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1 – 10 of 523
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: 7 June 2013

F. Soltanian, Mehdi Dehghan and S.M. Karbassi

The main purpose of this paper is to find convenient methods to solve the differential‐algebraic equations which have great importance in various fields of science and engineering.

Abstract

Purpose

The main purpose of this paper is to find convenient methods to solve the differential‐algebraic equations which have great importance in various fields of science and engineering.

Design/methodology/approach

The paper applies a semi‐analytical approach, using both the homotopy analysis method (HAM) and the modified homotopy analysis method (MHAM) for finding the solution of linear and nonlinear DAEs.

Findings

The results show that the new modification can effectively reduce computational costs and accelerates the rapid convergence of the series solution.

Originality/value

Some high index DAEs are investigated to present a comparative study between the HAM and the MHAM.

Article
Publication date: 19 May 2022

Jiří Malík and Ondřej Souček

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on…

Abstract

Purpose

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.

Design/methodology/approach

The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.

Findings

This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.

Practical implications

The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.

Originality/value

While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 August 1996

Manolis Papadrakakis, Yiannis Tsompanakis, Ernest Hinton and Johann Sienz

Investigates the efficiency of hybrid solution methods when incorporated into large‐scale topology and shape optimization problems and to demonstrate their influence on the…

Abstract

Investigates the efficiency of hybrid solution methods when incorporated into large‐scale topology and shape optimization problems and to demonstrate their influence on the overall performance of the optimization algorithms. Implements three innovative solution methods based on the preconditioned conjugate gradient (PCG) and Lanczos algorithms. The first method is a PCG algorithm with a preconditioner resulted from a complete or an incomplete Cholesky factorization, the second is a PCG algorithm in which a truncated Neumann series expansion is used as preconditioner, and the third is a preconditioned Lanczos algorithm properly modified to treat multiple right‐hand sides. The numerical tests presented demonstrate the computational advantages of the proposed methods which become more pronounced in large‐scale and/or computationally intensive optimization problems.

Details

Engineering Computations, vol. 13 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 30 November 2021

Chongbin Zhao, B.E. Hobbs and Alison Ord

The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.

Abstract

Purpose

The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.

Design/methodology/approach

The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.

Findings

The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.

Originality/value

Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

Details

Engineering Computations, vol. 39 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 14 December 2020

Lijun Zhang, Muhammad Mubashir Bhatti and Efstathios E. Michaelides

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of…

Abstract

Purpose

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

Design/methodology/approach

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

Findings

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

Originality/value

The obtained results are new and presented for the first time in the literature.

Details

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

Keywords

Article
Publication date: 1 May 1992

E. HINTON, N.V.R. RAO and J. SIENZ

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly…

Abstract

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

Article
Publication date: 11 January 2021

Mostafa Esmaeili, Hamed Hashemi Mehne and D.D. Ganji

This study aims to explore the idea of solving the problem of squeezing nanofluid flow between two parallel plates using a novel mathematical method.

Abstract

Purpose

This study aims to explore the idea of solving the problem of squeezing nanofluid flow between two parallel plates using a novel mathematical method.

Design/methodology/approach

The unsteady squeezing flow is a coupled fourth-order boundary value problem with flow velocity and temperature as the desired unknowns. In the first step, the conditions that guarantee the existence of a unique solution are obtained. Then following Green’s function-based approach, an iterative method for solving the problem is developed.

Findings

The accuracy of the method is examined by comparing the obtained results with existing numerical data, indicating excellent agreement between the two. In addition, the effects of nanoparticle shape and volume fraction on the flow and heat transfer characteristics are addressed. The results reveal that although the nanoparticle shape strongly affects the temperature distribution in the squeezing flow, it only has a slight impact on the velocity field. Furthermore, the highest and lowest Nusselt numbers belong to the platelets and spherical nanoparticles, respectively.

Originality/value

A semi-analytical method with computational support is developed for solving the unsteady squeezing flow problem. Moreover, the existence and uniqueness of the solution are discussed for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 September 1999

S.G. Ahmed

The oxygen diffusion problem is usually formulated in two stages: first, the steady state and second, the moving boundary stage. In this paper, we will consider the solution of…

Abstract

The oxygen diffusion problem is usually formulated in two stages: first, the steady state and second, the moving boundary stage. In this paper, we will consider the solution of the second stage in which a new semi‐analytical method for solving such a problem was developed. The present method starts by assuming a polynomial representing the profile of oxygen concentration, and then by some mathematical manipulation a system of linear equations is obtained. Numerical solution for the system with a simple scheme relating the moving boundary and its velocity leads to the unknown functions in the assumed polynomial.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 October 2015

Michael G. Papanikolaou, Michael G. Farmakopoulos and Chris A. Papadopoulos

Wear in journal bearings occurs when the operating conditions (high load, high temperature, low angular velocity or low viscosity), downgrade the ability of the bearing to carry…

189

Abstract

Purpose

Wear in journal bearings occurs when the operating conditions (high load, high temperature, low angular velocity or low viscosity), downgrade the ability of the bearing to carry load. The wear depth increases because the rotor comes in contact with the bearing surface. Wear in journal bearings affects their characteristics because of its influence on the thickness of the fluid film. This influence can be detected in the dynamic behavior of the rotor and especially in the dynamic stiffness and damping coefficients. The paper aims to discuss these issues.

Design/methodology/approach

In this paper, the effect of wear on the rotor dynamic stiffness and damping coefficients (K and C) of a short journal bearing is investigated. K and C in this work are estimated by using two methods a semi-analytical method and finite element (FE) analysis implemented in the ANSYS software.

Findings

The main goal of this research is to make the identification of wear in journal bearings feasible by observing the alternation of their dynamic coefficients. Both of the methods implemented are proven to be useful, while FE analysis can provide more accurate results.

Originality/value

This paper is original and has not been published elsewhere.

Details

International Journal of Structural Integrity, vol. 6 no. 5
Type: Research Article
ISSN: 1757-9864

Keywords

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