Search results

1 – 10 of 207
Article
Publication date: 6 February 2017

S. Abbasbandy, Elyas Shivanian, K. Vajravelu and Sunil Kumar

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection…

Abstract

Purpose

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering.

Design/methodology/approach

Homotopy–Padé method.

Findings

The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium.

Research limitations/implications

The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity.

Social implications

Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain.

Originality/value

In this study, the authors are using two modified methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 18 April 2017

L. Ahmad Soltani, E. Shivanian and Reza Ezzati

The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of…

Abstract

Purpose

The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs).

Design/methodology/approach

A major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter.

Findings

To demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem.

Originality/value

The more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

Article
Publication date: 25 September 2018

S. Abbasbandy and M. Mustafa

This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed…

Abstract

Purpose

This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.

Design/methodology/approach

Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.

Findings

The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.

Research limitations/implications

An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.

Originality/value

Current problem even in case of Newtonian fluid has not been attempted previously.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 22 March 2013

S. Abbasbandy and H. Roohani Ghehsareh

In this paper, an analysis is performed to find the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet.

Abstract

Purpose

In this paper, an analysis is performed to find the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet.

Design/methodology/approach

The cases of two dimensional and axisymmetric shrinking have been discussed. When the sheet is shrinking in the x‐direction, the analytical solutions are obtained by the Hankel‐Padé method. Comparison to exact solutions reveals reliability and high accuracy of the procedure, even in the case of multiple solutions. The case of sheet shrinking in the y‐direction is also considered, with success.

Findings

When the sheet shrinks in the x‐direction, the analytical solutions are obtained by Hankel‐Padé method. Also, when the sheet shrinks in the y‐direction, the obtained results with Hankel‐Padé method are presented.

Practical implications

Comparison to exact solutions reveals reliability and high accuracy of the procedure and convincingly could be used to obtain multiple solutions for certain parameter domains of this case of the governing nonlinear problem.

Originality/value

The numerical solutions are given for both two‐dimensional and axisymmetric shrinking sheets by using Hankel‐Padé method. It is clear that the Hankel‐Padé method is, by far, more simple, straightforward and gives reasonable results for large Hartman numbers and suction parameters.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 April 2015

M. Nawaz, A Zeeshan, R Ellahi, S Abbasbandy and Saman Rashidi

The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of…

Abstract

Purpose

The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic algorithm (GA). The main emphasis is to find the analytical and numerical solutions for the said mathematical model. The work undertaken is a blend of numerical and analytical studies. Effects of active parameters such as: Hartmann number, Prandtl number, Eckert number, Nusselt number, Skin friction and dimensionless fluids parameters on the flow and heat transfer characteristics have been examined by graphs and tables. Compression is also made with the existing benchmark results.

Design/methodology/approach

Analytical solutions of non-linear coupled equations are developed by optimal homotopy analysis method (OHAM). A very effective and higher order numerical scheme hybrid GA and Nelder-Mead optimization Algorithms are used for numerical investigations.

Findings

An excellent agreement with the existing results in limiting sense is noted. It is observed that the radial velocity is an increasing function of dimensionless material parameters α 1, α 2 and β. Temperature increases by increasing the values of M, Pr, Ec and γ. Non-Newtonian parameter β has similar effects on skin friction coefficient and Nusselt number. The wall heat transfer rate is a decreasing function of A and ß whereas it increases by increasing conjugate parameter γ.

Originality/value

The problem under consideration has been widely studied by many investigators due to its importance and engineering applications. But most of the studies as the authors have documented are for Newtonian or viscous fluids. But no such analysis is available in the literature which can describe the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of GA.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 25 February 2014

S. Abbasbandy, T. Hayat, A. Alsaedi and M.M. Rashidi

– In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues.

Abstract

Purpose

In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues.

Design/methodology/approach

In this paper, the authors used two methods: homotopy analysis method and numerical Keller-box method.

Findings

It is observed that skin friction coefficient in Oldroyd-B fluid is larger when compared with viscous fluid. Further, the relaxation and retardation times have opposite effects on the velocity components.

Practical implications

A comparative study between the series and numerical solutions for the skin friction is shown in the paper. The results indicated that both solutions are in well agreement.

Originality/value

This model is investigated for the first time, as the authors know.

Details

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

Keywords

Article
Publication date: 2 March 2015

A Chamkha, S Abbasbandy and A.M. Rashad

The purpose of this paper is to investigate the effect of uniform lateral mass flux on non-Darcy natural convection of non-Newtonian fluid along a vertical cone embedded…

Abstract

Purpose

The purpose of this paper is to investigate the effect of uniform lateral mass flux on non-Darcy natural convection of non-Newtonian fluid along a vertical cone embedded in a porous medium filled with a nanofluid.

Design/methodology/approach

The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved numerically by Keller box finite-difference method.

Findings

A comparison with previously published works is performed and excellent agreement is obtained.

Research limitations/implications

The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. It is assumed that the cone surface is preamble for possible nanofluid wall suction/injection, under the condition of uniform heat and nanoparticles volume fraction fluxes.

Originality/value

The effects of nanofluid parameters, Ergun number, surface mass flux and viscosity index are investigated on the velocity, temperature, and volume fraction profiles as well as the local Nusselt and Sherwood numbers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 June 2016

R Ellahi, E Shivanian, S Abbasbandy and T. Hayat

The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer…

Abstract

Purpose

The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer, magnetohydrodynamics and slip.

Design/methodology/approach

A hybrid technique based on pseudo-spectral collocation is applied for the solution of nonlinear resulting system.

Findings

Viscous fluid results which are yet not available can be taken as a limiting case of presented problem. The results for the case of Hartmann flow can be obtained as a special case when plate velocity is zero, i.e. pressure gradient induced flow. The results for the zero fluid slip and no thermal slip also become special cases of this work, and the results can be recovered by setting, and to zero. These solutions are valid not only for small but also for large values of all emerging parameters.

Originality/value

This model is investigated for the first time, as the authors know.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 19 September 2018

O.K. Koriko, I.L. Animasaun, A.J. Omowaye and T. Oreyeni

The purpose of this paper is to consider the problem of thermal destratification facing engineers and scientists during the motion of fluids which consist of rigid and…

149

Abstract

Purpose

The purpose of this paper is to consider the problem of thermal destratification facing engineers and scientists during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force. This paper provides an insight into the non-linear transfer of thermal radiation within the boundary layer.

Design/methodology/approach

Similarity transformation and parameterization of the non-linear partial differential equation are carried out. The approximate analytical solution of the governing equation which models the free convective flow of strong and weak concentration of micro-elements in a micropolar fluid over a vertical surface is presented.

Findings

It is observed that the velocity and temperature distribution are decreasing properties of thermal stratification parameter St. Maximum local skin friction coefficients are ascertained at an epilimnion level (St=0) when the magnitude of thermal radiation is small. Thermal stratification parameter has no significant effect on the temperature distribution in the flow near a free stream.

Originality/value

The relationship between stratification of temperature and the transfer of thermal energy during the problem of thermal destratification facing engineers and scientist during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force is unravelled in this paper.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 4 December 2017

Aurang Zaib, Mohammad Mehdi Rashidi, Ali J. Chamkha and Krishnendu Bhattacharyya

This paper aims to peruse the influence of second law analysis for electrically conducting fluid of a Casson nanofluid over a wedge. For activation energy, a modified…

Abstract

Purpose

This paper aims to peruse the influence of second law analysis for electrically conducting fluid of a Casson nanofluid over a wedge. For activation energy, a modified Arrhenius function is used.

Design/methodology/approach

The highly non-linear governing equations are developed using similarity transformations and then computed numerically via Keller–Box method.

Findings

The influences of emerging parameters on velocity, temperature distribution and concentration of nanoparticle are explained and presented via graphs and tables. Also, the behavior of fluid flow is investigated through the coefficient of skin friction, Nusselt and Sherwood numbers. Results reveal that the velocity profile enhances due to increasing Casson parameter and magnetic parameter, whereas the temperature distribution and concentration of nanoparticle decrease with larger vales of Casson parameter. It is inspected that the concentration boundary layer increases due to activation energy and decreases due to reaction rate and temperature differences.

Originality/value

The authors believe that all the numerical results are original and significant which are used in biomedicine, industrial, electronics and transportation. The results have not been considered elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 207