Influence of Volume Fraction of Dust Particles on Dusty Fluid Flow through Porous Rectangular Channel

International Journal of Mathematics Trends and Technology (IJMTT)
© 2017 by IJMTT Journal
Volume-50 Number-5
Year of Publication : 2017
Authors : K R Madhura, D S Swetha


K R Madhura, D S Swetha "Influence of Volume Fraction of Dust Particles on Dusty Fluid Flow through Porous Rectangular Channel", International Journal of Mathematics Trends and Technology (IJMTT). V50(5):261-275 October 2017. ISSN:2231-5373. Published by Seventh Sense Research Group.

This article provides a novel solutions to unsteady ow of dusty uid passing through porous rect- angular channel with the consideration of volume frac- tion of dust particles. Effects of magnetic parameter, porous parameter and volume fraction of dust particles on both uid and dust velocity profiles under different boundary conditions are analysed. Results are exhibited both analytically and numerically after solving the non- dimensional governing equations using Laplace transform, Fourier transform and Crank-Nicolson methods. Mathlab software is used to obtain numerical computation. The e ects of pertinent parameters are also exhibited in tab- ular and graphical forms. For the interest of physical and engineering field, skin friction at the boundaries are calculated.

[1] P.G. Safiman, On the stability of laminar ow of a dusty gas, Journal of uid mechanics, Vol. 13(1), pp. 120-128, 1962.
[2] P.K.Gupta, S.C.Gupta, Flow of a dusty gas through a channel with arbitrary time varying pressure gradient, J Appl Math Phys 27(1) (1976) 119-125. [3] Rudinger G, Some effects of finite particle volume on the dy- namics of the gas-particle mixtures , AIAA J 3(7) (1962) 1217- 1222.
[4] Sagdeev, R.Z., M.A.Lepntovich,Reviews of plasma physicsvol 4, Consultants Bureau, NEw York, (1966)p. 23.
[5] Miura, H.,Glass, I.IDevelopment of the ow induced by a piston impulsively in a dusty gas, Proc. R. Soc. Lond. A 397, (1985) 295-309.
[6] Robson Ramos, Luis E.B.Brandao, Roberto Schirru, Cesar Marques Salgado, Claudio M.N.A.Pereira, Ademir Xavier da Silva, Volume fraction calculation in multiphase system such as oil-water-gas using neutron, International nuclear atlantic conference, (2007).
[7] N.Aquelet, C.Seddon, M.Souli, M.Moatamedi, Initialisation of volume fraction in uid/structure interaction problem, IJCrash, 2(2005).
[8] Kai Bao, Xiaolong, Hui Zhang, Enhua Wu,Volume fraction based miscible and immiscible uid animation, Computer ani- mation and virtual worlds, (2010).
[9] Nayfeh A.H.,Oscillating two-phase ow through a rigid pipe, AIAA J , 4(10) (1966) 1868-1870.
[10] Sana Ahsan, Effect of volume fraction on non newtonian ow of dusty uid between two oscillating parallel plates, Interna- tional Journal of Emerging Technology and Innovative Engi- neering,1(7) (2015) 39-45.
[11] Debasish Deya, Hydro-magnetic oscillatory dusty uid with volume fraction and periodic pressure in a rotating channel , International Journal for Research in Applied Science and En- gineering Technology, 3(3) (2015) 869-877.
[12] Rakesh Kumar, Particulate couette ow with volume fraction of dust particles, Journal of Chemical, Biological and Physical Sciences 5(3) (2015) 2851-2862.
[13] I.Saidu, M.Y.Waziri, A.Roko, H.Musa, MHD effects on convective ow of dusty viscous uid with volume frac- tion of dust particles, ARPN J. of Engg. and Applied Sci- ences, 5(10) (2010), 86-91.
[14] R.K.Gupta, S.N.Gupta, Unsteady ow of a dusty uid through ducts with volume fraction, Proc. Indian natn. Sci. Acad, A 4 (1984) 350-364.
[15] Anil Tripathi, A.K.Sharma, K.K.Singh, E ect of porous medium and magnetic field on the ow of dusty visco- elastic second order oldroyd uid through a long rectangu- lar channel, International Journal of Mathematical Archive, 4(9) (2013), 243-247.
[16] K.R.Madhura, B.J.Gireesha, C.S.Bagewadi, Exact solutions of unsteady dusty uid ow through porous media in an open rectangular channel Adv. Theor. Appl MEch, 2(1) (2009) 1-17.
[17] K.K.Singh, Unsteady ow of a conducting dusty uid through rectangular channel with time dependent pressure gradi- ent, Indian J Pure Appl Math 8(9) (1977) 1124-1131.
[18] Ruchi Chaturvedi, R.K.Shrivatsav, Mohd. Salim Ahamad,The numerical analysis of MHD ow of dusty visco-elastic first or- der oldroyd uid when passing through a porous rectangular channel, International Journal of Modern Mathematical Sci- ences, 9(1) (2014) 46-57.
[19] B.C.Prasannakumara, B.J.Gireesha,P.T.Manjunatha, Melting phenomenon in MHD stagnation point ow of dusty uid over a stretching sheet in the presence of thermal radiation and non-uniform heat source/sink, International Journal for Computational Methods in Engineering Science and Mechanics , (2015) 1-18.
[20] Hai Long Liu, Junfeng Wang, Wook Ryol Hwang, Flow resis- tance of viscoelastic ows in fibrous porous media, Journal of Non-Newtonian Fluid Mechanics, 246 (2017) 21-30.
[21] Singh, C.B. Ram ,Unsteady ow of a electrically conducting dusty viscous liquid through a channel, Indian J. Pure and Appl. Math, 8(9)1977, 1022-1028.
[22] Prasad, V.R.Ramacharyulu, N.C.P, Unsteady ow of a dusty uid between two parallel plates under an impulsive pressure gradient, Def. Sci, Journal, 38 (1979)125-130.
[23] Nag S.K, Jana R.N, Datta.N Couette ow of a dusty gas , Acta Mechanica, Springer Vertag, 3(1979)33, 179-187.
[24] C.S.Bagewadi and B.J.Gireesha, A study of two dimen- sional unsteady uid ow under varying pressure gradi- ent, Tensor, N.S. 64 (2003) 232-240.
[25] A.J.Chamka, Unsteady laminar hydromagnetic uid particle ow and heat transfer in channels and circular pipes, Int. J. Heat and uid ow, 21 (2000) 740-746.
[26] Parveen sharma and C.L.Varshney, Thermal dispersion ef- fect onMHD ow of dusty gas and dusty particles through hexagonal channel, International journal of heat and mass transfer, 46 (2003) 2511-2514.
[27] P.T.Manjunatha, B.J.Gireesha, B.C.Prasannakumara, Effect of Radiation on Flow and Heat Transfer of MHD Dusty Fluid Over a Stretching Cylinder Embedded in a Porous Medium in Presence of Heat Source, Int J. Appl. Comput. Math (2015).
[28] Akhilesh K. Sahu, R.P.Chhabra, V. Eswaran, Two dimen- sional unsteady laminar ow of a power law uid across a square cylinder, Journal of Non-Newtonian Fluid Mechanics, 160 (2009) 157-167.
[29] Michael Schriber, Focus: The difference between round and square pipes, Physical review letters, 8,94 (2015).

Dusty fluid, rectangular channel, volume fraction of dust particles, porous medium.