Dirichlet series and approximate analytical solutions of MHD flow over a linearly stretching ‎sheet

Subject Areas : International Journal of Industrial Mathematics

Vishwanath B. ‎Awati‎ ¹ , Mahesh Kumar ‎N‎ ² , Krishna B. ‎Chavaraddi‎ ³

1 - Department of Mathematics, Rani Channamma University, Belagavi -591 156, India.
2 - Department of Mathematics, Rani Channamma University, Belagavi -591 156, India.
3 - Department of Mathematics, Govt. First Grade College, Naragund – 582 207, India.

Received: 2015-10-07 Accepted : 2015-10-07 Published : 2015-10-01

Keywords: Magnetohydrodynamics (MHD), Boundary layer flow, Shrinking sheet, Dirichlet series, Powell's method, Method of stretching ‎variable,

Abstract :

The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel the mathematical tools for their analysis. The solution of the resulting third order nonlinear boundary value problem with an infinite interval is obtained using fast converging Dirichlet series method and approximate analytical method viz. method of stretching of variables. These methods have the advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and they are valid in much larger parameter domain as compared with HAM, HPM, ADM and the classical numerical schemes. Also, these methods require less computer memory space as compared with pure numerical ‎methods.‎