Journal Vol – 12 No -1, July 2017

Abstract:

The paper is dealt with the problem of deformation of an aelotropic semi-infinite elastic plate with semi-cubical boundary. A part of the boundary near the vertex is under the action of normal pressure and the rest is free. The problem is solved by using complex variable technique and reducing the problem to that of solving Hilbert equation in a closed form.

Keywords:

Aelotropic medium,semi-cubical boundary,Hilbert equation,

Refference:

1) Kolossoff, G. V.: On One Application of the Theory of Functions of a
complex variable to a Plane Problem in the Mathematical Theory of
Elasticity, a dissertation at Dorpat (Yurieff) University (1909).
2) Muskhelishville, N. I.: Fundamental Problems of the Mathematical Theory of Elasticity ,Mir Publishers Moscow (1949).
3) Muskhelishville, N. I.: Singular Integral Equations Mir Publishers, Moscow
(1946).
4) Muskhelishville, N. I.: Some Basic Problems of the Mathematical Theory
of Elasticity, Moscow (1949). 5) Lechnitzky, S. G.: Theory of Elasticity of Anisotropic Bodies, Mir
Publishers, Moscow (1981). 6) Maikap, G. H. and Sengupta, P. R.: Proc. Math. Soc. B.H.U, Vol. 5 (1989),
p-87.
7) Paria, G.: Bull. Cal. Math. Soc., Vol. 44 (1952), p-180.
8) Paria, G.: J. Appl. Mech. AMSE., Vol. 24 (1957), p-122.
9) Ahmed, A.: Bull. Cal. Math. Soc., Vol. 62 (1970), p-123.
10) Milne-Thomson, L.M.: Plane Elastic Systems, Springer (1961)

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Abstract:

In the present numerical study, laminar convection over a vertical plate with convective boundary condition is presented.  It is found that the similarity solution is possible if the convective heat transfer associated with the hot fluid on the left side of the plate is proportional to x^1/2, and the thermal expansion coefficient β is proportional to x^-1. The numerical solutions thus obtained are analyzed for a range of values of the embedded parameters and for representative Prandtl numbers of 0.72, 1, 3 and 7.1. The results of the present simulation are then compared with the reports published in literature and find a good agreement.

Keywords:

Convective Boundary Condition,Laminar Convection,Matlab,Numerical Simulation,Vertical Plate,

Refference:

1) Blasius, H., “Grenzschichten in Flussigkeiten mit kleiner reibung,” Z. Math Phys.,
vol. 56, pp. 1–37, 1908.
2) Weyl, H., “On the Differential Equations of the Simplest Boundary Layer Problem,” Ann. Math., vol. 43, pp. 381–407, 1942.

3) Magyari, E., “The Moving Plate Thermometer,” Int. J. Therm. Sci., 47, pp. 14361441, 2008.

4) Cortell, R., “Numerical Solutions of the Classical Blasius Flat-Plate Problem,” Appl. Math. Comput., vol. 170, pp. 706–710, 2005.

5) He, J. H., “A Simple Perturbation Approach to Blasius Equation,” Appl. Math. Comput., vol. 140, pp. 217–222, 2003.

6) Bataller, R. C., “Radiation Effects for the Blasius and Sakiadis Flows With a Convective Surface Boundary Condition,” Appl. Math. Comput., vol. 206, pp. 832–840, 2008.

7) Aziz, A., “A Similarity Solution for Laminar Thermal Boundary Layer Over a Flat Plate With a Convective Surface Boundary Condition,” Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 1064–1068, 2009.

8) Makinde, O. D., and Sibanda, P., “Magnetohydrodynamic Mixed Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction,” ASME J. Heat Transfer, vol. 130, pp. 112602, 2008.

9) Makinde, O. D., “Analysis of Non-Newtonian Reactive Flow in a Cylindrical Pipe,” ASME J. Appl. Mech., vol. 76, pp. 034502, 2009.

10) Cortell, R., “Similarity Solutions for Flow and Heat Transfer of a Quiescent Fluid Over a Nonlinearly Stretching Surface,” J. Mater. Process. Technol., pp. 176–183, 2008.

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Abstract:

This paper is concerned with the motion of a non-Newtonian fluid of Reiner-Rivlin type through an annulus with porous walls in presence of radial magnetic field. Here, the inner cylinder rotates about its axis with a transient angular velocity while the outer one is kept fixed.

Keywords:

Reiner-Rivlin fluid,Circular cylinder,Radial magnetic field,transient angular velocity,Hankel functions,

Refference:

1)   Mahapatra, J. R . (1973) – Appl. Sci. Res., 27, 274.

2)   Khamrui, S. R . (1960) – Bull. Cal. Math. Soc., 52, 45.

3)  Watson, G. N. (1952) – Theory of Bessel functions.

4)  Sommerfeld , A. (1949) – Partial Differential Equation in

Physics, New York.

5)  Bagchi, K. C. (1966) – Appl. Sci. res., 16, 151.

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Abstract:

MHD free convection and mass transfer flow of an incompressible viscous fluid past a continuously moving infinite vertical porous plate is made in the presence of joule heating and thermal diffusion where the medium is also porous. The corresponding momentum, energy and concentration equations are made similar by introducing the usual similarity transformations. These similarity equations are then solved by Matlab software with Shooting Iteration technique. The solutions are obtained for the case of large suction. The effects of the various parameters entering in to the problem on the velocity field are shown graphically.

Keywords:

MHD free convection,mass transfer flow,joule heating,thermal diffusion,

Refference:

1) Bestman, A. R.-Astrophys. Space Sci., Vol. 173, p. 93 (1990).
2) Eckert, E. R. G. and Drake, R. M., Analysis of Heat and Mass Transfer, McGraw-Hill Book Co. New York 1972.
3) Georgantopoulos, G. A., Astrophys. Space Sci. 65(2), 433 (1979).
4) Hossain, M. A, ICTP, International print No. IC/9/265 (1990)
5) Kafousias, N. G. Nanousis, N.D. and Geograntopoulas, G. A., Astrophys. Space Sci. 64, (1979), 391.
6) Kafoussias, N. G., Astrophys. Space Sci. 192, 11 (1992).

7) Nanousis, N. Georgantopoulos, G. A. and Papaioannou, A., Astrophys. Space
Sci. 70, 377 (1980).
8) Raptis, A. A. and Singh, A. K., Int. Comm. Heat and Mass Transfer, 10(4), 313
(1983).

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Abstract:

In this paper, we introduce two notions of  property in fuzzy topological spaces by using quasi-coincidence sense and we establish relationship among our and others such notions. We also show that all these notations satisfy good extension property. Also hereditary, productive and projective properties are satisfied by these notions. We observe that all these concepts are preserved under one-one, onto, fuzzy open and fuzzy continuous mappings. Finally, we discuss initial and final fuzzy topologies on our second notion.

Keywords:

Fuzzy Topological Space,Quasi-coincidence,Fuzzy T₁ Topological Space,Good Extension,

Refference:

1) Ali, D. M. On certain separation and connectedness concepts in fuzzy topology, PhD, Banaras Hindu University, India, 1990.
2) Amin,M. R. Ali, D. M. and Hossain, M. S. On fuzzy bitopological spaces, Journal of Bangladesh Academy of Sciences, 32(2) (2014) 209- 217.
3) Amin,M. R. Ali, D. M. and Hossain, M. S. Concepts in fuzzy bitopological spaces, Journal of Mathematical and Computational Sciences, 4(6) (2014) 1055-1063.
4) Amin,M. R. and Hossain, M. S. On concepts in fuzzy bitopological spaces, Anals of Fuzzy Mathematics and Informatics, 11(6) (2016) 945- 955.
5) Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968), 182
192.
6) Ahmd, Fora. Ali Separations axioms for fuzzy spaces, Fuzzy Sets and Systems, 33(1989), 59-75.
7) Goguen, T. A. Fuzzy Tychonoff theorem, J. Math. Anal. Appl. 43(1973), 734-742.
8) Guler, A. C. Kale Goknur, Regularity and normality in soft ideal topological spaces, Anals of Fuzzy Mathematics and Informatics, 9(3) (2015), 373-383.
9) Hossain, M. S. and Ali, D. M. On T1 fuzzy bitopological spaces, J. Bangladesh Acad. Sci., 31(2007), 129-135.
10) Hutton, B. Normality in fuzzy topological spaces, J. Math. Anal. Appl. 50(1975), 74-79.
11) Kandil and El-Shafee: Separation axioms for fuzzy bitopological spaces, J. Inst. Math. Comput. Sci. 4(3)(1991), 373-383.
12) Lipschutz, S. General topology, Copyright 1965, by the Schaum publishing company.
13) Lowen, R. Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), 621-633.
14) Lowen, R. Initial and final fuzzy topologies and the fuzzy Tyconoff theorem, J. Math. Anal. Appl. 58(1977), 11-21.
15) Malghan, S. R. and Benchalli, S. S. On open maps, closed maps and local compactness in fuzzy topological spaces, J. Math. Anal. Appl. 99(2)(1984), 338-349.
16) Ming Pu. Pao. and Ming, Liu Ying. Fuzzy topology I. neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76(1980), 571-599.
17) Ming Pu. Pao. and Ming, Liu Ying.Fuzzy topology II. product and quotient spaces, J. Math. Anal. Appl. 77(1980), 20-37.
18) Rudin,W. Real and Complex Analysis, Copyright 1966, by McGraw Hill Inc.
19) Miah Saikh Shahjahan and Amin, Md Ruhul. Mappings in fuzzy Hausdorff spaces in quasi-coincidence sense, Journal of Bangladesh Academy of Sciences, (accepted).
20) Miah Saikh Shahjahan and Amin, M. R. Certain properties on fuzzy R0 topological spaces in quasi-coincidence sense, Annals of Pure and Applied, (accepted).
21) Srivastava, R. Lal S. N. and Srivastava, A. K. On fuzzy and topological spaces, J. Math. Anal. Appl. 136 (1988), 66-73.
22) Warren, R. H. Continuity of mappings in fuzzy topological spaces, Notices A.M. S. 21(1974), A-451.
23) Wong, C. K. Fuzzy topology: product and quotient theorem, J. Math. Anal. Appl. 45(1974), 512-521.
24) Wuyts, P. and Lowen, R. On separation axioms in fuzzy topological spaces, fuzzy neighborhood spaces, and fuzzy uniform spaces, J. Math. Anal. Appl. 93(1983), 27-41.
25) Zadeh, L. A. Fuzzy sets, Information and control, 8(1965), 338-353.

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Abstract:

The objective of this research paper is to investigate the unsteady flow of general type Visco-elastic, fluid under the action of a periodic pressure gradient through a non-conducting rectangular duct. Firstly, the  general  investigation have been focused methodically to consider the unsteady flow of the fluid in presence of a periodic pressure gradient. Secondly, two  important  deductions  have been made for Maxwell Fluid of  first order model and ordinary viscous fluid model. Finally, the author investigates the velocity of the  fluid  numerically .

Keywords:

Unsteady Flow,Periodic Pressure Gradient,Basic Rheological Equations,Visco- Elastic Fluid ,Maxwell Fluid,Ordinary Viscous Fluid,

Refference:

1) lamb H. , Hydrodynamics, New york, Dover Publications.Inc.(1945)
2) Pai S.I., Viscous flow theory Laminar Flow, Princeton N.H.D. Nostrand. Inc(1965)
3) Oldoroyd J.G ,Proc.Roy Soc ( London) A.218, 122(1985)
4) Maxwell J.c., phil. Trans Roy .soc ( london) A.157, PP 49-88(1867)
5) Cowling T.G, Magneto-Hydrodynamics, Bristol, England , Adam High Hilger Ltd(1976)
6) Kapur J.N ., Bhatt B.S. and Sacheti N.C ., Non Newtonian Fluid Flows , India, Pragatic Prakashan (1982)
7) Batchelor G.K, An introduction to Fluid dynamics, Cambridge University press(1967)
8) Milne-thomson L.M, Theoritical Hydrodynamics , New York, The Macmilan Co(1955)
9) Lighthill James, Waves in fluids, London, Cambridge university press(1988)
10) Sengupta P. R. and kundu S. MHD Flow of visco-elastic oldroydian fluid with periodic pressure gradient in a pours rectangular duct with a possible generalization, journal of pure and applied physics vol. 11 no.2 pp-57-199
11) Das, P.S. Sengupta P.R. and Debnath, L.k . Lamb’s Plane problem in thermo-visco-elastic micropolar medium with the effect of gravity , International journal of mathematics and mathematical science, U.S.A , Vol.15, No.5, PP 795-802,(1992)

12) P.S. Das , effect of visco-elasticity of Maxwell type on surface waves in sea water, Proc. 4th international Conference on vibration Problems(ICOVP), vol.A, PP.130-132,(1999)

13) Das P.S. , The unsteady Flow of Visco-elastic Maxwell Fluid of second order due to a transient pressure gradient through a rectangular duct , P.A.M.S , Vol.II, No.1-2, PP. 31-37,2000
14) Das P.S. , The unsteady Flow of Visco-elastic Rivlin-Ericksen Fluid of first order due to a transient pressure gradient through a rectangular duct , Indian journal of theoretical Physics , Calcutta , Vol. No.49, P.P. 71-77,2001
15) Das P.S. , The unsteady Flow of Visco-elasticity of general type on surface waves in seawater, indian journal of Pure and applied Mathematics , National Sc. academy, Vol. 33(I) , P.P. 21-30,2002
16) Das P.S. , (2002) , Indian journal of Theoretical Physics, Vol. 5, No.2

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