Archive

Abstract:

A runge-kutta-marson method and a Newton Iteration in shotting and matching technique are used to obtain the solutions of the government equation. These equations resulted from the unsteady motion of the magneto-hydrodynamic biviscosity fluid with heat and mass transfer through a uniform porous medium between two permeable parallel walls, taking into account obtained as a perturbation technique. During this work we calculate an estimation of the global error by using Zadunaisky technique . The effects of upper limit of apparent viscosity coefficient, Reynolds number, permeability parameter, Forschheimer number, magnetic parameter, the steady component of the pressure gradient, the amplitude of the pulsation, Prandit number, Eckert number, Schmidt number, Soret number and the time on the velocities, temperature and concentration distribution are depicted graphically.  

Keywords:

non-Newtonian fluid, heat transfer,mass transfer, plates,

Refference:

I. S.N. Majhi and V.R. Nair,; Int. j. Eng. Sci. 32(1994), 839-846.

II. J.P. Bitoun and D. Bellet: Biorheology 23 (1986), 51.

III. Ramachandra Rao and Rathna Devanathan : Z.A.M.P. 24(1973), 203.

IV. D.J. Schneck and S. Ostrach: J. Fluids Eng. 16(1975), 353.

V. R.I. Macey: Bull. Math. Biophys.25(1963), 1.

VI. R.I. Macey:Bull. Math. Biophys. 27(1965), 117.

VII. G. Radhakrishamacharya, Peeyush Chandra and M.P. Kaimal: Bull. Math. Bio 1. 43(1981), 151.

VIII. Nabil T.M. Eldabe and Salwa M.G. Elmohandis: Phys. Soc. japan 64. (1995) 4165.

IX.Nabil T.M. Eldabe and Salwa M.G. Elmohandis: Fluid Dynamic Research. 15(1995), 313.

X. C.L. Varshney: J. Pure Appl. Math. 10(1979), 1558.

XI. Raptis, C. Peridikis and G. Tzivanidis: J.Phys. D. Appl. Phys.14(1981), 99.

XII. Raptis, N. Kafousias and C. Massalas: ZAMM 62 (1982), 489.

XIII. Raptis and C. Peridikis: Int J. Engng. Sci.21(1983), 1327.

XIV.Elsayed F. Elshehawey, Ayman M.F. Sobh and Elsayed M.E. Elbarbary: J. Phys.Soc. japan.69 (2000),476.

XV. S.N. Murthy, tran: ASME J. Heat Transfer, 122(2000). 476.

XVI. P.E. Zadunaisky : Number. Math. 27(1988), 21.

XVII. M. Nakayama and T Sawada: J. Biomech. Eng. 110(1988),137.

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Abstract:

The objective of this investigation is to study general surface waves and Rayleigh, love and stoneley waves as particular cases in visco-elastic solids under initial stress of hydrostatic tension or compression. Firstly, the general theory of surface waves in visco-elastic solids under initial stress has been formulated. The visco-elasticity of the solid medium involving time rate of stress and strain is considered to be of first order, The investigated problem and the wave-velocity equations are in fair agreement with the corresponding results of the classical problems in absence of viscosity and initial stress.

Keywords:

Surface wave,Visco-elastic solid,Initial stress,

Refference:

I. A.E.H. Love, A Treatise on the Mathematical theory of Elasticity, Cam. Univ. Press. Fourth Ed.(1953).

II. M.A. Boit. Mechanics of incremental Deformations, John Wiley & Sons, Inc. New York (1965).

III. M.A. Boit. Theory of Elasticity with Large Displacements and Rotations, John Wiley & Sons, Inc. New York, Chapman & Hall LTD. London.(1939).

IV. M.A. Boit. Nonlinear theory of Elasticity and the linearized case for a body under initial stress philosophical Magazing, 27,(1939),468.

V. M.A. Boit. Jour. Appl. Phys., 10,(1939),860.

VI. M.A. Boit.Jour. Appl. Phys.,2 1940, 552.

VII. C.P.Yu, and S. Tang,ZAMP, 17, 1966, 766.

VIII. W.Flugge, Visco-elasticity, Blaisdell publishing Co. London.(1967).

IX. D.R.Bland, The Theory of Linear Visco-elasticity, Pergamon press, London.(1960).

X. S.C. Hunter, Visco-elastic waves, progress in Solid Mechanics(eds), I.N. Sneddon and R.Hill, North interscience , Amsterdam, New York. (1960).

XI. Sri H. Jeffreys, Min. Nat. R. Aste. Soc. Geophys. Suppl 1 (1925) 282.

XII. Sri H. Jeffreys, Min. Nat. R. Aste. Soc. Geophys. Suppl 3 (1935)253.

XIII. Sri H. Jeffreys, Min. Nat. R. Aste. Soc. Suppl.7 (1957),332.

XIV. Sri H. Jeffreys, The Earth, Cambridge University Press, Fourth Edition. (1959).

XV. L Rayleight, (Struff, J.W) Proc. Lond. Math. Soc. 17, (1885), 4.

XVI. R. Stoncley, Proc. Roy. Soc.A- 106,(1924), 416.

XVII.R. Stoncley, Mon. Nat. R. Astr. Sog. Geophys. Suppl. 4,(1937) 43.

XVIII. Stoncley, R.(1955), Rayleigh waves in a medium with two surface layers, MOn.Nat.R.Astr.Soc.Geophys. Suppl.6(1955) 610,7,(1955),7.

XIX. W.Voigt, Theoretische Studien uber die Elasticitats Verhaltniss der Krystalle, Abh. Ges. Wiss. Gottingen 34(1887).

XX. S. Dey, & P.K..De, (1999), Sadhana, 24,(1999) 215.

XXI. D.P. Acharya, & Asit Mondal, Sadhana,27,(2002) 605.

XXII. P.K. Pal, D. Acharya, & P.R. Sengupta, Sadhana,, 22, (1997) 659.

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Abstract:

The unsteady free convection flow of an electrically conducting fluid past an impulsively stared verical plate acted on by a uniform transverse magnetic field has been considered. The solutions are obtained analytically and their natures are shown graphically for different values of the Hartmann number.

Keywords:

convection flow ,magnetic flow,vertical plate ,Hartmann number,

Refference:

I. K. Stewartson: Quart. Jour. Mech. Appl. Math. 4 (1951) 182.

II.K. Stewartson: Quart. Jour. Mech. Appl. Math. 26 (1973) 143.

III. M.G. Hall: Proc. Royal Soc.(London) Series A, 310( 1969) 401.

IV. I. Tani and N.J.Yu: Proceedings of “I.U.T.A.M 1971 Symposium” , E.A Eichelbrenner, 11 (1972) 886.

V. C.R. Illingwerth: Proc.Camb. Society 56 (1950) 603.

VI. V.M. Soundalgekar: ASME Jour. of Heat Transfer 99 (1977) 499.

VII. V.M. Soundalgekar: Jour of Appl. Mech. 46 (1979) 757.

 

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Abstract:

using the Galerkin's procedure, the problem of tharmal stresses and nonlinear tharmal deformation has been analysed for a shallow shell panel. The Variation of the central deflection for a square panel has been shown in tabular from.

Keywords:

thermal stress,thermal deformation,shallow shell panel,

Refference:

I. W.P.Chang and S.C.Jen: Int. J. Solids & Structures, 22(3),(1986) 267.

II. P.Biswas: 5th ICOVP, Moscow (IMASH), October (2001) 8.

III. E.H. Mansfield: Proc. Royal Society(London), Vol.A-379, (1982) 15.

IV. L.H.Donnel: Beams, Plates and shells, McGraw Hill Pub.Co., New York,1976.

V. S.Timoshenko and S.W.Krieger: Theory of plates and Shells, McGraw Hill Pub.Co.1959.

VI. W.Nowacki: Thermoelasticity, Addision Wesley Pub. Co. New York, 1962.

 

 

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Abstract:

in this note, an attempt has been made to investigate the propagation of small disturbance incompressible magnetic fluid and the nature of the disturbance has been studied. It has been noticed that the disturbance velocity in magnetic fluids due to magnetic-striction pressure, is different from that in ordinary non-magnetic fluids.

Keywords:

magnetic fluid,propagation of small disturbance ,magneto-striction pressure,

Refference:

I.  Rosenweigh, R.E. Ferrohydro dynamics, Cambridge University Press.(1964).

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Abstract:

In this paper an attempt has been made to study unsteady flow of a visco-elastic Oldroydian fluid in a circular pipe. Using Laplace transformation technique the basic equations of motion and boundary conditions have been modified and using these modified equations and boundary conditions the solutions of the problem has been derived.

Keywords:

visco elastic Oldroydion fluid ,unsteady flow ,circular pipe,

Refference:

I. Snedden, 1.N., Fouries Transformers, Mc Grow-Hill Book Co. New York. 1951.

II. Sengupta, P.R. and Ghosh, S.K. River Behaviour and Control. 25. 1976.

III. Sengupta, P.R. and Ghosh, S.K., Acta Ciencia Indica, 2,99. 1976.

IV. Paul, S.K. and Sengupta, P.R. India Jour. Theo. Phys. 34, 349. 1986.

V. Panja, S. and Sengupta P.R. Proc. Intern AMSE conf. New Delhi. (India).1991.

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Abstract:

The aim of this paper is to investigate the problem of steady flow of micropolar fluid  in an annulus bounded by two co-axial circular cylinders of radii a and b, b being greater than a. The annular flow takes place under the action of constant pressure gradient. The velocity and microrotatioin component as well as the rate of discharge of the fluid through the annulus and time of efflux have been derived analytically in closed froms. Numerical calculations have been  given to find out the velocity in viscous fluid and a percentage decrease in micropolar fluid and a persentage decrease in micropolar fluid over viscous fluid corresponding to this flow have been compared. The microrotation has also been calculated. It is clear from the numberical calculations that the fluid velocity is always less in micropolar fluid than in viscous fluid. Also the rate of discharge in micropolar fluid is considerably less than that of viscous fluid. In fact, all important results are less in micropolar fluid than the viscous fluid.

Keywords:

micropolar fluid,cylinder,steady flow,circular pipe,

Refference:

I. A.C. Eringen, Intern. J. Engg. Sci., 2 (1964), 205.

II. A.C. Eringen, Proc. XI Intern. Congress of Appl. Math. Springer Verlag. (1965).

III. A.C. Eringen, Proc. 5th Symposium of Navel Hydrodynamics, Bergen, Sept. 10 (1964).

IV. A.C. Eringen, Nonlinear Theory of continuous Media. MacgrawHill. (1962).

V. A.C. Eringen, J.Math. Mech. 16,(1966).

VI. P.R. Sengupta and S.K. Paul. Phy. Sci. 22, (1988), 4.

VII. S.K Paul and P.R. Sengupta,(1967)- Rev. Roum. Sci. Techn. Mech. Appl., 32,(1967) 2.

VIII. P.C. Ghosh and P.R. Sengupta,(1963)- North Bengal Univ. Review, (Sci. & Techno.) 4, (1963) 2.

IX. P.R. Sengupta and P.C. Ghosh, Journal of Technology, XXVIII. (1982), I

X. P.R. Sengupta and S.K. Paul, Journal of Technology, XXVIII, (1982),2

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Abstract:

The effect of radiation on combined free and forced convection flow of an elactrically conducting viscous fluid through an open-ended vertical channel permeated by a uniform transverse magnetic field has been considered. The temperature in the wall has been supposed to very linearly with distance and there is no heat flux on the boundaries. Assuming optically thin limit, the experience for volocity, induced magnetic field, temperature and the non dimensional flow-rate are obtained and the influence of radiation on these quantities are observed either graphically or in tabulated forms.  

Keywords:

Viscus fluid,Convection flow,Magnetic fluid,Heat flux,Radiation,

Refference:

I. M.F. Romig: Advances of Heat Transfer (Ed. T.F.Invine, Jr., J.P.Hartnett), vol.1 Academic Press, New York, 1964.

II. R Siegel: J. Appl. Mech. 25 (1958) 415.

III. M.Perlmutter, R. Siegel.: Report NASA TN D 875, August 1965.

IV. R.A.Alpher : Int. J. Heat & Mass Transfer 3 (1961) 108.

V. G.Z. Gershuni,  E.M. Zhukhovitsky: Sob. Phys JEPT 34(1958) 461.

VI. C.P.Yu. : AIAA.J.3(1965) 1184.

VII. R.Greif, I.S. Habib, J.C. Lin: J.Fluid Mech.46 (1971) 513.

VIII. R. Viskanta :  Z.Angev. Math & Phys. 14(1965) 353.

IX. P.S. Gupta , A.S. Gupta : Int.J. Heat & Mass Transfer 17(1974) 1437.

X. D.C. Sanyal, and S.K. Samantha, Czeck.J.Phys B39, p-384(1989).

XI. A.C.Cogley, W.C. Vincenti, S.E. Gilles: AIAA. J. 6 (1968) 551.

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Abstract:

The aim of this paper is to study the radial vibration of a non-homogeneous sherically anisotroplc elastic spherical shell with an isotropic elastic inclusion as the core. The non-homogeneous of the material is characteised by taking linear vibration with radial distance of elastic parameters and mass density. This property of non-homogeneity is assumed to be satisfied by the entire shell of the sphere, while the core of the spherical shell behaves like an inclusion of isotropic homogeneouselastic mass. Satisfying the appropriate boundary conditions, the frequency of vibration of the composite solid sphere has been determined. results obtained by other authors may be deduced from our more general result as special cases.

Keywords:

spherical shell,anisotropic elasti ,radial vibration ,elastic inclusion,

Refference:

I. A.E.H. Love , A treatise on the Mathematical theory of Elasticity, Dover publication.(1952).

II. A.E.H. Love, Some problem of Geodynamics, Cambridge University pPress, London.(1911).

III. R.F.S. Hearmon, An Introduction to Applied Anisotropic Elasticity, Oxford University Press, London.(1961).

IV. S.G. Lekhnitski, Theory of Elasticity of an Anisotropic elastic body. Holden Day Inc.(1963).

V. W. Olszak, non-homogeneous in Elasticity and Plasticity-Proceeding of the Internal Union of Theoretical and Applied Mechanics Symposium, pergamon press.

VI. P.R. Sengupta, Problem of twised elastic sphere with a concentric inhomogeneous spherical inclusion, Jour. Sci. Engg. Res. Vol-8, No-2, pp.193-203 (1964).

VII.P.R. Sengupta, Inclusion in elastic solids of work-hardening materil, Ind. Jour. Mech. & Math. Part-II, Special Issue. pp.80-89 (70th birth anniversasry volume of Prof. B.Sen, F.N.A.) (1969).

VIII.P.R. Sengupta, & A.N. Basumallick, Radial deformation of a non-homogeneous spherically anisotropic elastic sphere with a concentric spherical inclusion, Ind. Jour. Mech. & Math, Vol-8, No-2, pp.1-9(1970).

IX. J.G. Chakraborty, radial and rotatory vibration of a spherical shell of aeolotropic elastic material, Bull. Soc. Vol-47, No.4 (1965).

X. S.P. Sur, Radial and rotatory vibration of a sphere of non-homogeneous spherically aeolotropic material of unifrom density. Ind. Jour. Mech. Math. Vol-II, No.1 (1964).

XI. P.R. Sengupta & S.K. Roy, Radial vibration of a sphere of general viscoelastic solid, Gerlands Beitr. Geophysik, Leipzig, 92, 5, s.435-442 (1983).

XII. P.R. Sengupta & S.K. Roy, Rotatory vibration of a sphere of general viscoelastic solid, Gerlands Beitr. Geophysik, Leipzig, 92, 1, s.70-76 (1983).

XIII. H.M. Youssef, dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, Appl. Math. Mech., 26, 4,pp.470-475. (2005).

XIV. S. Banerjee & S.K. Roy Chowdhury, Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity, Computers Math. Applic., 30,1, pp.91-98. (1995).

XV. M.Rakshit & B. Mukhopadhyay: An electro-magneto-thermo-visco-elastic problem in an infinite medium with a cylindrical hole, Int. J. Eng. Sci., 43, pp.925-936, (2005).

XVI. M.A.Ezzat.Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for parfact conductor cylindrical region, Int. J. Eng. Sci., 42, pp.1503-1519, (2004).

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Abstract:

We introduce and study a refined real valued measure on a  -algebra

Keywords:

refined real number ,refined measure space,non-archimedean,

Refference:

I. M.K. Bose and R. Tiwari, ‘The refined real number system and the refined measure’ , submitted for publication.

II. K.Hrbacek and T. Jech, introduction to set theory, Marcel Dekker, Inc., 1999.

III. A.Robinson, Nonstandard Analysis, Princeton University Press, 1996.

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Abstract:

Runge-kutta-Marson Method and Newton Iteration in shooting and matching technique ware used to obtain the solutions of the system of the non-linear ordinary differential equations, which describe the two-dimensional flow of a Johnson-segalman fluid with heat and mass Transfer in a planer channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength. Accordingly, we obtained the solutions of the momentum, the energy and the concentration distributions of the problem were illustrated graphically. Effect of some parameter of this problem such as, Weissenberg number W, total flux number F, Eckeret number, Prandtle number P, Soret number S, Schmidt S, Reaction number Rc, Reaction Parameter R, and reaction order m on these formula were were discussed. Also we estimate the global error for the numberical values of Solution by using Zadunaisky technique.

Keywords:

Johnson-Segalman fluid ,heat transfer ,mass transfer ,global error , peristaltic,

Refference:

I. Hayat T., Wang Y., Hutter K., Asghar S, and Siddiqui A.M., “Peristaltic Transport of an Oldroyd_B Fluid in a planer channel”. Mathematical problems in Engineering, Vol.4 pp.347-376, (2004).

II. Ayukawa, K., Kawa T., and Kimura M, “Streamlines and path lines in peristaltic flow at high Reynolds number”. Bull. Japan Soc. Mech. Engrs. Vol.24, pp.948-955.(1981).

III. Hamin M., “The flow through a channel due to transversely Oscillating walls”, Israel  J. Tec., Vol.6, pp. 67-71, (1968).

IV. Hayat T.,  Wang Y., Siddiqui A.M. and Butter K.,  “Peristaltic motion of a Johnson-Segalman Fluid in a planer channel.”  Mathematical problems in Engineering, vol.1, pp. 1-23.(2003).

V.  Takabatake S. and Ayukawa K., “Numerical study of Two-dimensional peristaltic Flows”,  J.Fluid Mech., Vol.122, pp.439-465,(1982).

VI. Halfen LN., and Castenholz RW., “Gliding in the blue-green alga: a possible mechanism” Nature, Vol.225, pp.1163-1165, (1970).

VII. Kolkka RW., Malkus DS., Hansen MG., Lerly GR. and Worthing RA, “Spurt Phenomenon of the Johnson-Segalman Fluid and related models”, Journal of Non-Newtonian Fluid Mechanics, Vol.29, pp.303-335, (1988).

VIII. Mcleish TCB, and Ball RC., “A molecular approach to the spurt in polymer melt flow”, Journal of polymer Science (B) , Vol.24, pp.1735-1745, (1986).

IX. Malkus D.S., Nohel JA., and Ploher BJ., “Dynamics of Shear flow of a non-Newtonian fluid”, Journal of computational physics, Vol.87, pp.464-497, (1990).

X. Kalika DS., and Denn MM., “Well slip in and extrudate distortion in liner low-density Polyethylene”, Journal of Rheology, Vol.31, pp.815-834, (1987).

XI. Ramamurthy Av., “Wall slip in Viscous Fluids and influence of material of Construcation”, Journal of Rheology,Vol.30 pp.337-357, (1986).

XII. Kraynik AM., and Schowater WR., “Slip at the wall and extrudate roughness with aqueous solutions polyvinyl alcohol and sodium borate”. Journal of Rheology, Vol.25, pp.95-114, (1981).

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Abstract:

The couette flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the fluid at the lower plate and it's corresponding removal by constant suction through the upper plate has been analyzed when both the plates are in motion. Due to this type of injection, the flow becomes Three-dimensional. For small perturbation approximate, the analytical method is applied to obtain the expressions for the velocity and temperature fields. The effect of injection/ suction velocity on the flow field, skin Friction and heat transfer are reported and discussed with the help of graphs and tables.

Keywords:

porous plate, Couette flow,transpiration colling,

Refference:

I. H. Schlichting: Boundary Layer Theory, McGraw Hill, New York (1960).

II. K.Gerstan and J.F. Gross: J. Appl. Maths. Phys., ZAMP, 25(1974) 399.

III. P.Singh, V.R.Sharma and U.N. Mishra: Appl. Sci. Res., 345(1978), 105.

IV. P.Singh, V.R.Sharma and U.N. Mishra: Int. J. Heat Mass transfer, 1,(1978) 1117.

V. K.D. Singh: ZAMM, 73 (1993) 58.

VI. R.C. Chaudhary; Pawan Kumar Sharma: Jour. of Zhejiang Univ. Sc., 4(2003), 181.

VII. E.R.G. Eckert: Heat and Mass transfer, McGraw Hill, New York(1958)

VIII. K.D. Singh; Rakesh Sharma: Z. Naturforsch., 56a(2001) 596.

IX. K.D. Singh: ZAMP, 50(1999) 661.

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Abstract:

This paper studies Nonlinear free vibration of thin circular plates with clamped immovable boundary under thermal loading. A steady-state temperature, field, characterized by constant surface temperatures measured from stress free temperature, is considered. The basic governing differential equations have been derived in the von Karman sense in terms of displacement components and solved with the help of Galerkin Procedure. Parametric studies have been presented to understand the Nonlinear free vibrations of thin isotropic elastic circular plates under thermal loading. This study reveals some interesting Nonlinear dynamic features of such structures which may prove useful to the designers.

Keywords:

elastic plate ,vibration ,thermal loading ,surface temperature ,stress free temperature,

Refference:

I. Pal, M.C., 1969, “Large Deflections of Heated Circular Plates,” ACTA Mechanica, Vol.8,pp.82-103.

II. Pal, M.C.,1970a, “Large Amplitude Free vibration of Circular plates subjected to Aerodynamic Heting,” International Journal of Solid and Structures, vol.6, pp.301-313.

III. Jones R. and Mazumdar J., 1974, “Transverse Vibrations of Shallow Shells by the Method of constant Deflection Contours”, Journalof Acoustical Society of American, vol.56, No.5 pp.1487-1492.

IV. Biswas, P. and Kapoor, P., 1984a, “Nonlinear free vibrations and Thermal Buckling of Circular Plate at Elevated Temperature”. Indian Journal of pure and Applied Mathematical, vol.15,no.7, pp.809-812.

V. Bswas, P. and Kapoor, P, 1984b, “Nonlinear free vibrations of orthotropic circular plates at Elevated Temperature”. Journal of the indian isstitute of Science, Bangalore, vol.65(B), pp.87-93.

VI. Sachdeva, R.C., (1988), “Fundamentals of Engineering Heat and Mass Transfer”, New Age International (P) Limited, Publishers (ISBN: 81-224-0076-0).

VII. Chia, C.Y., 1980, “Nonlinear Analysis of Plates,”  McGraw Hill International Book Company.

VIII. Nash,W. and Modeer, J., 1959, “Certain Approximate Analysis of the Nonliner Behavior of Plates and Shallow Shells,”  Proceedings of Symposium on the Theory of Thin Elastic Shells, Delft, The Netherlands,pp. 331.

 

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Abstract:

In the paper we study he relation between the generalised order (generalised type) of a transcendental meromorphic function and that of a differental monomial by it. We also establish some theorems on the relationship between the generalised order ( generalised type) of a meromorphic function and that of a differental polynomial generated by it under  different conditions.

Keywords:

differential monomials,meromorphic function,differential polynomial,

Refference:

I. N. Bhattacharjee and I Lahiri: Growth and value distribution of polynomials, Bull. Math. Soc. Sc. Math. Roumanie Tome, Vol.39(87), np.1-4(1996), pp.85-104.

II. W. Doeringer: Exceptional values of differential polynomials, Pacific J.Math, vol.98, no.1(1982), pp.55-62.

III. W.K.Hayman: Meromorphic function, The Clarendon Press, oxford (1964).

IV. I.Lahiri: Generalised order of the derivative of a Meromorphic function, Soochow J.Math. Vol.14, no.1(1988), pp.85-92.

V. I.Lahiri: Deficiencies of differental polynomials, Indian J.Pure Appl. Math, Vol.30.no.5(1999), pp.435-447.

VI. I.Lahiri and S.K.Dutta : Growth and Value distribution of differential monomials, Indian J. Pure Appl. Math., vol.32, no.12(2001), pp.1831-1841.

VII. D. Sato : On the rate of growth of entire functions of fast growth, Bull. Amer. Math.Soc., vol.69(1963), pp.411-414.

VIII. L.R.Sons : Deficiencies of monomials, Math.Z, vol.111(1969), pp.53-68.

IX. L.Yang : Value distribution theory and new research on it, Science press, Beijing.(1982).

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Abstract:

The aim of this paper is to investigate the distribution of stresses due to expansion of a spherical cavity at the center of a non-homogeneous metallic sphere of finite radius for an elasto-plastic solid under an increasing internal pressure, the external pressure remaining constant. The non-homogeneity of the elastic material is characterised by supposing that the lame constrants very exponentially as the function of radial distance. The case of ideal plastic solid has been deducted from this general case.

Keywords:

non-homogeneous sphere, ,ductile metal, ,internal and external pressure, spherical cavity, ,

Refference:

I.  R. Hill (1950) : Theory of Plasticity, Oxford University Press, p-317

II.  A.E.H. Love(1952) : The Mathematical Theory of Elasticity, Dover Publication, p-164, London.

III.  Saint-Venant(1865) : Jour. De-Math, Primes at appl.(lonvilla) t-10.

IV.  S.G. Lekhnitskii (1963) : Theory of elasticity of an Anisotropic Elastic Body, Holden-Dey, Inc, p-390.

V.  H.C.Hopkins (1960) : Progress in solid Mechanics, Vol.1, p-80, Edited by I.N.Eneddon and R.Hill, North Holland Publishing Company, Amsterdem.

VI.  P.R.Sengupta (1969) : Ind.Jour. Mech and Math., Special issue, aprt-II, p-80, prof. B.sen, D.Se., F.N.I., 70th Birth Anniversary volume.

VII.  L.K. Roy (1992) :  Proc. Nat. Acad. Sci. India, 62(A), III p-445.

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