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Article
Publication date: 5 September 2016

Abbas Saadatmandi and Zeinab Sanatkar

The purpose of this paper is to develop an efficient method for solving the magneto-hydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a…

Abstract

Purpose

The purpose of this paper is to develop an efficient method for solving the magneto-hydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous isothermal stretching sheet.

Design/methodology/approach

The paper applied a collocation approach based on rational Legendre functions for solving the third-order non-linear boundary value problem, describing the MHD boundary layer flow of an UCM fluid over a porous isothermal stretching sheet. This method solves the problem on the semi-infinite domain without transforming domain of the problem to a finite domain.

Findings

This approach reduces the solution of a problem to the solution of a system of algebraic equations. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem. The authors also compare the results of this work with some recent results and show that the new method is efficient and applicable.

Originality/value

The method solves this problem without use of discrete variables and linearization or small perturbation. Also it was confirmed by the theorem and figure of absolute coefficients that this approach has exponentially convergence rate.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 3 August 2012

Mehdi Dehghan, Jalil Manafian and Abbas Saadatmandi

Rosenau‐Hyman equation was discovered as a simplified model to study the role of nonlinear dispersion on pattern formation in liquid drops. Also, this equation has…

Abstract

Purpose

Rosenau‐Hyman equation was discovered as a simplified model to study the role of nonlinear dispersion on pattern formation in liquid drops. Also, this equation has important roles in the modelling of various problems in physics and engineering. The purpose of this paper is to present the solution of Rosenau‐Hyman equation.

Design/methodology/approach

This paper aims to present the solution of the Rosenau‐Hyman equation by means of semi‐analytical approaches which are based on the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM).

Findings

These techniques reduce the volume of calculations by not requiring discretization of the variables, linearization or small perturbations. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. These results reveal that the proposed methods are very effective and simple to perform.

Originality/value

Efficient techniques are developed to find the solution of an important equation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 9 August 2011

Mehdi Dehghan, Jalil Manafian Heris and Abbas Saadatmandi

The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.

Abstract

Purpose

The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.

Design/methodology/approach

This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems.

Findings

This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations.

Originality/value

The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh‐Nagumo equation illustrates its effectiveness.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 12 June 2017

Ali Saleh Alshomrani, Sapna Pandit, Abdullah K. Alzahrani, Metib Said Alghamdi and Ram Jiwari

The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of…

Abstract

Purpose

The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. These types of equations describe a variety of physical models in the vibrations of structures, nonlinear optics, quantum field theory and solid-state physics, etc.

Design/methodology/approach

Dirichlet boundary conditions cannot be handled easily by cubic trigonometric B-spline functions. Then, a modification is made in cubic trigonometric B-spline functions to handle the Dirichlet boundary conditions and a numerical algorithm is developed. The proposed algorithm reduced the hyperbolic-type wave equations into a system of first-order ordinary differential equations (ODEs) in time variable. Then, stability-preserving SSP-RK54 scheme and the Thomas algorithm are used to solve the obtained system. The stability of the algorithm is also discussed.

Findings

A different technique based on modified cubic trigonometric B-spline functions is proposed which is quite different from the schemes developed (Abbas et al., 2014; Nazir et al., 2016) and depicts the computational modelling of hyperbolic-type wave equations.

Originality/value

To the best of the authors’ knowledge, this technique is novel for solving hyperbolic-type wave equations and the developed algorithm is free from quasi-linearization process and finite difference operators for time derivatives. This algorithm gives better results than the results discussed in literature (Dehghan and Shokri, 2008; Batiha et al., 2007; Mittal and Bhatia, 2013; Jiwari, 2015).

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Article
Publication date: 20 September 2011

Mehdi Dehghan and Fatemeh Shakeri

Multi‐point boundary value problems have important roles in the modelling of various problems in physics and engineering. This paper aims to present the solution of…

Abstract

Purpose

Multi‐point boundary value problems have important roles in the modelling of various problems in physics and engineering. This paper aims to present the solution of ordinary differential equations with multi‐point boundary value conditions by means of a semi‐numerical approach which is based on the homotopy analysis method.

Design/methodology/approach

The convergence of the obtained solution is expressed and some typical examples are employed to illustrate validity, effectiveness and flexibility of this procedure. This approach, in contrast to perturbation techniques, is valid even for systems without any small/large parameters and therefore it can be applied more widely than perturbation techniques, especially when there do not exist any small/large quantities.

Findings

Unlike other analytic techniques, this approach provides a convenient way to adjust and control the convergence of approximation series. Some applications will be briefly introduced.

Originality/value

The paper shows how an important boundary value problem is solved with a semi‐analytical method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Content available

Abstract

Details

Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 27 May 2014

Masood Khan, Azeem Shahzad, Asia Anjum and Fazal M. Mahomed

– The purpose of this paper is to find analytic approximate solutions for time-dependent flow and heat transfer of a Sisko fluid.

Abstract

Purpose

The purpose of this paper is to find analytic approximate solutions for time-dependent flow and heat transfer of a Sisko fluid.

Design/methodology/approach

The homotopy analysis method is used to find a family of travelling wave solutions of the governing non-linear problem.

Findings

The effects of different parameters on the velocity and temperature profiles are shown graphically.

Originality/value

The analytic solutions of the system of non-linear ordinary differential equations are constructed in the series form for various values of the power index.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 25 February 2014

Hany Hassan and Mohammad Mehdi Rashidi

– The paper aims to find an accurate analytic solution (series solution) for the micropolar flow in a porous channel with mass injection for different values of Reynolds number.

Abstract

Purpose

The paper aims to find an accurate analytic solution (series solution) for the micropolar flow in a porous channel with mass injection for different values of Reynolds number.

Design/methodology/approach

In this paper, the homotopy analysis method (HAM) with different numbers of unknown convergence-control parameters has been used to derive accurate analytic solution for micropolar flow in a porous channel with mass injection. The possible optimal value of convergence-control parameter determined by minimizing the averaged residual error.

Findings

The results obtained from HAM solution with two parameters are compared with numerical results and that obtained from HAM solution with only one parameter. The results show that this method gives an analytical solution with high order of accuracy with a few iterations. As shown in this paper, by minimizing the averaged residual error, the authors can get the possible optimal value of the convergence-control parameters which may give the fastest convergent series.

Practical implications

The HAM with different numbers of unknown convergence-control parameters can be used to obtain analytic solutions for many problems in sciences and engineering.

Originality/value

This paper fulfils an identified need to evaluate the accurate analytic solution (series solution) of practical problem.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 2 October 2017

M. Mustafa, T. Hayat and A. Alsaedi

The purpose of this paper is to analyze the heat transfer effects on the stretched flow of Oldroyd-B fluid in a rotating frame. Cattaneo–Christov heat conduction model is…

Abstract

Purpose

The purpose of this paper is to analyze the heat transfer effects on the stretched flow of Oldroyd-B fluid in a rotating frame. Cattaneo–Christov heat conduction model is considered, which accounts for the influence of thermal relaxation time.

Design/methodology/approach

Based on scale analysis, the usual boundary layer approximations are used to simplify the governing equations. The equations so formed have been reduced to self-similar forms by similarity transformations. A powerful analytic approach, namely, homotopy analysis method (HAM), has been applied to present uniformly convergent solutions for velocity and temperature profiles.

Findings

Suitable values of the so-called auxiliary parameter in HAM are obtained by plotting h-curves. The results show that boundary layer thickness has an inverse relation with fluid relaxation time. The rotation parameter gives resistance to the momentum transport and enhances fluid temperature. Thermal boundary layer becomes thinner when larger values of thermal relaxation time are chosen.

Originality/value

To the authors’ knowledge, this is the first attempt to study the three-dimensional rotating flow and heat transfer of Oldroyd-B fluid.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 12 October 2018

Tasawar Hayat, Tayyaba Ayub, Taseer Muhammad, Ahmed Alsaedi and M. Mustafa

The purpose of this paper is to construct mathematical model for squeezed flow of carbon-water nanofluid between parallel disks considering Darcy–Forchheimer porous…

Abstract

Purpose

The purpose of this paper is to construct mathematical model for squeezed flow of carbon-water nanofluid between parallel disks considering Darcy–Forchheimer porous medium. Thermal conductivity of carbon nanotubes is estimated through the well-known Xue model. Such research work is not carried out in the past even in the absence of Darcy–Forchheimer porous space. Forchheimer equation is preferred here to account for both low and high velocity inertial effects. Researchers also found that dispersion of carbon nanotubes in water elevates the thermal conductivity of resulting nanofluid by 100 per cent.

Design/methodology/approach

Homotopy analysis method (HAM) is used for the convergent series solutions of the governing system.

Findings

Nusselt number at the lower disk increases when squeezing parameter Sq enlarges. This illustrates that heat transfer rate at the lower wall can be enhanced by increasing the squeezing velocity of the lower disk. The results demonstrate a decreasing trend in temperature profile for increasing volume fraction of carbon nanotubes. Moreover, improvement in heat transfer rate because of existence of carbon nanotubes is also apparent. A significant enhancement in temperature profile is depicted when inertial permeability coefficient is enhanced. Skin friction coefficients at the lower and upper disks are higher for MWCNTs in comparison to the SWCNTs.

Originality/value

To the best of author’s knowledge, no such consideration has been given in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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