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Article
Publication date: 24 March 2021

Zahia Amrouchi, Frederic Messine, Clement Nadal and Mohand Ouanes

In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is…

Abstract

Purpose

In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is addressed. The purpose of this study is to propose to include torque ripples as an extra constraint in the optimization phase involving de facto the study of a semi-infinite optimization problem.

Design/methodology/approach

Based on the use of a well-known analytical model describing the electromagnetic behavior of an SPMM, this analytical model has been supplemented by the calculus of the dynamic torque and its ripples to carry out a more accurate optimized sizing method of such an electromechanical converter. As a consequence, the calculated torque depends on a continuous variable, namely, the rotor angular position, resulting in the definition of a semi-infinite optimization problem. The way to solve this kind of semi-infinite problem by discretizing the rotor angular position by using a deterministic global optimization solver, that is to say COUENNE, via the AMPL modeling language is addressed.

Findings

In this study, the proposed approach is validated on some numerical tests based on the minimization of the magnet volume. Efficient global optimal solutions with torque ripples about 5% (instead of 30%) can be so obtained.

Research limitations/implications

The analytical model does not use results from the solution of two-dimensional field equations. A strong assumption is put forward to approximate the distribution of the magnetic flux density in the air gap of the SPMM.

Originality/value

The problem to design an SPMM can be efficiently formulated as a semi-infinite global optimization problem. This kind of optimization problems are hard to solve because they involve an infinity of constraints (coming from a constraint on the torque ripple). The authors show in this paper that by using analytical models, a discretization method and a deterministic global optimization code COUENNE, this problem is efficiently tackled. Some numerical results show that the deterministic global solution of the design can be reached even if the step of discretization is small.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 40 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 29 September 2023

Tasneem Firdous Islam, G.D. Kedar and Sajid Anwar

The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This…

Abstract

Purpose

The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered.

Design/methodology/approach

This study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture.

Findings

The paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings.

Research limitations/implications

The research presented in this article is primarily hypothetical and focused on the analysis of mathematical models.

Originality/value

To the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field.

Details

Multidiscipline Modeling in Materials and Structures, vol. 19 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 7 June 2013

K. Parand and L. Hosseini

The aim is to present in this paper an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite…

Abstract

Purpose

The aim is to present in this paper an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.

Design/methodology/approach

The authors introduce a new orthogonal system of rational functions induced by general Jacobi polynomials with the parameters alpha and beta. It is more flexible in applications. In particular, alpha and beta could be regulated, so that the systems are mutually orthogonal in certain weighted Hilbert spaces.

Findings

This approach is applied for solving a non‐linear system two‐point boundary value problem (BVP) on semi‐infinite interval, describing the flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. The new approach reduces the solution of a problem to the solution of a system of algebraic equations.

Originality/value

The paper presents an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.

Details

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

Keywords

Article
Publication date: 3 May 2013

Michael Kijowski and Ludger Klinkenbusch

The purpose of this paper is to compare exact and Physical‐Optics‐approximated results of the electromagnetic field scattered by a perfectly conducting semi‐infinite elliptic cone…

Abstract

Purpose

The purpose of this paper is to compare exact and Physical‐Optics‐approximated results of the electromagnetic field scattered by a perfectly conducting semi‐infinite elliptic cone illuminated by a plane wave. The results are important for judging the reliability of Physical‐Optics based field estimations of electrically large environments which include tip‐like structures (e.g. airport scenarios).

Design/methodology/approach

The spherical‐multipole analysis is applied to determine the exact total field outside a perfectly conducting semi‐infinite elliptic cone. The underlying boundary‐value problem is solved by a separation of variables of the Helmholtz equation in sphero‐conal coordinates leading to a two‐parametric eigenvalue problem with two coupled Lamé differential equations. The exact scattered far field is determined from the exact surface current on the cone using a bilinear expansion of the dyadic Green's function. The Physical‐Optics (PO) field is evaluated similarly starting from a surface current which is directly found from the incident magnetic field.

Findings

The diffraction coefficients of the exact scattered field and the PO scattered field are compared for different parameters (polarization and angle of incidence) of the plane wave. Reasonably well corresponding results are obtained for those angles of incidence of the plane wave where the entire cone is illuminated, otherwise the error of the PO approximation is increasing not just in the shadow region.

Originality/value

If carefully applied, the Physical‐Optics method can be useful and sufficient to obtain fields scattered by cone‐like structures.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 July 2017

V. Rajesh, A.J. Chamkha, Ch. Sridevi and A.F. Al-Mudhaf

The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite

Abstract

Purpose

The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transfer

Design/methodology/approach

The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell–Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari–Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank–Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically.

Findings

The present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and ϕ values. But an increase in M reduces the local Nusselt number.

Originality/value

This paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a magnetic field. Further the present study is relevant to nanofluid materials processing, chemical engineering coating operations exploiting nanomaterials and others.

Details

Engineering Computations, vol. 34 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 1997

H.S. Takhar, P. Ganesan, K. Ekambavanan and V.M. Soundalgekar

Presents a finite‐difference solution to transient free convection flow past a semi‐infinite vertical plate in which the plate temperature T¢w(x) varies as the power of the axial…

Abstract

Presents a finite‐difference solution to transient free convection flow past a semi‐infinite vertical plate in which the plate temperature T¢w(x) varies as the power of the axial co‐ordinate in the form T¢ + axn. Gives numerical results for fluids with Prandtl numbers Pr = 0.7 (air) and Pr = 7 (water) for three representative exponent values under non‐uniform surface heating conditions. Finds that the time to reach the steady‐state increases as the value of n or Pr increases. The steady‐state local skin‐friction falls by increasing the exponent n and Pr; however, the steady‐state local Nusselt number increases with n at a distance along the plate far away from the leading edge but decreases with increasing n near the leading edge of the plate. Also, the average Nusselt number increases and the average skin‐friction decreases as n increases because of enhanced heating of the plate.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 February 1996

H.S. Takhar, Rama Subba Reddy Gorla and V.M. Soundalgekar

Free convection heat transfer due to the simultaneous action ofbuoyancy, radiation and transverse magnetic field is investigated for asemi‐infinite vertical plate. Solutions are…

Abstract

Free convection heat transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated for a semi‐infinite vertical plate. Solutions are derived by expanding the stream function and the temperature into a series in terms of the parameter ζ = x1/2 L–1/2, where L is the length of the plate. Velocity and temperature functions are shown on graphs and the numerical values of functions affecting the shear stress and the rate of heat transfer are entered in a table. The effects of the magnetic field parameter λ and the radiation parameter F on these functions are discussed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 8 August 2016

Vladimir Kobelev

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length…

Abstract

Purpose

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.

Design/methodology/approach

The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.

Findings

The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.

Research limitations/implications

Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.

Practical implications

The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.

Originality/value

The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 21 January 2013

B. Liu, J. Yang and Q. Jiang

We study the propagation of shear-horizontal waves in a piezoelectric plate of monoclinic crystals in contact with a semi-infinite viscous fluid as an acoustic wave sensor for…

Abstract

We study the propagation of shear-horizontal waves in a piezoelectric plate of monoclinic crystals in contact with a semi-infinite viscous fluid as an acoustic wave sensor for measuring fluid viscosity or density. Mindlin's first-order theory for piezoelectric plates and the theory of Newtonian fluids are used. Approximate dispersion relations for long face-shear and thickness-twist waves are given analytically. Numerical results showing the effects of the fluid and the piezoelectric coupling in the plate on basic wave propagation characteristics are presented.

Details

World Journal of Engineering, vol. 9 no. 6
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 4 January 2016

Rajesh Vemula, A J Chamkha and Mallesh M. P.

The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started…

Abstract

Purpose

The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature.

Design/methodology/approach

The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations.

Findings

The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m.

Research limitations/implications

The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered.

Practical implications

The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods).

Originality/value

This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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