Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall

A. Sami Bataineh, O. R. Isik, Ishak Hashim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method.

Original languageEnglish
Pages (from-to)2149-2156
Number of pages8
JournalAlexandria Engineering Journal
Volume55
Issue number3
DOIs
Publication statusPublished - 1 Sep 2016

Fingerprint

Magnetohydrodynamics
Heat transfer
Fluids
Error correction
Polynomials

Keywords

  • Bernstein operational matrix method
  • Bernstein polynomials
  • Error analysis
  • Heat transfer
  • MHD flow
  • Residual correction procedure

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall. / Bataineh, A. Sami; Isik, O. R.; Hashim, Ishak.

In: Alexandria Engineering Journal, Vol. 55, No. 3, 01.09.2016, p. 2149-2156.

Research output: Contribution to journalArticle

@article{771d964eca2a4197b044c72fda4ce486,
title = "Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall",
abstract = "In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method.",
keywords = "Bernstein operational matrix method, Bernstein polynomials, Error analysis, Heat transfer, MHD flow, Residual correction procedure",
author = "Bataineh, {A. Sami} and Isik, {O. R.} and Ishak Hashim",
year = "2016",
month = "9",
day = "1",
doi = "10.1016/j.aej.2016.06.022",
language = "English",
volume = "55",
pages = "2149--2156",
journal = "AEJ - Alexandria Engineering Journal",
issn = "1110-0168",
publisher = "Alexandria University",
number = "3",

}

TY - JOUR

T1 - Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall

AU - Bataineh, A. Sami

AU - Isik, O. R.

AU - Hashim, Ishak

PY - 2016/9/1

Y1 - 2016/9/1

N2 - In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method.

AB - In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method.

KW - Bernstein operational matrix method

KW - Bernstein polynomials

KW - Error analysis

KW - Heat transfer

KW - MHD flow

KW - Residual correction procedure

UR - http://www.scopus.com/inward/record.url?scp=84991832983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991832983&partnerID=8YFLogxK

U2 - 10.1016/j.aej.2016.06.022

DO - 10.1016/j.aej.2016.06.022

M3 - Article

VL - 55

SP - 2149

EP - 2156

JO - AEJ - Alexandria Engineering Journal

JF - AEJ - Alexandria Engineering Journal

SN - 1110-0168

IS - 3

ER -