New Analytical Study of the Effects Thermo-Diffusion, Diffusion-Thermo and Chemical Reaction of Viscous Fluid on Magneto Hydrodynamics Flow in Divergent and Convergent Channels
- 1 Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, Iraq
- 2 Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq
Abstract
In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied . The governing partial differential equation was transformed in to a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically , this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating th e order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters w as analyzed and discussed graphically.
- Eckert, E.R.G. and Drake, R.M. (1972) Analysis of Heat and Mass Transfer. McGraw-Hill Book Company, New York.
- Olajuwon, B.I. (2011) Convection Heat and Mass Transfer in a Hydromangetic Flow of a Second Grade Fluid in the Presence of Thermal Radiation and Thermal Diffusion. International Communication in Heat and Mass Transfer, 38, 377-382. https://doi.org/10.1016/j.icheatmasstransfer.2010.11.006
- Kumar, A.G.V., Goud, Y.R. and Varma, S.V.K. (2012) Thermal Diffusion and Radiation Effects on Unsteady MHD Flow through Porous Medium with Variable Temperature and Mass Diffusion in the Presence of Heat Source Sink. Advance in Applied Science Research, 3, 1494-1506.
- Davidson, P.A. (2006) An Introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge.
- Gailitis, A. and Lielausis, O. (2006) On a Possibility to Reduce the Hydrodynamical Resistance of a Plate in an Electrolyte. Applied Magnetohydrodynamics, 12, 143-146.
- Henoch, C. and Stace, J. (1995) Experimental Investigation of a Salt-Water Turbulent Boundary-Layer Modified by an Applied Stream Wise Magneto Hydrodynamic Body Force. Physics of Fluids, 7, 1371-1383. https://doi.org/10.1063/1.868525
- Ellahi, R., Raza, M. and Vafai, K. (2012) Series Solutions of Non-Newtonian Nanofluids with Reynolds’ Model and Vogel’s Model by Means of the Homotopy Analysis Method. Mathematical and. Computer Modelling, 55, 1876-1891. https://doi.org/10.1016/j.mcm.2011.11.043
- Khan, U., Ahmed, N. and Tauseef Mohyud-Din, S. (2016) Thermo-Diffusion, Diffusion-Thermo and Chemical Reaction Effects on MHD Flow of Viscous Fluid in Divergent and Convergent Channels. Chemical Engineering Science, 141, 17-27. https://doi.org/10.1016/j.ces.2015.10.032
- Hatami, M., Sheikholeslami, M., Hosseini, M. and Ganji, D.D. (2014) Analytical Investigation of MHD Nanofluid Flow in Non-Parallel Walls. Journal of Molecular Liquids, 194, 251-259. https://doi.org/10.1016/j.molliq.2014.03.002
- Hatami, M., Sheikholeslami, M. and Ganji, D.D. (2014) Nanofluid Flow and Heat Transfer in an Asymmetric Porous Channel with Expanding or Contracting Wall. Journal of Molecular Liquids, 195, 230-239. https://doi.org/10.1016/j.molliq.2014.02.024 https://doi.org/10.1016/j.molliq.2016.10.073
- Turkyilmazoglu, M. (2014) Extending the Traditional Jeffery-Hamel Flow to Stretchable Convergent/Divergent Channels. Computers and Fluids, 100, 196-203. https://doi.org/10.1016/j.compfluid.2014.05.016