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Article
Publication date: 1 January 1996

J. Shi

This paper investigates the issue of linear stability analysis for twoand three level explicit and implicit one‐dimensional finite differentnumerical schemes. A new…

Abstract

This paper investigates the issue of linear stability analysis for two and three level explicit and implicit one‐dimensional finite different numerical schemes. A new approach which is based on the von Neumann method method is presented. This approach was validated by testing some popular numerical schemes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 6 June 2016

Akil Jassim Harfash and Ahmed K. Alshara

The purpose of this paper is to explore a model for thermal convection in a plane layer when the density-temperature relation in the buoyancy term is quadratic. A heat…

Abstract

Purpose

The purpose of this paper is to explore a model for thermal convection in a plane layer when the density-temperature relation in the buoyancy term is quadratic. A heat source/sink varying in a linear fashion with a vertical height expressed as z was allowed, functioning as a heat sink in an area of the layer and as a heat source in the remainder.

Design/methodology/approach

First, the authors present the governing equations of motion and derive the associated perturbation equations. Second, the authors introduce the linear and nonlinear analysis of the system. Third, the authors transform the system to velocity-vorticity-potential formulation and introduce a numerical study of the problem in three dimensions.

Findings

First, the linear instability and nonlinear stability thresholds are derived. Second, the linear instability thresholds accurately predict the onset of instability. Third, the required time to arrive at the steady state increases as Ra tends to RaL . Fourth, the authors find that the convection has three different interesting patterns.

Originality/value

With the modernday need for heat transfer or insulation devices in industry, particularly those connected with nanotechnology, the usefulness of a mathematical analysis of such resonance became apparent. Thus, this study is believed to be of value.

Details

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

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Article
Publication date: 14 June 2021

Pascalin Tiam Kapen, Cédric Gervais Njingang Ketchate, DIdier Fokwa and Ghislain Tchuen

This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower…

Abstract

Purpose

This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower plate is fixed and the upper plate animated by a uniform rectilinear motion.

Design/methodology/approach

The nanofluid is composed of water as a regular fluid, silver (Ag) and alumina (Al2O3) as nanoparticles. The mathematical model takes into account other effects such as the magnetic field and the aspiration (injection/suction). Under the assumption of a low magnetic Reynolds number, a modified Orr–Sommerfeld-type eigenvalue differential equation governing flow stability was derived and solved numerically by Chebyshev’s spectral collocation method. The effects of parameters such as volume fraction, Darcy number, injection/suction Reynolds number, Hartmann number were analyzed.

Findings

It was found the following: the Darcy number affects the stability of the flow, the injection/suction Reynolds number has a negligible effect, the volume fraction damped disturbances and the magnetic field plays a very important role in enlarging the area of flow stability.

Originality/value

The originality of this work resides in the linear and temporal stability analysis of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects.

Details

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

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Article
Publication date: 1 September 2003

R.E. Khayat and N. Ashrafi

A hybrid spectral/boundary element approach is proposed to examine the influence of Couette channel flow on transient coating of highly elastic fluids. The viscoelastic…

Abstract

A hybrid spectral/boundary element approach is proposed to examine the influence of Couette channel flow on transient coating of highly elastic fluids. The viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson‐Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a non‐linear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 January 1992

M.G. MACARAEG

The present study is concerned with the stability and transition of a spatially evolving wake emanating from a splitter plate. Temporal linear stability calculations at…

Abstract

The present study is concerned with the stability and transition of a spatially evolving wake emanating from a splitter plate. Temporal linear stability calculations at different streamwise locations indicate significantly higher growth rates for mean flow profiles which occur near the trailing edge. Spatial simulations using these near wake mean flows exhibit non‐linear roll‐up for a case with Mach numbers of 2.76 and 1.87 on either side of the wake. If a similarity shear layer mean flow profile with these conditions is utilized in the simulation, no roll‐up is obtained.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 12 January 2010

A.A. Avramenko and A.V. Kuznetsov

The purpose of this paper is to investigate a combined bioconvection and thermal instability problem in a horizontal layer of finite depth with a basic temperature…

Abstract

Purpose

The purpose of this paper is to investigate a combined bioconvection and thermal instability problem in a horizontal layer of finite depth with a basic temperature gradient inclined to the vertical. The basic flow, driven by the horizontal component of temperature gradient, is the Hadley circulation, which becomes unstable when the vertical temperature difference and density stratification induced by upswimming of microorganisms that are heavier than water become sufficiently large.

Design/methodology/approach

Linear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method.

Findings

The steady‐state solution of this problem is obtained. Linear stability analysis of this steady‐state solution for the case of three‐dimensional disturbances is performed; the numerical problem is solved using the collocation method. The stability problem is governed by three Rayleigh numbers: the bioconvection Rayleigh number and two thermal Rayleigh numbers characterizing temperature gradients in the vertical and horizontal directions, respectively.

Research limitations/implications

Further research should address the application of weakly non‐linear analysis to this problem.

Practical implications

The dependence of the critical bioconvection Rayleigh number on the two thermal Rayleigh numbers and other relevant parameters is investigated.

Originality/value

This paper presents what is believed to be the first research dealing with the effect of inclined temperature gradient on the stability of bioconvection in a suspension of gyrotactic microorganisms.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 8 January 2020

Xin He, XiaoPing Li and Jinrong Yang

The purpose of this paper is to investigate the mechanism of sheets ply separation induced by air flow through numerical simulation with two-way FSI (fluid-structure…

Abstract

Purpose

The purpose of this paper is to investigate the mechanism of sheets ply separation induced by air flow through numerical simulation with two-way FSI (fluid-structure interaction) simulation using ANSYS and theoretical speculation.

Design/methodology/approach

The paper primarily establishes a simplified physical model of the sheets ply separation induced by air flow. Then, the force of the air flow acting on the sheet has been analyzed based on the model, and the main factor leading to separation was obtained. Furthermore, the parameter analysis was investigated based on linear stability analysis, from which the factors that affect stable separation are obtained. Finally, a series of numerical simulations are performed to verify the conclusions.

Findings

This study shows that the main separation factor is the variable air pressure in the gap between the sheets caused by the dynamic pressure air flow. Increasing the inlet velocity of the flow field will increase the separation distance but excessive velocity will lead to instability. The viscous resistance acting on the sheet and the bending stiffness of the sheet are factors that stabilize the system, and the sheet density and the restoring force can lead to instability.

Originality/value

The paper is one of the first in the literature that investigates the problem of sheets ply separation induced by air flow, which is the primary method for multi-layer separation in sheets de-stacking operations, especially for the high-speed occasion.

Details

Engineering Computations, vol. 37 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 10 July 2017

R. Rashidi Meybodi, M. Zare Mehrjardi and A.D. Rahmatabadi

The purpose of this paper is to study tilt angle effects as design parameters of noncircular bearings, on the linear dynamic analyses of micropolar lubricated circular…

Abstract

Purpose

The purpose of this paper is to study tilt angle effects as design parameters of noncircular bearings, on the linear dynamic analyses of micropolar lubricated circular, two, three and four lobe journal bearings.

Design/methodology/approach

Reynolds equation in dynamic state is modified considering the micropolarity characteristics of lubricant, and it is solved using generalized differential quadrature method. The perturbed components of the dynamic pressure are extracted based on the linear dynamic model. To explain the transient state of the governing equation, through the linear dynamic approach, the whirling motion of rotor around the steady state position is assumed to be harmonic.

Findings

It is observed from the results that tilt angle has significant effects on the steady state and stability performance of lobed journal bearings. It may be selected suitably to improve the performance of rotor-bearing system, while all other lubricant properties and noncircular bearing design parameters are kept fixed. Results show that among the three types of bearings considered, the dynamic performance of two lobe bearings are more affected by the variation of tilt angle.

Originality/value

The present study is mainly concerned with the effects of tilt angle as a design parameter on the stability performance of a hydrodynamic noncircular journal bearing lubricated with micropolar fluid.

Details

Industrial Lubrication and Tribology, vol. 69 no. 4
Type: Research Article
ISSN: 0036-8792

Keywords

Abstract

Details

Monetary Policy, Islamic Finance, and Islamic Corporate Governance: An International Overview
Type: Book
ISBN: 978-1-80043-786-9

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Article
Publication date: 7 April 2020

J.I. Ramos and Carmen María García López

The purpose of this paper is to determine both analytically and numerically the solution to a new one-dimensional equation for the propagation of small-amplitude waves in…

Abstract

Purpose

The purpose of this paper is to determine both analytically and numerically the solution to a new one-dimensional equation for the propagation of small-amplitude waves in shallow waters that accounts for linear and nonlinear drift, diffusive attenuation, viscosity and dispersion, its dependence on the initial conditions, and its linear stability.

Design/methodology/approach

An implicit, finite difference method valid for both parabolic and second-order hyperbolic equations has been used to solve the equation in a truncated domain for five different initial conditions, a nil initial first-order time derivative and relaxation times linearly proportional to the viscosity coefficient.

Findings

A fast transition that depends on the coefficient of the linear drift, the diffusive attenuation and the power of the nonlinear drift are found for initial conditions corresponding to the exact solution of the generalized regularized long-wave equation. For initial Gaussian, rectangular and triangular conditions, the wave’s amplitude and speed increase as both the amplitude and the width of these conditions increase and decrease, respectively; wide initial conditions evolve into a narrow leading traveling wave of the pulse type and a train of slower oscillatory secondary ones. For the same initial mass and amplitude, rectangular initial conditions result in larger amplitude and velocity waves of the pulse type than Gaussian and triangular ones. The wave’s kinetic, potential and stretching energies undergo large changes in an initial layer whose thickness is on the order of the diffusive attenuation coefficient.

Originality/value

A new, one-dimensional equation for the propagation of small-amplitude waves in shallow waters is proposed and studied analytically and numerically. The equation may also be used to study the displacement of porous media subject to seismic effects, the dispersion of sound in tunnels, the attenuation of sound because of viscosity and/or heat and mass diffusion, the dynamics of second-order, viscoelastic fluids, etc., by appropriate choices of the parameters that appear in it.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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