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Abstract:

The object of present praper is to investigate one- dimensional dynamical problem of coupled thermo- elasticity in a semi infinite elastic non - simple medium when its surface is under suddenly applied constant pressure. The solution of the problem has been deduced using Laplace transfrom in Bromwich integral from. The author determined the value of the surface displacements in  non - simple medium for small values of time t numerically and presented graphically.

Keywords:

thermo-elasticity,non-simple medium,surface displacements,

Refference:

I. Chen. P.J., & Gurtin, M.E. (1968): ZAMP, Vol. 19, pp.614.

II. Chen, P.J., Gurtin, M.E. & Williams, W.O. (1969): ZAMP, Vol.20,PP.107.

III. Nowacki, W. (1962) : “Thermoelasticity” Addison Wesley Publising Co.pp.5,8,11,40,133,159, N.Y..

IV. Iesan, D. (1970): ZAMP, Vol.21,pp.583.

V. Chakraborty, S.(1972) : Bulletin of calcutta Mathematical Society, Vol.64, pp.129.

VI. Erdelyi, A. (1954) : Tales of Integral Transforms, McGraw Hill Book col. Inc Vol.1, New York.

VII. Das, N.C., Lahiri, A., & Bhakta , P.C. , Bull. Cal. Math. Soc., 90, pp-235-250 (1998)

VIII. Kar, T.K., Lahiri, A., J.Math., NBU., Vol-1, No.-2, (2008), pp-165-172.

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Abstract:

The object of the present paper is to investigate the propagation of waves in an elastic layer immersed in an infinite liquid and under the influence of gravity. The corresponding velocity equation has been derived. In the limiting case the wave velocity equation so obtained is in good agreement with the corresponding classical problem when gravitational effects are vanishing small.

Keywords:

elastic layer, propagation of waves,effect of gravity,

Refference:

I. Voigt, W (1887) : Theorestische Studien iiber die elasticitats varhattnisse der krystalle- I,II. Abh.Konigh Ges derwise. Gottingen 34.

II. Biot, M.A. (1965) : Mechanics of incmental deformation. Willy, New York, pp 44-45, 273-81.

III. Bromwich, T.J.I.A (1898) : Proc.London.Math.Soc.30,  98-120.

IV. Love, A.E.H (1952) : The Mathematical Theory of Elasticity, Dover, pp-164.

V. De, S.N. and Sengupta, P.R. (1974) : J. Acoust.Soc.Amer., Vol.55. No.5 pp.919-21.

VI. De, S.N. and Sengupta, P.R (1975) : Gerlands. Beitr Geophysik, Lepizing 84, 6. s 509-514.

VII. Bhattacharyya, P.C. and Sengupta, P.R. (1984) : Influence of gravity on propagation of waves in a composite elastic layer, Ranchi, Uni. Math. Jour. Vol-15(1984).

VIII. Acharya, D.P., Roy I and Chakraborty, H.S. (2008) : On interface Waves in second order thermo- visco elastic solid media under the influence of gravity, J.Math. Sci., Vol-3 No.3 (2008). pp 286-298.

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Abstract:

Following Deissler's approach the decay for the concentration fluctuation of a dilute contaminant undergoing a first order chemical reaction in MHD turbluent flow at times before the final period in a rotating system for the case of multi-point and multi-time correlation equations is studied. Two-point, two-time and three-point, correlation eqyations have been obtained and to make the set of  equations determinate, the trams containing quadruple correlations in compraison with second and third order correlation terms. The solution obtained gives the decay law for the concentration fluctuations before the final period in a rotating system.

Keywords:

MHD turbulent flow, rotating system,concentration fluctuation,

Refference:

I. S.Chandrasekher, Proc. R.Soc. London A204(1951) 435.

II. S.Corrsin J.Appl.Phys. 22(1951) 469.

III. R.G. Deissler, Phys. Fluid 1 (1958) 111.

IV.R.G. Deissler, Phys. Fluid 3(1960) 176.

V. P.Kumar and S.R. Patel, Phys, Fluid 17 (1971) 1364.

VI. P.Kumar and S.R. Patel, Int J. Eng.Soc. 13(1975) 305.

VII. A.L. Loeffler and R.G. Deissler, Int J.Heat Mass transfer 1(1961) 312.

VIII. S.R. Patel, Int J.Eng. Sci. 12(1975)159.

IX. S.A. Sarker and N. Kishore, Int J.Eng. Sci. 29 (1991)1479.

X. S.A. Sarker and M.A. Islam, Indian J.Pure and Appl. Math. 8(2001)32.

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Abstract:

This paper is concerned with the steady flow of a micropolar fluid an infinite flat plate subjected to unifrom suction.

Keywords:

micro polarfluid,steady flow, flate plate,uniform suction,

Refference:

I. Eringen, A.C. (1964)- Simple Microfluids; Int. Jour. Engng. Sci. 2, 205.

II. Hoyl, J.W. and Fabula, A.C. (1964)- The effect of additives on fluid.

III. Willson, A.J. (1969)- Basic flowes of a micropolar liquid; Appl. Sci. Res., 20,338.

IV. Willson, A.J. (1968)- The flow of a micropolar liquid layer down an inclined plane; Proc. Camb. Phil. Soc., 64,513.

V. Willson, A.J. (1970)- Boundary layer in micropolar liquid ; Proc. Camb. Phil. Soc.., 67,469.

VI. Sengupta, P.R. and Ghosh, P.C. (1982)- Asymptotic suction problem in the unsteady flow of  micropolar liquid; Journal of Technology, XXVII, 1,21.

VII. Gupta, P.S. and Gupta, A.S (1972)- Steady flow of Micropolar Liquids; Acta Meachanica, 15,141.

 

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Abstract:

A two dimensional natural convection flow of a viscous incompressible and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a unifrom transverse magnetic field. The governing equations are reduced to non-similar boundary layer equations by introducing coordinate transformations appropriate to the cases (i) near the leading edge (ii) in the region for away from the leading edge and (iii) for the entire regime from leading edge to down stream. the governing equations for the flow in the up stream regime are investigated by perturbation method for smaller values of the stream wise distributed magnetic field parameter. The equations governing the flow for large and for all have been investigated by employing the implicit finite difference method with Killer box scheme. The effect of prandit number pr and the magnetic filed parameter on the skin fricition as well as on the rate of heat transfer for the fluid of low prandtl number will be shown in tabular from. The effect of Pr and different level of velocity, in the boundary layer region, will also be shown graphically.

Keywords:

viscous incompressible fluid, convection flows,skin friction,heat transfer,

Refference:

I. Sparrow, E.M. and Gregg, J.L.: Buoyancy effects in forced convection flow and heat Transfer. ASME J. Appl. Mech., Vol.83, 133-134 (1959).

II. Merkin, J.H.: The effect of buoyancy forces on the boundary layer flow over semi-infinite vertical flat plate in a unifrom free stream, J. Fluid Mech., vol.35, pp.439-450 (1969).

III. Lioyd, J.R. and Sparrow, E.M, : Combined forced and free convection flow on a vartical surface. Int. J. Heat Transfer. vol.13, pp.434-438(1970).

IV. Wilks, G. and Hunt, R.: Continuous transformation computation of boundary layer equations between similarity regimes. J. Comp. Phys., vol.40, (1981).

V. Raju, M.S., Liu, X.R. and Law, C.K.: A formulation of combined forced and free convection past a horizontal and vertical surface . Int. J. Heat mass Transfer, vol.27 pp.2215-2224 (1984).

VI. Tingwei, G., Bachrun, P. and Daguent, M. (1982): Influence de la converction natural le convection force and dessus d’ume surface plane vertical vomise a un flux de rayonnement. Int. J. Heat Mass Transfer, vol.25 pp.1061-1065 (1982).

VII. Sparrow, E.M. and Cess, R.D.: Effect of magnetic filed on free convection heat transfer. Int. J. Heat Transfer, vol.3. pp.267-274 (1961).

VIII. Riley, N.: Magnetohydrodynamic free convection. J. Fluid Mech., vol.18, pp. 267-277(1964).

IX. Kuiken, H.K.: Magnetohydrodynamic free convection in a strong cross-field. J. Fluid Mech., vol.40,pp.21-38 (1970).

X. Sing, K.R. and Cowling, T.G.: Thermal convectiv in Magnetohydrodynamic boundary layer. J. Mech. Appl. Math. vol.16, pp.1-5 (1963).

XI. Crammer, E.M. and Pai, S.I.: Megnetofluid Dynamics for Engineering and applied Physicists. McGrow-Hill, New York, (1974).

XII. Wilks, G.: Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross-field. J. Appl. Phys., vol.27, pp.621-631, (1976).

XIII. Wilks, G. and Hunt, R: Magnetohydrodynamic free convection about a semi-infinite vertical plate at whose surface the heat flux is unifrom. J. Appl. Math. Phys. (ZAMP), vol.34, January, (1984).

XIV. Hossain, M.A. and Ahmed, M.: MHD forced and free convection boundary layer flow near the leading edge. Int. J. Heat Mass transfer, vol.33. pp.571-575 (1984).

XV. Hossain, M.A., Pop I. and Ahmed, M.: MHD Free Convection Flow From an isothermal plate inclined a small angle to the horizontal. J. Theo. Appl. Fluid Mech., Vol.1, pp.194-207, (1996).

XIV. Cebeci, T. and Bradshaw, P.: Physical and computational aspects of convective heat transfer. Springer, New York, (1984).

 

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Abstract:

In this paper thermal stresses in an aeolotropic thin rotating annular disc under transient shearing strees applied on the outer edge are derived when the modulus of elasticity and the coefficient of thermal expansion very expansion very exponentially as the nth power of the radial distance from the center of the circular disk, corresponding result for homogeneous case are deduced as a special case and and found in agreement with the previous results. Numberical results are presented in a tabular from and graphically.

Keywords:

thermal stresses,thermal expansion,aeolotropic,shearing stress,

Refference:

I. De,A.And Choudhury, M.’Thermal stress in a non-homogeneous thin rotating annular circular disk having transient shearing stress applied on the outer edge.’ Bulletin of Calcutta Mathematical society. Vol-98,No-6,pp-128-128(2006).

II. Gogulwar, V.S and Deshmukh, K.C., “Thermal stresses in a thin circular plate with heat sources”,  Journal of Indian Academy of Mathematics, Vol-27,No-1,pp-129-141(2005).

III. Ghosh, R.E. On the loaded elastic half space with a depth varying poisson ratio. ZAMP,  Vol-20, No-5, pp-691,(1969).

IV. Love ,A.E.H. ‘A treatise on the mathematical theory of elasticity’ 2nd Edn, Dover publication, New York (1944).

V. Mollah, S.A.  “thermal stress in non-homogeneous circular dise of varying thickness rotating about a central axix.” Pure and applied mathematical science, Vol-3, No-12, pp-(55-60) (1976).

VI. Mollah, S.A. ‘Stresses in an in-homogeneous circular dise with axial hole of transversely isotropic material.’ Journal of Indian Mathematical science, Vol-1, No-2, pp-5-10 (1990).

VII. Mollah, S.A. ‘Thermal stress in a non-homogeneous thin rotating circular disk having transient shearing stress applied on the outer edge.’ Gaiit, Journal of Bangladesh Mathematical Society, Vol-1, No-1,pp-59. (1990).

VIII. Timoshenko, S. and goodier, J.N. Theory of Elasticity, 2nd edition, McGraw-Hill, pp-406-434(1955).

IX. Wankhede, P.C., “On the Quasi static thermal stresses in a circular plate”, Indian Journal of pure and Applied Mathematics, Vol-13, No-11, pp-1273-1277 (1982).

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Abstract:

In this artical, an approximate technique has been presented for obtaining the analytical approximate solutions of second order strongly  nonlinear differential systems with small damping and slowly varying coefficients based on the He's homotopy perturbation and the extended from of the Krylov-bogoliubov-Mitroppolskii method. An example is given to illustrate the efficiency and implementation of the presented method. The first order analytical approximate solutions obtained by the presented method show a good  agreement with the corresponding numerical solutions for the several damping effects.

Keywords:

doffing equation ,damping effect ,homotopy perturbation ,varying coefficients ,

Refference:

I.  Krylov N.N and Bogoliubov N.N., Introduction to nonlinear mechanics, princeton  University Press, New Jersey, 1947.

II. Bogoliubov N.N and Mitropolskii Yu., Asymptotic methods in the theory of nonlinear oscillation, Gordan and Breach, New York,1961.

III. Mitropolskii Yu. A,. Problems on asymptotic methods of non-stationary oscillations(in Russian), Izdat, Nauka, Moscow, 1964.

IV. Nayfeh A.H., Introduction to Perturbation Techniques, Wiley, New York,1981.

V. Murdock J.A., Perturbations: Theory and Methods, Wiley, New York, 1991.

VI. Hall H.S.and Knight S.R ., Higher Algebra, Radha Publishing house, culcutta,(Indian Edition) , pp-480-438, 1992.

VII. Lim C.W. and Wu B.S., A new analytical approach to the Duffing harmonic oscillator. Physics Letters A 311(2003) 365-373.

VIII. He Ji-Huan, homotopy perturbation technique, Computer Methods in applied Mechanies and Engineering. 178(1999) 257-262.

IX. He Ji.Huan, coupling method of a homotopy perturbation technique and a perturbation technique for nonlinear problems, International Journal of Nonliner Machanies, 35 (2000) 37-43.

X. He J.H., New interpreetation of homotopy perturbation method, International Journal of Modern Physics B, Vol.20, No.18 (2006) 2561-2568.

XI. Belendez A., Hernandez A., Beledez T., Fernandez E., Alvarez M.L. and Neipp C., Application of Homotopy perturbation method to Duffing hrmonic  oscillator, International Journal of Nonlinear Science and Numerical Simulation 8(1) (2007) 78-88.

XII. Hu H., Solution of a quadratic nonlinear oscillator by the method of harmonic balance, Journal of Sound and Vibrartion 293 (2006) 462-468.

XIII. Roy K.C. and Alam M. Shamsul, Effect of higher approximation of Krylov-  Bogoliubov- Mitropolskii solution and matched asymptotic differential systems with slowly varying coefficients and damping near to a turning point, Viennam journal of mechanics, VAST, vol.26, 182-192 (2004).

XIV. Arya J.C. and Bojadziev G.N., Time depended oscillating system with damping, slowly varying parameters and delay, Acta Mechanica, vol.41 (1981) 109-119.

XV. Bojadziev G.N., Damped nonlinear oscillations modeled by a 3- dimensional differential system, Acta Mech. 48 (1983) 193-201.

XVI. Alam M. Shamsul, Azad M. Abul Kalam and Hoque M.A., A general Struble’s technique for solving an nth order weakly nonlinear differential system with damping, International Journal of Nonlinear Mechanies, 41 (2006) 905-918.

XVII. Uddin M. Alhaz and Sattar M. Abdus, An approximate techique for solving strongly nonlinear differential system with damping system with damping effects, Indian Journal of Mathematices, (Submitted,2010).,

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Abstract:

The aim of the present paper is to investigate the influence of autofrettage on stress distribution and load bearing capacity of a thick spherical shell. Appling the maximum shear stress Theory and distortion energy theory an analytical equation for optimum radius c of elastic-plasic juncture, c(opt) is deduced in autofrettage technology. It revealed that the autofrettage increases the pressure inside the wall of a thing spherical shell that it can contain.

Keywords:

autofrettage,stress distribution,shear strees,elastic-plastic juncture,

Refference:

I. Harvey JF Theory and desing of pressure vessels. New York: Van Nostrand Reinhold Company Ltd, 1985

II. Brownell LE, Young EH. Process equipment design. New York: John Wiley & sons, 1959.

III. Yu G. Chemical pressure vessel and equipment (in Chinese). Beijing: Chemical Industries Press, 1980.

IV. Boresi Ap, Sidebottom OM, Seely FB, Smith JOI. Advanced machanies of materials, 3rd edn New York: John Wiley & sons, 1978.

V. Kong.F.Determining the opimum radius of the elastic-plastic junction, RC, for thick wall Autofrettage cylinder by graphic method, (in Chinese). Petrochemical equipment, 1986;15:11.

VI. Timashenko S. Strenth of materials, New York: Van Nostrand Reinrand Company Ltd,1978.

VII. Rao Singiresu S: Engineering optimization.

VIII. Srinath, L.S.: Advance Machanics of solied, of materials, Tata McGraw-Hill Publising Company Ltd, New Delihi,1998.

IX. Zhu, Ruilin and Yang Jinlai, International Journal of Pressure Vessel and piping 75 (1998) 443-446.

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Abstract:

In this paper the author generalize several results of normal near lattices in terms of n-ideals. It has been proved that the near lattices of finitely generated principal n-ideals Pn(S) is normal if and only if each prime n-ideals. Also if  and only if

Keywords:

nearlattics,ideals ,normal nearlattics,

Refference:

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Abstract:

The object of the present paper is to investigate the joint effect of couple-stress and gravity on the propagation of waves in an elastic layer. It is found that the velocity of propagation of waves in an elastic layer increases due to the presence of couple-stress and the effect of gravity has some effect on the wave velocity when the length of the wave is small compared with the thickness of the layer. It is clear from the phase velocity equation that joint effect of couple-stresses and gravity is superposing effect when this two are acting separately.

Keywords:

elastic layer,couple-stress ,gravity,wave propagation,

Refference:

I. Voigt, W (1887): Theorestische studien iibet die elasticitats varhattnisse der krystalle–I,II. Abh.. Konigh Ges Derwise. Gottingen 34.

II. Cosserat, E and Cosserat, F. (1909): Theore das Crops-Deformations. Willy, New York. pp.44-45, 273-81.

III. Biot, M.A.(1965): Mechanics of Incremental deformation. Willy. New York pp.44-45, 273-81.

IV. Bromwich, T.J.I.A (1898): Proc. Londan. Math. Soc. 30, 98-120.

V. Love, A.E.H. (1952): The Mathematical Theory of Elasticity, Dover, pp.164

VI. De, S.N. and Sengupta, P.R. (1975): Gerlands. Beitr Geophysik, Lepizing 84, 6. s 509-514.

VII.De, S.N. and Sengupta, P.R. (1974): J. Acoust. Soc. Amer., vol.55. no.5,pp.919-21.

VIII. Mindlin, R.D. and Tiesten, H.F (1962): Effect of couple-stress in linier elasticity, Arch. Rat. Mech. Analysis, 11, 415-448.

IX. Bhattacharyya, P.C. and Sengupta, P.R.(1984): Influence of gravity on propagation of waves in composit elastic layer, Ranchi, Uni. Math. Jour. vol-15(1984)

X. Acharya, D.P., Roy, I (2008): on interface waves in second order thermo – visco elastic solid media under the influence of gravity, J.Mech. Cont.& Math. Sci., vol-3, no-3, pp-286-298.

XI. Sengupta, P.R and Ghosh, B. (1980): Effect of couple-stresses on the steady-state response to moving Loads in the semi-infinite elastic medium, J.Math. Stu., Vol-48, no-2, pp 183-200.

 

 

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