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1 – 10 of over 2000
Article
Publication date: 6 August 2018

Ali Belhocine and Wan Zaidi Wan Omar

The purpose of this paper is to re-examine the assumptions implicit in Leveque’s approximation, and the variation of the temperature and the thickness of the boundary layer were…

Abstract

Purpose

The purpose of this paper is to re-examine the assumptions implicit in Leveque’s approximation, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge–Kutta fourth-order (RK4) method. Finally, other important thermal results obtained from this analysis, such as approximate Nusselt number in the thermal entrance region, was discussed in detail. After that, the analytical results of the present paper are validated with certain previous investigations which were found in the specialized literature.

Design/methodology/approach

By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This paper gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form and presents a similarity solution. The calculation methodology for numerical resolution is based on the RK4 technique.

Findings

The profiles of the solutions are provided from which the authors infer that the numerical and exact solutions agreed very well. Another result that the authors obtained from this paper is the number of Nusselt in the thermal entrance region for which a parametric study was carried out and discussed well for the impact of scientific contribution.

Originality/value

The novelty of this paper is the application of the RK4 with a step size control, as a sequential numerical method of a ODEs system compared with the exact similarity solution of the thermal boundary layer problem.

Details

World Journal of Engineering, vol. 15 no. 4
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 18 September 2007

Anati Ali, Norsarahaida Amin and Ioan Pop

The purpose of this paper is to study the unsteady boundary layer flow of a micropolar fluid past a circular cylinder which is started impulsively from rest.

Abstract

Purpose

The purpose of this paper is to study the unsteady boundary layer flow of a micropolar fluid past a circular cylinder which is started impulsively from rest.

Design/methodology/approach

The nonlinear partial differential equations consisting of three independent variables are solved numerically using the 3D Keller‐box method.

Findings

Numerical solutions for the velocity profiles, wall skin friction and microrotation profiles are obtained and presented for various values of time t and material parameter K with the boundary condition for microrotation n=0 (strong concentration of microelements) and n=1/2 (weak concentration of microelements). The results are presented along the points on the cylinder surface, starting from the forward to the rear stagnation point, for small time up to the time when the boundary layer flow separates from the cylinder.

Originality/value

It is believed that this is the first paper that uses the 3D Keller‐box method to study the unsteady boundary layer flow of micropolar fluids. In the last four decades, there has been overhelming interest shown by researchers in micropolar fluids and still many problems are unsolved. The paper shows not only the fundamental importance of this problem, but also the implications for situations of practical interest.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 February 2020

Sihem Gherieb, Mohamed Kezzar, Abdelaziz Nehal and Mohamed Rafik Sari

The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring…

Abstract

Purpose

The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring shooting technique and analytically via a new modified analytical technique called improved generalized Adomian decomposition method (improved-GDM).

Design/methodology/approach

It is well established that the generalized decomposition method (GDM) (Yong-Chang et al., 2008), which uses a new kind of decomposition strategy for the nonlinear function, has proved its efficiency and superiority when compared to the standard ADM method. In this investigation, based on the idea of improved-ADM method developed by Lina and Song (Song and Wang, 2013), the authors proposed a new analytical algorithm of computation named improved-GDM. Thereafter, the proposed algorithm is tested by solving the nonlinear problem of the hydro-magnetic boundary layer flow over a flat plate.

Findings

The proposed improved generalized decomposition method (I-GDM) introduces a convergence-control parameter “ω’’ into the GDM, which accelerates the convergence of solution and reduces considerably the computation time. In fact, the key of this method is mainly based on the best selection of the convergence-control parameter ω.

Originality/value

The paper presents a new efficient algorithm of computation that can be considered as an alternative for solving the nonlinear initial boundary layer value problems. Obtained results show clearly the accuracy of the proposed method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 30 June 2021

A.Z. Zaher, Khalid K. Ali and Kh. S. Mekheimer

The study of the electro-osmotic forces (EOF) in the flow of the boundary layer has been a topic of interest in biomedical engineering and other engineering fields. The purpose of…

Abstract

Purpose

The study of the electro-osmotic forces (EOF) in the flow of the boundary layer has been a topic of interest in biomedical engineering and other engineering fields. The purpose of this paper is to develop an innovative mathematical model for electro-osmotic boundary layer flow. This type of fluid flow requires sophisticated mathematical models and numerical simulations.

Design/methodology/approach

The effect of EOF on the boundary layer Williamson fluid model containing a gyrotactic microorganism through a non-Darcian flow (Forchheimer model) is investigated. The problem is formulated mathematically by a system of non-linear partial differential equations (PDEs). By using suitable transformations, the PDEs system is transformed into a system of non-linear ordinary differential equations subjected to the appropriate boundary conditions. Those equations are solved numerically using the finite difference method.

Findings

The boundary layer velocity is lower in the case of non-Newtonian fluid when it is compared with that for a Newtonian fluid. The electro-osmotic parameter makes an increase in the velocity of the boundary layer. The boundary layer velocity is lower in the case of non-Darcian fluid when it is compared with Darcian fluid and as the Forchheimer parameter increases the behavior of the velocity becomes more closely. Entropy generation decays speedily far away from the wall and an opposite effect occurs on the Bejan number behavior.

Originality/value

The present outcomes are enriched to give valuable information for the research scientists in the field of biomedical engineering and other engineering fields. Also, the proposed outcomes are hopefully beneficial for the experimental investigation of the electroosmotic forces on flows with non-Newtonian models and containing a gyrotactic microorganism.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 September 2013

Sima Samadpoor, Hadi Roohani Ghehsareh and Saeid Abbasbandy

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions…

Abstract

Purpose

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are investigated.

Design/methodology/approach

In this work, the governing partial differential equations are transformed to a nonlinear ordinary differential equation by using some proper similarity transformations. Then an efficient semi-analytical method, the Laplace Adomian decomposition method (LADM) is applied to obtain semi-analytical solutions of the similarity solutions in both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. To improve the accuracy and enlarges the convergence domain of the obtained results by the LADM, the study has combined it with Padé approximation.

Findings

Accuracy and efficiency of the presented method are illustrated and denoted through the tables and figures. Also the effects of the suction parameter λ and slip parameter K on the fluid velocity and on the tangential stress are investigated.

Originality/value

The similarity solutions of the governing partial differential equation are obtained analytically by using an efficient developed method, namely the Laplace Adomian decomposition-Padé method. The analytic solutions of nonlinear ordinary differential equation are constructed for both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 September 2011

Mohammad Mehdi Rashidi and Eemaeel Erfani

The purpose of this paper is to investigate the nano boundary‐layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary…

Abstract

Purpose

The purpose of this paper is to investigate the nano boundary‐layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two‐dimensional stretching surface; and viscous flows over an axisymmetric stretching surface.

Design/methodology/approach

The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

Findings

Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM‐Padé can have wide application in engineering problems especially for boundary‐layer problems.

Originality/value

The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

Details

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

Keywords

Article
Publication date: 20 September 2011

Azizah Mohd Rohni, Syakila Ahmad and Ioan Pop

The purpose of this paper is to theoretically investigate the steady two‐dimensional boundary‐layer flow past a moving semi‐infinite flat plate in a water‐based nanofluid…

Abstract

Purpose

The purpose of this paper is to theoretically investigate the steady two‐dimensional boundary‐layer flow past a moving semi‐infinite flat plate in a water‐based nanofluid containing three different types of nanoparticles: copper (cuprum) Cu, alumina (aluminium oxide) Al2O3, and titania (titanium dioxide) TiO2. The effects of moving parameter λ as well as solid volume fraction parameter φ on the flow and heat transfer characteristics are studied. Taking into account the rising demands of modern technology, including chemical production, power stations and microelectronics, there is a need to develop new types of fluids that will be more effective in terms of heat exchange performance.

Design/methodology/approach

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.

Findings

There is a region of unique solutions for λ>0, however, multiple (dual) solutions exist for λc<λ≤0 and no solutions for λ<λc<0. A reverse flow is formed when λ<0.

Research limitations/implications

The solutions can be obtained up to a certain value of the moving parameter (critical value or turning point). The boundary layer separates from the plate beyond the turning point hence it is not possible to get the solution based on the boundary‐layer approximations after this point. To obtain further solutions, the full Navier‐Stokes equations have to be solved.

Originality/value

The present results are original and new for the boundary‐layer flow and heat transfer of a moving flat plate in a nanofluid. Therefore, this study would be important for the scientists and engineers in order to become familiar with the flow behaviour and properties of such nanofluids, and the way to predict the properties of this flow for the process equipments.

Details

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

Keywords

Article
Publication date: 1 August 2016

M.Y. Malik, Arif Hussain, T. Salahuddin and M. Awais

– The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.

Abstract

Purpose

The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.

Design/methodology/approach

The boundary layer approach is employed to simplify the governing equations. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. In order to solve this system of ordinary differential equations numerically, shooting method in conjunction with Runge-Kutta-Fehlberg method is used.

Findings

The effects of physical parameters involved in velocity and temperature profiles are shown through graphs. It is observed that Sisko fluid parameter and curvature parameter enhances fluid velocity while motion of fluid is retarded by increasing magnetic field strength. Additionally temperature of fluid raise with curvature parameter while it fall down for larger values of Prandtl number. Skin friction coefficient and Nusselt number are computed and presented in graphs and tables for further analysis. It can be seen that curvature parameter increases both skin friction and Nusselt number while magnetic field and Prandtl number decayed skin friction and Nusselt number, respectively. Also Sisko parameter enlarges skin friction coefficient. The accuracy of solution is verified by comparing it with existing literature.

Originality/value

The computed results are interested for industrial and engineering processes, especially in cooling of nuclear reactors.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 1966

John K. Wimpress

THE shortened runway has become an order of the day. Commercial operators want to offer jet service to communities with small airports. Military services seek to use small…

Abstract

THE shortened runway has become an order of the day. Commercial operators want to offer jet service to communities with small airports. Military services seek to use small, unprepared fields—or no fields at all, just clearings.

Details

Aircraft Engineering and Aerospace Technology, vol. 38 no. 6
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 11 January 2011

Y.Y. Lok, A. Ishak and I. Pop

The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of…

Abstract

Purpose

The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied.

Design/methodology/approach

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.

Findings

The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.

Practical implications

The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface.

Originality/value

The present results are original and new for the MHD flow near the stagnation‐point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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