MHD Flow of an Unsteady Dusty Fluid Through an Inclined Channel in Anholonomic Co-ordinate System

T.Nirmala, B.J.Gireesha, C.S.Bagewadi, C.S.Vishalakshi "MHD Flow of an Unsteady Dusty Fluid Through an Inclined Channel in Anholonomic Co-ordinate System ", *International Journal of Mathematics Trends and Technology (IJMTT). *V41(3):238-268 January 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

**Abstract**

The focus of this paper is to introduce the concept of Neutrosophic point, Neutrosophic quasi coincident, Neutrosophic feebly open sets and Neutrosophic feebly closed sets in Neutrosophic Topological spaces. Also we analyse their characterizations and investigate their properties. This concept is the generalization of intuitionistic topological spaces and fuzzy topological spaces. Using this neutrosophic feebly open sets and neutrosophic feebly closed sets, we define a new class of functions namely neutrosophic feebly continuous functions. Further, relationships between this new class and the other classes of functions are established.

**References**

[1] E.Amos Magnetic effect on pulsatile flow in a constricted axis-symmetric tube, Indian Journal Pure Appl. Math., 34(9) (2003) 1315-1326.

[2] S.G.Agrawal and N.K.Varshney, MHD flow of a dusty gas induced by the motion of a semi-infinite flat place moving with the velocity decreasing, Jour.of.M.A.C.T.Com, 19(97) (1986).

[3] C.S.Bagewadi and B.J.Gireesha, A study of two dimensional steady dusty fluid flow under varying temperature, Int. Journal of Appl. Mech. & Eng., 94 (2004) 647-653.

[4] C.S.Bagewadi and B.J.Gireesha, A study of two dimensional unsteady dusty fluid flow under varying pressure gradient, Tensor, N.S., 64 (2003) 232-240.

[5] C.S.Bagewadi, B.C.PrasannaKumara and B.J.Gireesha, Transition Motion of an Unsteady Dusty Fluid Through an Open Rectangular Channel, Anal. Uni. Oradea, fasc. Math., XVI (2009).

[6] Barret O’ Nell, Elementary Differential Geometry, Academic Press, New York & London, 1966. [7] G.S.Beavers and D.D.Joseph, Boundary conditions at a naturally permeable wall, Jour.Fluid.Mech., 30(167) (1967)

[8] N.C.Ghosh, B.C.Ghosh and L.Debnath, The hydromagnetic flow of a Dusty Visco-Elastic fluid between two infinite parallel plates, Int. J. Computers and Math. with Applications, 39(2000) 103-116. [9] Indrasena, Steady rotating hydrodynamic-flows, Tensor, N.S., 32 (1978) 350-354.

[10] J.W.Johnson, Rectangular roughness in an open channels, Trans. Am. Geophysics Un., 25 (1944) 906-914.

[11] R.P.Kanwal, Variation of flow quantities along streamlines, principal normals and bi-normals in threedimensional gas flow, J.Math., 6 (1957) 621-628.

[12] J.T.C.Liu, Flow induced by an oscillating infinite plat plate in a dusty gas, Phys. Fluids, 9 (1966) 1716-1720.

[13] Kaur and R.G.Sharma, Run-up flow of viscous incompressible fluid through elliptical tube, Jour.of.M.A.C.T., 18 (53)(1985)

[14] D.H.Michael and D.A.Miller, Plane parallel flow of a dusty gas, Mathematika, 13 (1966) 97-109.[15] P.Mitra, Flow of a viscous incompressible dusty gas between two concentric circular cylinders, Jour.of Math.Phy.Sci., 13 (1979)

[16] P.W.Norey, The laminar flow of dust gas between rotating cylinders, Quart.Jour.Mech.and Appl.Maths., 21 New York, 1968.

[17] G.Purushotham and Indrasena, On intrinsic properties of steady gas flows , Appl.Sci. Res., A 15(1965) 196-202.

[18] P.G.Saffman, On the stability of laminar flow of a dusty gas, Journal of Fluid Mechanics, 13(1962) 120-128.

[19] K.K.Singh, Unsteady flow of Rivlin-Ericksen viscoelastic fluid throuch confocal, elliptical cylinders with time dependent pressure gradient, Acta Ciencia Indica , 4(1978) 212.

[20] Shri Ram, B.K.Guptha and N.P.Singh, unsteady flow of a dusty viscous stratified fluid through an inclined open rectangular channel, Jour,Math.Phy.Sci., 27(2)(1993) 117-128.

[21] Satyaprakash, Liquid flowing down an open inclined channel, Indian J. Pure Appl. Math., 2(1971) 1131.

[22] S.Saxena and G.C.Sharma, Unsteady flow of an electrically conducting dusty viscous fluid between two parallel plates, Indian J. Pure Appl. Math., 18 (12)(1987) 103-109.

[23] C.Truesdell, Intrinsic equations of spatial gas flows, Z.Angew.Math.Mech, 40 (1960) 9-14.

[24] Tyn Myint-U, Partial Differential Equations of Mathematical Physics, American Elsevier Publishing Company, 40 New York, (1965).

[25] P.D.Verma and H.K.Vyas Viscous flow down an open inclined channel with naturally permeable bed.,

Indian Journal Pure Appl. Math., 11(2) (1980) 165-172. [26] V.A.Vanoni, Velocity Distribution in Open Channels , Civil Engineering, 11 (1941) 356-357.

**Keywords**

Frenet frame field system; inclined angle, channel, dusty fluid; velocity of dust phase and fluid phase, conducting dusty fluid, magnetic field.