Eur. Phys. J. Plus (2017) 132: 326
https://doi.org/10.1140/epjp/i2017-11598-1

Regular Article

Investigation of magneto-hemodynamic flow in a semi-porous channel using orthonormal Bernstein polynomials

¹ Department of Mathematics, Yazd University, Yazd, Iran
² Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, 4800 Cao An Rd., Jiading, 201804, Shanghai, China
³ ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai, China

^* e-mail: e_hosseini@stu.yazd.ac.ir

Received: 10 April 2017
Accepted: 16 June 2017
Published online: 27 July 2017

Abstract

In this paper, the problem of the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field is investigated numerically. Using a Berman’s similarity transformation, the two-dimensional momentum conservation partial differential equations can be written as a system of nonlinear ordinary differential equations incorporating Lorentizian magneto-hydrodynamic body force terms. A new computational method based on the operational matrix of derivative of orthonormal Bernstein polynomials for solving the resulting differential systems is introduced. Moreover, by using the residual correction process, two types of error estimates are provided and reported to show the strength of the proposed method. Graphical and tabular results are presented to investigate the influence of the Hartmann number (Ha) and the transpiration Reynolds number (Re on velocity profiles in the channel. The results are compared with those obtained by previous works to confirm the accuracy and efficiency of the proposed scheme.