A new analytical study of MHD stagnation-point flow in porous media with heat transfer

Abstract The similarity solution for the MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium gives a system of nonlinear partial differential equations. These equations are solved analytically by using a novel analytical method (DTM-Pade technique which is a combination of the differential transform method and the Pade approximation). This method is applied to give solutions of nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the Prandtl number, permeability parameter, Hartmann number and suction/blowing parameter on the velocity and temperature profiles.

[1]  Shaher Momani,et al.  Comparing numerical methods for solving fourth-order boundary value problems , 2007, Appl. Math. Comput..

[2]  T. Y. Na,et al.  Computational methods in engineering boundary value problems , 1979 .

[3]  Mohd. Salmi Md. Noorani,et al.  Application of the differential transformation method for the solution of the hyperchaotic Rössler system , 2009 .

[4]  Zaid M. Odibat,et al.  Differential transform method for solving Volterra integral equation with separable kernels , 2008, Math. Comput. Model..

[5]  H. Takhar,et al.  Flow through a porous medium , 1987 .

[6]  A. Raptis,et al.  Hydromagnetic free convection flow through a porous medium between two parallel plates , 1982 .

[7]  Karl Hiemenz,et al.  Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder , 1911 .

[8]  K. Yih The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media , 1998 .

[9]  I. Hashim,et al.  Approximate analytical solution for MHD stagnation-point flow in porous media , 2009 .

[10]  P. D. Ariel,et al.  Hiemenz flow in hydromagnetics , 1994 .

[11]  Moustafa El-Shahed,et al.  Application of differential transform method to non-linear oscillatory systems , 2008 .

[12]  Ibrahim Özkol,et al.  Solution of differential-difference equations by using differential transform method , 2006, Appl. Math. Comput..

[13]  Mohammad Mehdi Rashidi,et al.  New analytical method for solving Burgers' and nonlinear heat transfer equations and comparison with HAM , 2009, Comput. Phys. Commun..

[14]  Cha'o-Kuang Chen,et al.  Solving partial differential equations by two-dimensional differential transform method , 1999, Appl. Math. Comput..

[15]  S. Çatal Solution of free vibration equations of beam on elastic soil by using differential transform method , 2008 .

[16]  D. W. Beard,et al.  Elastico-viscous boundary-layer flows I. Two-dimensional flow near a stagnation point , 1964, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  Fatma Ayaz,et al.  Solutions of the system of differential equations by differential transform method , 2004, Appl. Math. Comput..

[18]  Ibrahim Özkol,et al.  Solutions of integral and integro-differential equation systems by using differential transform method , 2008, Comput. Math. Appl..

[19]  S. Momani,et al.  Application of generalized differential transform method to multi-order fractional differential equations , 2008 .

[20]  M. Rashidi,et al.  A Novel Analytical Solution of the Thermal Boundary-Layer over a Flat Plate with a Convective Surface Boundary Condition Using DTM-Padé , 2009, 2009 International Conference on Signal Processing Systems.

[21]  Shaher Momani,et al.  A generalized differential transform method for linear partial differential equations of fractional order , 2008, Appl. Math. Lett..

[22]  H. Takhar,et al.  Magnetohydrodynamic free convection flow of water at 4°C through a porous medium , 1994 .

[23]  P. Ariel Stagnation point flow with suction : an approximate solution , 1994 .

[24]  Ji-Huan He Homotopy perturbation technique , 1999 .

[25]  Mohammad Mehdi Rashidi,et al.  New Analytical Solution of the Three-Dimensional Navier-Stokes Equations , 2009 .