<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.</p></abstract>

This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.

Dirichlet series and analytical solutions of MHD viscous flow with suction / blowing

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer...

f_w	Dirichlet series method			Numerical	Method of stretching of variables
f_w	a	γ	f″(0)	f″(0)	f″(0)
−1	−0.0965256	1.0189385	−0.8456998	−0.849425600	−0.858678
0	−0.0621294	1.2387362	−1.0819500	−1.082828844	−1.080120
1	−0.0406485	1.5109842	−1.3537160	−1.371011260	−1.358680

M	Dirichlet series method			Numerical	Method of stretching of variables
M	a	γ	f″(0)	f″(0)	f″(0)
1	−0.0621294	1.2387362	−1.0819500	−1.082828844	−1.080120
2	−0.0356405	1.5870945	−1.4727840	−1.473039150	−1.471960
5	−0.0156185	2.3469129	−2.2732890	−2.273317103	−2.273030

Dirichlet series and analytical solutions of MHD viscous flow with suction / blowing

Published Online: Aug 13, 2017

Page range: 341 - 350

Received: Mar 09, 2017

Accepted: Aug 13, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00028

Keywords
Magnetohydrodynamics (MHD), boundary layer flow, Dirichlet series, Powell method, method of stretching variables

© 2017 Vishwanath B. Awati, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Various values of suction or blowing parameters fw obtained by Dirichlet series and method of stretching of variables with their numerical values for M = 1.

Various values of magnetic parameters M obtained by Dirichlet series and method of stretching of variables with their numerical values for fw = 0.

Dirichlet series and analytical solutions of MHD viscous flow with suction / blowing

Published Online: Aug 13, 2017

Page range: 341 - 350

Received: Mar 09, 2017

Accepted: Aug 13, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00028

KeywordsMagnetohydrodynamics (MHD), boundary layer flow, Dirichlet series, Powell method, method of stretching variables

© 2017 Vishwanath B. Awati, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Various values of suction or blowing parameters fw obtained by Dirichlet series and method of stretching of variables with their numerical values for M = 1.

Various values of magnetic parameters M obtained by Dirichlet series and method of stretching of variables with their numerical values for fw = 0.

Keywords
Magnetohydrodynamics (MHD), boundary layer flow, Dirichlet series, Powell method, method of stretching variables