## Approximate Solution for Magnetohydrodynamics Fluid Flow between Two Circular Discs

 AUTHOR(S): Fatma Ayaz, Hayriye Yetim, Nilay Akgonullu Pirim TITLE Approximate Solution for Magnetohydrodynamics Fluid Flow between Two Circular Discs PDF ABSTRACT This study is related to the unsteady magnetohydrodynamic (MHD) squeezing flow of a viscous incompressible fluid between two parallel discs one of which is fixed and permeable. The flow is assumed 2-D and the effects of heat transfer are taken into account. The governing Navier Stokes and heat equation given in cylindrical coordinates with the help of the similarity transformations are reduced into a system of coupled non-linear ordinary differential equations. Then, the solution of the resulting system is obtained in the form of truncated Taylor series where the coefficients are evaluated by using differential transform method, namely DTM. This method is a generalized algebraic way for obtaining Taylor series coefficients of a smooth function and that reduces the computational_x000D_cost. Here, we have investigated the flow properties in terms of suction/injection coefficient as well as the other flow parameters. The illustrative examples show that the present results are very consistent with existing ones. KEYWORDS Magnetohydrodynamic Fluid, Navier Stokes Equations, Heat Equation, Differential Transform Method: Typing manuscripts, LATEX REFERENCES  M.A. Siddiqui,S. Irum, A. Ansari, Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation, Mathematical Modelling and Analysis, 13(4)(2008), 565-576.  A.S. Berman, Laminar flow in channel with porous wall. Journal of Applied Physics , 24 (1953), 1232-1235.  J.R. Sellers, Laminar flow in channels with porous flow at high suction Reynolds number, Journal of Applied Physics, 26 (1955), 489-.  S.W, Yuan, Further Investigation of Laminar Flow in Channels with Porous Walls, Journal of Applied Physics, 27(3) (1956), 267-269.  R.M. Terill, G. M. Shrestha, Laminar flow through parallel and uniformly porous walls of different permeability, ZAMP 16 (4) (1965), 470-482.  W.F. Hughes, R.A. Elco, Magnetohydrodynamic lubrication flow between parallel rotating disks, Journal of Fluid mechanics, 13 (1962), 21-32.  D.J. Kuzma, E.R. Maki, R.J. Donelly, The magnetohydrodynamic squeeze film, Journal of Tribology, 110 (1988), 375-377.  E.A. Hamza, The magnetohydrodynamic effects on a fluid film squeezed between two rotating surfaces, Journal of Physics, D: Applied Physics, 24 (1991), 547-554.  S.Bhattacharyya, A.Pal, Unsteady mhd squeezing flow between two parallel rotating discs, Mechanics Research Communications, 24(6) (1997), 615- 623.  A.M. Siddiqui, S. Irum, A.R. Ansari, Unsteady squeezing flow of a viscous MHD fluid between parallel plates, Mathenmatical Modeling and Analysis, 13 (2008) 565576.  G. Domairy, A. Aziz, Approximate analysis of MHD squeeze flow between two parallel discs with suction or injection by homotopy perturbation method, Mathematical Problems in Engineering, (article ID/ 2009/603916).  A.A. Joneidi, G. Domairry, M. Babaelahi, Effect of mass transfer on the flow in the magnetohydrodynamic squeeze film between two parallel disks with one porous disk, Chemical Engineering and Communications, 198 (2011) 299311.  M. Sajid, I. Ahmad, T. Hayat, M.Ayub, Series solution for unsteady axisym-metric flow and heat transfer over a radially stretching sheet. Communications in Non-Linear Science and Numerical simululations, 13 (2008), 2193-2200.  S.I. Khan, N. Ahmed, U. Khan, S.U. Jan, S.T. Mohyud-Din, Heat Transfer analysis for squeezing flow between parallel disks, Journal of the Egyptian Mathematical Society,23 (2015), 445-450.  Ayaz, F., On the two-dimensional differential transform method, Appl. Math. Comput., 143(2- 3)(2003),361-374.  Ayaz, F., Solutions of the system of differential equations by differential transform method, Appl. Math. Comput., 147(2)(2004),547-567.  V. S. Erturk, S. Momani, Differential Transform Technique for Solving Fifth-Order Boundary Value Problems, Math. Comput. Appl. (2008), 13(2), 113-121 Cite this paper Fatma Ayaz, Hayriye Yetim, Nilay Akgonullu Pirim. (2018) Approximate Solution for Magnetohydrodynamics Fluid Flow between Two Circular Discs. International Journal of Mechanical Engineering, 3, 1-8 Copyright © 2018 Author(s) retain the copyright of this article.This article is published under the terms of the Creative Commons Attribution License 4.0