load conditions is presented. The nonlinear fluid film bearing forces are derived using a closedform twodimensional pressure solution obtained from Reynolds equation for dynamic case. An implicit twodimensional NewtonRaphson method is employed to determine journal center velocity by solving the equations of motion incorporating journal inertia and unbalance forces. A global technique is used to ensure convergence towards the root in each iteration. Finally, two connecting rod big end bearings are studied to demonstrate the effect of inertia forces at high speed.

Key words: 
transient trajectory, thick fluid film lubrication, nonlinear journal orbit. 
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10.
PRESSURE DROP DURING THE FLOW OF
VISCOPLASTIC FLUIDS THROUGH DUCTS
Václav DOLEJŠ, Bedøich ŠIŠKA and Petr DOLEÈEK
Department of Chemical Engineering, University of Pardubice,
532 10 Pardubice, CZECH REPUBLIC
An equation of RabinowitschMooney type together with the corresponding relations for consistency variables has been adopted for an approximate calculation of pressure drop in flow of viscoplastic fluids through straight ducts. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with the published analytical solution of flow of RobertsonStiff fluid through an annulus and with numerical solution of flow of Bingham fluid through ducts of rectangular cross section.

Key words: 
pressure drop calculation, viscoplastic fluid, annular duct, rectangular duct. 
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11.
HYDRODYNAMIC AND THERMAL ANALYSIS
OF FLUIDYNE HEAT ENGINE
Cihat ARSLANTÜRK and A. Feridun ÖZGÜÇ
Istanbul Teknik Üniversitesi,
Makina Fakültesi 80191, Gümüºsuyu,
Istanbul, TURKEY
Fluidyne is an easytobuild and quiet heat engine using lowgrade heat sources and not having any moving solid parts. Although Fluidyne’s efficiency is quite low compared with efficiencies of other heat engines, it has an important advantage of using recovered heat. In this study, a mathematical model that analyses Fluidyne is developed. The model utilizes the equations of conservation of mass written for liquid columns and working fluid. Sets of differential equations are solved using RungeKutta Method. In order to investigate the validation of the model, theoretical results are compared with experimental results and the results in literature.

Key words: 
fluidyne, heat engine. 
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12.
FREE AND FORCED CONVECTION FROM
A VERTICAL CYLINDER WITH CONSTANT SURFACE HEAT FLUX.
PART I : AN ASYMPTOTIC SOLUTION
Nicoleta SCURTU
Department of Fluid Mechanics and Thermotechnics,
Transilvania University, R2200 Brasov,
ROMANIA
Ioan POP
Faculty of Mathematics, University of Cluj, R3400 Cluj, CP 253,
ROMANIA
Adrian POSTELNICU
Department of Fluid Mechanics and Thermotechnics,
Transilvania University, R2200 Brasov,
ROMANIA
A theoretical study is conducted in this paper for the development of the steady threedimensional boundary layer, which is induced by a horizontal forced convection flow past an infinitely long vertical cylinder. It is assumed that the cylinder is partially prescribed with a constant heat flux q_{w}, while the other part of the cylinder is held at the ambient temperature T_. It is also assumed that the secondary flow is induced in the boundary layer by the buoyancy forces. A series solution method is used to solve the governing nonlinear set of partial differential equations near the thermal leading edge. It is shown that the effect of the horizontal free stream on the boundary layer gradually increases as one moves upward away from the thermal leading edge along the cylinder. The solution has been obtained for different values of the Prandtl number, Pr, and it is shown that for Pr = 0.733 and Pr = 6.7 the present results are in excellent agreement with those known from the literature.

Key words: 
freeforced convection, numerical solution, vertical cylinder, boundary layer. 
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13.
A SIMPLE TRAJECTORY MODEL FOR THE NEAR AND FAR FIELD
OF A JET IN A CROSSFLOW
T.H.Toften, A.E.Holdo, P.R.Bullen
Department of Aerospace, Civil,
Mechanical and Automotive Engineering,
Faculty of Engineering and Information Sciences,
University of Hertfordshire,
Hatfield, Herts. AL10 9ab, ENGLAND
Even with the present day extensive use of Computational Fluid Dynamics (CFD), simplified analytical expressions for Fluid Dynamic phenomena have their applications in highlighting significant mechanisms and aiding initial engineering estimates. The present work shows that experimental data for the trajectory of the centre line of jets exposed to a crossflow can be found from a single expression. The expression is derived from first principles and unlike most other power law formulas the exponents are not empirically determined from measurements. In comparison with other single expressions based on dimensional analysis, which results in differing expressions for differing parts of the flow field, the equation presented here combines the asymptotic assumptions into a single expression.

Key words: 
jet in crossflow, analytical solution, trajectory model. 
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14.
SUPPRESSION OF CHAOTIC OSCILLATIONS OF GAS
BUBBLES BY POLYMER ADDITIVES
E.A. BRUJAN
Department of Hydraulics, University "Polytechnica",
7206 Bucharest, ROMANIA
The effect of polymer concentration on the bifurcation structure of a bubble oscillator is theoretically examined in terms of bifurcation diagrams and phase diagrams. The equation describing the driven spherical oscillations of a gas bubble in CMC aqueous solutions is obtained by using a Williamson model fluid. The numerical results reveal the suppression of chaotic oscillations of bubbles by polymer additives.

Key words: 
ultrasonics, bubble oscillation, bifurcations, chaos, polymers. 
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