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1 – 10 of over 2000
Article
Publication date: 7 June 2013

Mehmet Merdan, Ahmet Gökdoğan, Ahmet Yildirim and Syed Tauseef Mohyud‐Din

In this article, the aim is to obtain an approximate analytical solution of time‐fraction generalized Hirota‐Satsuma coupled KDV with the help of the two dimensional differential

Abstract

Purpose

In this article, the aim is to obtain an approximate analytical solution of time‐fraction generalized Hirota‐Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions.

Design/methodology/approach

Two dimensional differential transformation method (DTM) is used.

Findings

In this paper, the fractional differential transformation method is implemented to the solution of time‐fraction generalized generalized Hirota‐Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial.

Originality/value

This is an original work in which the results indicate that the method is powerful and significant for solving time‐fraction generalized generalized Hirota‐Satsuma coupled KDV type differential equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 2006

Eugeniusz Kurgan and Paweł Schmidt

Distribution of the electric potential and current density in the electrode of the proton exchange membrane fuel cell.

Abstract

Purpose

Distribution of the electric potential and current density in the electrode of the proton exchange membrane fuel cell.

Design/methodology/approach

Multicomponent model based on Maxwell‐Stefan equations is used to formulate generalized Fick's law. Next, mass conservation laws for gas components and equation of continuity for current density vector are formulated.

Findings

The problem is expressed by three non‐linear partial differential equations in total molar contraction of the gas mixture, oxygen and water vapor concentration describing multicomponent Maxwell‐Stefan mass transport and fourth equation for electric potential distribution. The final system of partial differential equations describing the problem is highly non‐linear and mutually coupled not only directly but also through the non‐linear boundary condition and is solved by finite element method.

Research limitations/implications

There are some convergence problems for some sets of the material parameters. Only one part of the fuel cell was modeled.

Practical implications

This approach allows one to calculate all important parameters required to develop and design the practical systems as well to optimize the performance from the geometrical and material parameters point of view.

Originality/value

The presented approach combines distribution of mass transport using Maxwell‐Stefan model and electric potential described by Laplace equation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 10 August 2015

Nivedita Sharma

The purpose of this paper is to present a model to analyze free vibrations in a transradially isotropic, thermoelastic hollow sphere subjected to stress free, thermally insulated…

Abstract

Purpose

The purpose of this paper is to present a model to analyze free vibrations in a transradially isotropic, thermoelastic hollow sphere subjected to stress free, thermally insulated or stress free, isothermal and rigidly fixed, thermally insulated or rigidly fixed, isothermal boundary conditions.

Design/methodology/approach

The potential functions along with spherical wave solution have been used to reduce the system of governing partial differential equations to a coupled system of ordinary differential equations in radial coordinates after employing non-dimensional quantities. Matrix Frobenius method of extended power series has been employed to obtain accurate solution of coupled differential equations in terms of radial coordinates. The mathematical model of the considered problem has been solved analytically to obtain the characteristics equations after imposing the appropriate boundary conditions at the outer and inner surfaces of the hollow sphere. The characteristic equations which govern various types of vibration modes expected to exist have been derived in the compact form. The special cases of spheroidal and toroidal modes of vibrations have been deduced from the characteristic equations and discussed.

Findings

The toroidal mode has been found to be independent of temperature change. The magnitude of lowest frequency and damping factor are significantly affected in the presence of thermal field and increase with an increase in the spherical harmonics in addition to geometry of the structure.

Originality/value

The matrix Frobenius method has been used to develop analytical solutions and functional iteration technique to carry out numerical simulations of such structures for the first time. The simulated results are presented graphically and compared with the available literature.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 11 October 2018

Prabhugouda Mallanagouda Patil, Geeta Hadimani, Shashikant A., P.S. Kulkarni and Mukesh Kumar

This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of…

Abstract

Purpose

This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of suction/blowing, volumetric heat source/sink and velocity ratio parameter will be studied in this analysis.

Design/methodology/approach

The modeled governing equations for the assumed problem are dimensional nonlinear partial differential equations in nature. To reduce these equations, non-similar transformations are used to get the dimensionless nonlinear partial differential equations. Then, quasi-linearization technique is used to linearize these non-dimensional nonlinear partial differential equations. Finally, an implicit finite difference scheme is used to discretize the resulting equations.

Findings

The physical explanations are provided for the variations of various non-dimensional governing parameters over the velocity and temperature profiles. Also, the effects of these dimensionless parameters on skin friction coefficient and heat transfer rate are scrutinized in a manner which highlights their physical interpretation. The detailed discussion exhibits the fact that the streamwise co-ordinate velocity ratio parameter, partial slip parameter and the thermal jump parameter have significant influence over the flow and thermal fields.

Originality/value

This work has not been reported in the literature to the authors’ best of knowledge.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 January 2019

Abhishek Kumar Singh, A.K. Singh and S. Roy

The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The…

Abstract

Purpose

The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.

Design/methodology/approach

The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.

Findings

The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.

Originality/value

The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 22 March 2021

Iyyappan G. and Abhishek Kumar Singh

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects…

Abstract

Purpose

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur.

Design/methodology/approach

The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh.

Findings

The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2.

Originality/value

The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 July 2020

Joan Carles Mico, Salvador Amigó, Antonio Caselles and Pantaleón D. Romero

The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the…

Abstract

Purpose

The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the biological levels of description.

Design/methodology/approach

The relationship between the two mentioned levels of description is provided by two mathematical models as follows: the response model and the bridge model. The response model (an integro-differential equation) is capable to reproduce the personality dynamics as a consequence of a determined stimulus. The invariance principle asserts that the response model can reproduce personality dynamics at the two levels of description. The bridge model (a second-order partial differential equation) can be deduced as a consequence of this principle: it provides the co-evolution of the general factor of personality (GFP) (mind), the it is an immediate early gene (c-fos) and D3 dopamine receptor gene (DRD3) gens and the glutamate neurotransmitter (body).

Findings

An application case is presented by setting up two experimental designs: a previous pilot AB pseudo-experimental design (AB) pseudo-experimental design with one subject and a subsequent ABC experimental design (ABC) experimental design with another subject. The stimulus used is the stimulant drug methylphenidate. The response and bridge models are validated with the outcomes of these experiments.

Originality/value

The mathematical approach here presented is based on a holistic personality model developed in the past few years: the unique trait personality theory, which claims for a single personality trait to understand the overall human personality: the GFP.

Article
Publication date: 18 November 2013

Paras Ram and Vikas Kumar

The aim of the present study is to examine the ferrohydrodynamic laminar boundary layer flow of electrically non-conducting magnetic fluid on a uniformly heated and radially…

Abstract

Purpose

The aim of the present study is to examine the ferrohydrodynamic laminar boundary layer flow of electrically non-conducting magnetic fluid on a uniformly heated and radially stretchable disk with or without rotation in the presence of an externally applied magnetic field.

Design/methodology/approach

Governing equations give rise to highly non-linear coupled partial differential equations which are reduced to a set of ordinary differential equations in dimensionless form by the means of conventional similarity transformation. These equations are further discretized using central finite difference scheme. And, the solution is obtained in MATLAB environment by finding the missing boundary conditions using shooting method.

Findings

The effects of magnetic field dependent viscosity and rotation strength parameter on velocity and temperature profiles are investigated. Besides, the other significant physical quantities such as radial and tangential skin frictions, rate of heat transfer and boundary layer displacement thickness are also computed. The obtained results are discussed quantitatively and qualitatively.

Originality/value

Heat transfer in ferrofluid flow over a radially stretchable and uniformly heated rotating disk has not been investigated yet.

Details

Multidiscipline Modeling in Materials and Structures, vol. 9 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 1 January 2009

X.Q. Zhang

widely‐used hypoelastic model for four well‐known objective stress rates under a four‐phase stress cycle associated with axial tension and/or torsion of thin‐walled cylindrical…

Abstract

widely‐used hypoelastic model for four well‐known objective stress rates under a four‐phase stress cycle associated with axial tension and/or torsion of thin‐walled cylindrical tubes. Here, two kinds of models based upon the Cauchy stress and the Kirchhoff stress will be treated. The reduced systems of differential equations of these rate constitutive equations are derived and studied for Jaumann, Green‐ Naghdi, logarithmic and Truesdell stress rates, separately. Analytical solutions in some cases and numerical solutions in all cases are obtained using these reduced systems. Comparisons between the residual deformations are made for different cases. It may be seen that only the logarithmic stress rate results in no residual deformation. In particular, results indicate that Green‐Naghdi rate would generate unexpected residual deformation effect that is essentially different from that resulting from Jaumann rate. On the other hand, it is realized that this study accomplishes an alternative, direct proof for the nonintegrability problem of Truesdell’s hypoelastic rate equation with classical stress rates. This problem has been first treated successfully by Simo and Pister in 1984 using Bernstein’s integrability conditions. However, such treatment needs to cope with a coupled system of nonlinear partial differential equations in Cauchy stress. Here, a different idea is used. It is noted that every integrable hypoelastic equation is just an equivalent rate form of an elastic equation and hence should produce no residual deformations under every possible stress cycle. Accordingly, a hypoelastic model with a stress rate has to be non‐integrable, whenever a stress cycle can be found under which this model generates residual deformation. According to this idea of reductio ad absurdum, a well‐designed stress cycle is introduced and the corresponding residual deformations are calculated. Unlike the treatment of Bernstein’s integrability conditions, it may be a simple and straightforward matter to calculate the final deformations for a given stress cycle. This has been done in this study for several well‐known stress rates.

Details

Multidiscipline Modeling in Materials and Structures, vol. 5 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 4 June 2020

Uma M, Dinesh PA, Girinath Reddy M and Sreevallabha Reddy A

A study on convective aspects was carried out on a Couette flow in an irregular channel by applying a constant uniform magnetic field parallel to the channel flow.

Abstract

Purpose

A study on convective aspects was carried out on a Couette flow in an irregular channel by applying a constant uniform magnetic field parallel to the channel flow.

Design/methodology/approach

The dynamic study of such a flow resulted in highly nonlinear coupled partial differential equations. To solve these partial differential equations analytically, regular perturbation method was invoked for velocity, temperature and concentration with a combined parameter of Soret and Forchheimer. The numerical computational results have been extracted for various nondimensional parameters with regard to fluid and particle flow as well as for temperature and solute concentration.

Findings

The current article presents a novel approach to assess the effects of drag force as well as the diffusion-based interactions between the velocity, temperature and concentrations with the aid of Soret and Dufour on two-dimensional MHD mixed with a dusty viscoelastic fluid.

Originality/value

The results found are in good agreement with the earlier studies in the absence of nonlinear effect of Forchheimer model.

Details

Multidiscipline Modeling in Materials and Structures, vol. 17 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

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