
Archive issue  vol.8, No.3
2.
FORCE ANALYSIS MODEL FOR OPTIMIZATION OF FIXTURES
F. CUS and U. ZUPERL
University of Maribor, Faculty of Mechanical Engineering
Smetanova ul. 17, P.O. Box 224, SI2000 Maribor, SLOVENIA
emails: franc.cus@unimb.si, uros.zuperl@unimb.si
The paper discusses the neuralanalytical model for the analysis and optimization of fixtures, suitable for clamping of thinwall products likely to undergo deformation due to clamping and cutting forces during machining. A programme FIXAN has been worked out for the evaluation of fixturing scheme, for the calculation of the optimum magnitude and positioning of clamping forces required to enable the workpiece to be safely clamped during machining. The model is suitable for the analysis of fixtures intended for fixing of prismatic and cylindrical products. The model takes into consideration the friction occurring between the workpiece and the fixture components. The described procedure ensures a reduction in the time of fixture planning and prevention of defects and deformation during the machining process.

Key words: 
fixture analysis, milling, optimization, neural networks. 
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3.
FINITE AMPLITUDE LONG WAVE INSTABILITY OF A FILM OF CONDUCTING FLUID FLOWING DOWN AN INCLINED PLANE IN PRESENCE OF ELECTROMAGNETIC FIELD
B.S. DANDAPAT and A. MUKHOPADHYAY
Physics and Applied Mathematics Unit, Indian Statistical Institute
203 B.T. Road, Calcutta  700 108, INDIA
email: dandapat@isical.ac.in
Stability characteristics of a thin conducting liquid film flowing down, on a nonconducting plane in the presence of the electromagnetic field is investigated under the assumption of a small magnetic Reynolds number. A surface evolution equation is derived by using the longwave approximation method. A linear and nonlinear stability analysis of the evolution equation shows that the magnetic field stabilizes the flow whereas the electric field stabilizes or destabilizes the flow depending on its orientation with the flow. It is found that both the subcritical instability and supercritical stability are possible in a finite amplitude regime. Two critical Hartmann numbers M_{c} and M_{c}>(M_{c}) are observed for subcritical and supercritical zones respectively. The existence of a subcritical unstable zone may be ruled out when M_{c}>M_{c} which is independent of other parameters whereas supercritical and explosive zones are possible till M_{c}<M_{c} which depends on flow parameters.

Key words: 
thin film, conducting film, electromagnetic field, stability of MHD flow, finite amplitude analysis. 
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4.
TRANSIENT FREE CONVECTION FLOW OF VISCOUS DISSIPATIVE FLUID PAST A SEMIINFINITE INCLINED PLATE
P. GANESAN and G. PALANI
School of Mathematics, Anna University
Chennai  600025, INDIA
email: ganesan@annauniv.edu
An analysis is performed to study the transient free convection flow of a viscous incompressible fluid past a semiinfinite inclined plate with viscous dissipation. The dimensionless governing equations are unsteady, coupled and nonlinear integro partial differential equations. An analytical method fails to give a solution. Hence an implicit finite difference scheme of CrankNicolson method is employed. The effect of the dissipation parameter on the velocity, temperature, skin friction and Nusselt number are studied in detail. It is observed that greater viscous dissipative heat causes a rise in the temperature irrespective of the Prandtl number.

Key words: 
viscous dissipation, inclined plate, convective flow, unsteady, finitedifference. 
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5.
INSTABILITY OF THE INTERFACE BETWEEN FLUIDS OF DIFFERENT DENSITIES FLOWING THROUGH A COMPLEX VERTICAL HYDRAULIC SYSTEM
A. GRYGORIEV, K. JEŻOWIECKAKABSCH and H. SZEWCZYK
Faculty of Mechanical and Power Engineering, Wrocław University of Technology
Wybrzeże Wyspiańskiego 27, 50370 Wrocław, POLAND
email: grigor@itcmp.pwr.wroc.pl
The impact of the gas density difference on formation of flow patterns of fluids of different density was analysed. Physical modelling of a nonisothermal laminar flow of a gas mixture in a vertical epitaxial reactor chamber was carried out and the model flow was visualised. Visualisation studies, performed using a smoke method, confirmed that the stability of a gas interface determines the flow pattern in the chamber. The RayleighTaylor instability occurs in the flow through a reactor, which, together with the KelvinHelmholtz instability and with the superposition of convection flows on the principal flow, shapes the flow pattern in the whole reactor chamber. On the basis of results of visualisation studies, the possibility of making the flow through a vertical reactor stable was indicated if the inlet guide apparatus is applied and the flow direction is reversed.

Key words: 
RayleighTaylor instablity, KelvinHelmholtz instability, epitaxial reactor, flow visualisation. 
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6.
HYDRODYNAMIC SQUEEZEFILM CHARACTERISTICS IN POROUS ANNULAR DISKS USING THE BRINKMAN MODEL
J.R. LIN and W.H. LIAO
Department of Mechanical Engineering, Nanya Institute of Technology
P.O. Box 3242259, ChungLi 320, Taiwan, R.O.C.
email: jrlin@ms18.hinet.net
Based on the Brinkman model (BM) with the assumption that the pressure gradient across the porous region is an unknown function, the effects of viscous shear stresses upon the squeezingfilm motion in porous annular disks are considered. Using the Brinkman equations and applying the continuity conditions at the interface for the velocities, shear stresses and pressures, two coupled modified Reynolds equations governing the squeezefilm pressure are obtained. The film pressure equation is solved and applied to evaluate the loadcarrying capacity and the heighttime relationship. According to the results obtained, the BM predicts quite a different squeezing action to those derived by the slipflow model (SFM) and the Darcy model (DM). Comparing with the SFM, the viscous shear effects of the BM increase the loadcarrying capacity and the response time. But, these trends are reversed as compared to the DM. On the whole, the effects of viscous shear stresses are more pronounced for moderatevalue permeability parameters and a highervalue radius ratio. A design example for porous annular disks is also illustrated for engineering applications.

Key words: 
annular disks, porous matrix, squeeze films, Brinkman model, load capacity, response time. 
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7.
THE EFFECT OF THERMAL/GRAVITY MODULATION ON THE ONSET OF CONVECTION IN A HORIZONTAL ANISOTROPIC POROUS LAYER
M.S. MALASHETTY and D. BASAVARAJA
Department of Mathematics, Gulbarga University
Gulbarga  585 106, INDIA
email: malashettyms@yahoo.com
An investigation is carried out to study theoretically the stability of a fluidsaturated anisotropic porous medium, heated from below, for the case of a timeperiodic wall temperature/gravitational field. The Darcy model is employed and only the infinitesimal disturbance are considered. A method based on a small amplitude of the modulation is used to compute the critical values of the Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of the frequency of the modulation, the Prandtl number, the porous parameter, and the anisotropy parameter. We found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the wall temperature or by the gravity modulation. The temperature modulation is shown to give rise to both subcritical and supercritical motions whereas gravity modulation always leads to subcritical motions. It is also found that the lowfrequency thermal/gravity modulation and the small anisotropy parameter have a significant effect on the stability of the system.

Key words: 
convection, modulation, anisotropy, porous medium. 
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8.
FREE VIBRATION OF ISOTROPIC THICK/THIN PLATES USING A SUBPARAMETRIC SHEAR DEFORMABLE ELEMENT
M.C. MANNA, S. HALDAR
Department of Applied Mechanics, Bengal Engineering College (Deemed University)
Howrah  711 103, West Bengal, INDIA
email: mcmanna@appmech.becs.ac.in
A.H. SHEIKH
Department of Ocean Engineering and Naval Architecture
Indian Institute of Technology, Kharagpur  721 302, INDIA
A free vibration analysis of isotropic plates is investigated in this paper. A sixteen node subparametric element having thirtysix degrees of freedom is developed for this purpose. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The entire formulation is made based on the firstorder shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios, aspect ratios and boundary conditions are analyzed. The results show an excellent agreement with the available published analytical results.

Key words: 
free vibration, subparametric element, firstorder shear deformation, rotary inertia, thickness ratios. 
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9.
EFEECT OF RADIATION ON RAYLEIGHBENARD CONVECTION IN FERROMAGNETIC FLUIDS
S. MARUTHAMANIKANDAN
Department of Mathematics, Bangalore University, Central College Campus
Bangalore 560 001, INDIA
email:dsmanikandan@yahoo.com
The effect of radiative transfer on the onset of thermal convection in a ferromagnetic fluid layer bounded by two parallel plates and heated from below is considered using Goody's approach. The fluid between the plates absorbs and emits thermal radiation. The MilneEddington approximation is employed in obtaining the initial static state. Considering infinitesimal perturbations, the critical magnetic Rayleigh number is obtained using the RayleighRitz method. It is found that radiation inhibits the onset of convection in both the transparent and opaque media. Further, the opaque medium is shown to release heat for convection more slowly than the transparent medium. It is also found that radiation affects the cell size at the onset of convection in the case of transparent medium only. The results have implications in energy conversion devices and in smart material applications.

Key words: 
radiation, ferromagnetic fluid, MilneEddington approximation, convection, transparentopaque approximations. 
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10.
A CRITICAL REVIEW OF DAM ANALYSIS METHODOLOGIES
P. SARKAR, S.CH. DUTTA and N. NANDI
Department of Applied Mechanics, Bengal Engineering College (Deemed University)
Howrah 711 103, West Bengal, INDIA
email: thesarkar@netscape.net
email: scdind@netscape.net
Dams in many countries including India were primarily designed on the basis of approximate hand calculation based method. A frequent occurrence of floods due to a failure of such dams and embankments clearly points to the need of a review of the procedure of dam analysis methodologies and to suggest a reasonably accurate one. The paper is a limited effort for the same, based on three Indian dams. As a very preliminary step of the whole plan of checking the safety of Indian dams, an analysis of three dams having similar features as that of Chirpatia Dam (Rajasthan), an earthen embankment dam, Koyna Dam (Maharastra), a concrete gravity dam and the earthen embankment surrounding Ash Pond of Bakreswar Thermal Power Project (West Bengal), have been carried out with the help of twodimensional and threedimensional finite element discretisation under static loading conditions. The result is then compared with the corresponding results obtained from a conventional hand calculation based on approximate gravity method of analysis. The comparison of the results exhibited a considerable increase in compressive stresses in twodimensional finite element analysis with respect to what is obtained in the conventional hand calculation based approximate gravity method. Both of these methods considered an inplane stress distribution along a crosssection of the dam and hence, could not recognize any possibility of stress generation perpendicular to the crosssection. In this context, a threedimensional study reveals that considerable stresses may generate even in the longitudinal direction of a dam that is generally ignored in hand calculation based gravity method of analysis and twodimensional analysis due to the assumption of the twodimensional nature of the problem. A rigorous finite element analysis also shows that even tensile stress may generate under static loading conditions which can hardly be predicted from the conventional method. It is also observed that hand calculation based on slipcircle method and twodimensional analysis cannot adequately recognize the possibility of shear failure at many points in the body of the dam though their vulnerability due to itself and so it is necessary to point out by a rigorous threedimensional modeling and analysis. Thus, the study suggests the unavoidable necessity of threedimensional analysis for a safe design of dams.

Key words: 
dam, earthen, hand calculation based approximate method, threedimensional analysis. 
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11.
MIXED RADIATIONCONVECTION BOUNDARY LAYER FLOW OF AN OPTICALLY DENSE FLUID ALONG A VERTICAL FLAT PLATE IN A NONDARCY POROUS MEDIUM
H.S. TAKHAR
Department of Engineering, Manchester Metropolitan University
Manchester M1 5GD, U.K.
O.A. BÉG
Fire Engineering Science, LCB
North Street, Leeds, LS2, U.K.
A.J. CHAMKHA
Department of Mechanical Engineering, Kuwait University
Safat 13060, KUWAIT
D. FILIP and I. POP
Faculty of Mathematics and Computer Science, University of Cluj
R3400 Cluj, CP 253, ROMANIA
email: popi@math.ubbcluj.ro
The combined effects of thermal radiation flux, thermal conductivity, Reynolds number and nonDarcian (Forcheimmer drag and Brinkman boundary resistance) body forces on steady laminar boundary layer flow along a vertical surface in an idealized geological porous medium are investigated. The classical Rosseland onedimensional diffusion approximation is implemented in the energy equation to avoid solving the general integrodifferential equation for radiative transfer. Pseudosimilarity transformations are invoked and the resulting highly coupled and nonlinear set of ordinary differential equations for momentum and energy equations are solved numerically using a welltested and highly accurate shooting RungeKutta quadrature with a MersonGill algorithm. It is shown that the dimensionless velocity functions generally increase with rising radiation parameter and the Prandtl number, and the dimensionless temperature functions decrease as the nonDarcian body forces decrease. It is also shown that the dimensionless temperature functions rise in magnitude with rising radiation parameter and the Prandtl number but are depressed by lowered nonDarcian resistance parameter and rising Reynolds number. Generally radiation is seen to substantially boost the overall heat transfer.

Key words: 
porous medium, nonDarcy model, thermal radiation, mixed convection, numerical results. 
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12.
Brief note
TRANSIENT FREECONVECTIVE FLOW IN A VERTICAL CHANNEL DUE TO SYMMETRIC HEATING
B.K. JHA and A.K. SINGH
Department of Mathematics, Banaras Hindu University
Varanasi  221005, INDIA
email: ashok@banaras.ernet.pl
H.S. TAKHAR
Department of Engineering and Technology
The Manchester Metropolitan University
Manchester, M1 5GD, U.K.
email: hstakhar@man.ac.uk
This paper presents a closed form solution for a transient free convective flow of a viscous and incompressible fluid in a vertical channel due to symmetric heating of channel walls. The Laplace transform technique has been used to obtain the expression for the velocity and temperature fields by solving the governing differential equations. The influence of the physical parameters on the velocity field, skinfriction, rate of heat transfer and volumetric flux of the fluid are carefully analysed. A correlation between the steady state time and the Prandtl number has been developed. It is observed that the nature of correlation is linear when the Prandtl number is greater than one while cubic for the Prandtl number is less than one.

Key words: 
free convection, symmetric heating, Laplace transform, Prandtl number. 
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13.
Brief note
A NOTE ON THE OCCURRENCE OF INTEGRODIFFERENTIAL EQUATIONS IN ENGINEERING MECHANICS
Y. PALA and G. KARADERE
Uludag University, Engineering Faculty
Görükle, 16059, Bursa, TURKEY
email: ypala@uludag.edu.tr
The study of dynamics of packages of mass m delivered from a conveyor to a smooth circular ramp of radius r is important in transport technology and engineering dynamics. The present paper is devoted to reanalysing this problem since the inclusion of frictional forces results in an integrodifferential equation that in general needs the utilisation of Neumannseries. The integrodifferential equation thus obtained is transformed into a first order differential equation that can easily be solved analytically.

Key words: 
engineering, mechanics, analytical solution, integrodifferential equation, differential equation with variable equation. 
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