Sharif Digital Repository

This note considers the effect of different Darcy numbers on the onset of natural convection in a horizontal, fluid-saturated porous layer with uniform internal heating. It is assumed that the two bounding surfaces are maintained at constant but equal temperatures and that the fluid and porous matrix are in local thermal equilibrium. Linear stability theory is applied to the problem, and numerical solutions obtained using compact fourth order finite differences are presented for all Darcy numbers between Da = 0 (Darcian porous medium) and Da → ∞ (the clear fluid limit). The numerical work is supplemented by an asymptotic analysis for small values Da. © 2007 Elsevier Masson SAS. All rights... 

To overcome the problem of magneto hydrodynamic instabilities at the aluminum-cryolite interface in aluminum reduction cells, the use of a simple and efficient model has been suggested. In this paper a new model for evaluation of magneto hydrodynamic instabilities in aluminum reduction cells is proposed. This model is in the form of a wave equation for interfacial oscillations and is constructed based on Shallow Water approximation and linear stability analysis. In this model two terms for linear friction in each molten layer of aluminum and cryolite has been considered and also Lorentz forces in cryolite layer have not been neglected. By accounting of these additional terms in our model,... 

The hydrodynamics of two immiscible fluids in a rectangular Hele-Shaw cell under the influence of a magnetic field is studied, both theoretically and numerically. A linear stability analysis is conducted to determine the effect of magnetic fields on the formation of viscous fingers. As a result, an analytical solution is found to calculate the growth rate of perturbations. For numerical simulation of the two-phase flow, the interfacial tension is treated as a body force using the continuum surface force model and the interface tracking is performed by the volume of fluid method. The variations of the width and growth rate of fingers in an unstable displacement versus Hartmann number, a... 

In this paper, a hybrid atomistic-structural element for studying the mechanical behaviour of carbon nanotubes is introduced. Non-linear formulation for this element is derived based on empirical inter-atomic potentials. This hybrid element is capable of taking into account the non-linear nature of inter-atomic forces as well as the non-linearity arising from large deformations. Using these capabilities, the stability analysis of carbon nanotubes under axial compressive loading is performed and the post-buckling behaviour is predicted. Also, the dependence of axial buckling force on nanotube radius is shown  

Instability and breakup of a liquid jet under the influence of a gaseous crossflow in the presence of an electric field is investigated. A dispersion relation for disturbances on the jet surface is derived for the combined effects based on pioneer linear stability analysis for low speed limits. Effects of Weber, Bond and Ohnesorge numbers on the growth rate of disturbances are studied. The theoretical analysis developed for breakup length is used for comparisons with experimentally obtained breakup lengths. Measured breakup lengths were predicted satisfactorily by the linear theory in the region of low crossflow velocities (0–4 m/s) and electric field intensities (0–3×105 V/m). © 2017... 

Linear stability analysis is used to characterize the dynamics of a plane jet by incorporating non-modal stability analysis besides classical global temporal stability analysis. It is explained that similar shapes of different global modes are the result of non-normal characteristics of linearized Navier Stokes equations. Optimal initial disturbances and their eigenfunctions together with transient energy growth are obtained for different time horizons and Reynolds numbers of the jet in the linear unstable configuration. These structures are localized at the upstream of the jet nozzle at the boundary layer. The transient growth of the inlet perturbation in limited time bounds is found in the... 

Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes. These instabilities have an important role in the mixing process. In this work, the linear stability analysis in spatial framework is used to study the stability characteristics of a particle-laden stratified two-layer flow. The effect of parameters such as velocity-to-density thickness ratio, bed slope, viscosity as well as particle size on the stability is considered. A simple iterative method applying the pseudospectral collocation method that employed Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, the flow becomes stable for Richardson... 

In this study, factors affecting the noise generation by instability waves in a subsonic jet with acoustic Mach number of 0.5 are investigated using linear stability analysis. The base flow required for instability analysis is obtained by modeling the jet stream based on the k-ϵ turbulence model and using the empirical coefficients suggested by Thies and Tam [1]. The resulting base flow profiles are used to solve the linear instability equation, which governs the pressure perturbation for obtaining the eigenvalues and eigenfunctions. The results of linear instability analysis for phase and amplitude of pressure fluctuations are compared against the existing experimental data, which... 

In this study, factors affecting the noise generation by instability waves in a subsonic jet with acoustic Mach number of 0.5 are investigated using linear stability analysis. The base flow required for instability analysis is obtained by modeling the jet stream based on the k-ϵ turbulence model and using the empirical coefficients suggested by Thies and Tam [1]. The resulting base flow profiles are used to solve the linear instability equation, which governs the pressure perturbation for obtaining the eigenvalues and eigenfunctions. The results of linear instability analysis for phase and amplitude of pressure fluctuations are compared against the existing experimental data, which... 

This paper considers the onset of free convection in a horizontal fluid-saturated porous layer with uniform heat generation. Attention is focused on cases where the fluid and solid phases are not in local thermal equilibrium, and where two energy equations describe the evolution of the temperature of each phase. Standard linearized stability theory is used to determine how the criterion for the onset of convection varies with the inter-phase heat transfer coefficient, H, and the porosity-modified thermal conductivity ratio, γ. We also present asymptotic solutions for small values of H. Excellent agreement is obtained between the asymptotic and the numerical results. © Springer... 

Based on the first-order shear deformation and Donnell's shell theory with von Karman non-linearity, one decoupled stability equation for buckling analysis of functionally graded (FG) and multilayered cylindrical shells with transversely isotropic layers subjected to various cases of combined thermo-mechanical loadings is developed. To this end, the equilibrium equations are uncoupled in terms of the transverse deflection, the force function and a new potential function. Using the adjacent equilibrium method, one decoupled stability equation which is an eighth-order differential equation in terms of transverse deflection is obtained and conveniently solved to present analytical expressions... 

Elongated cylindrical structures with non-uniform diameters, under cross-flow, are often encountered in marine engineering and energy harvesting devices. In this work, the vortex-induced vibrations of elastically supported circular tapered and wavy cylinders with different cross sections areas are studied numerically using a wake oscillator model. The effect of the tapering ratio on the amplitude of oscillation is particularly analyzed. For tapered cylinders it is found that the amplitude of oscillation under flow decreases strongly when a critical tapering is reached. This is consistent with experimental data. A similar effect is found in wavy cylinders. A third system, consisting of a... 

Elongated cylindrical structures with non-uniform diameters, under cross-flow, are often encountered in marine engineering and energy harvesting devices. In this work, the vortex-induced vibrations of elastically supported circular tapered and wavy cylinders with different cross sections areas are studied numerically using a wake oscillator model. The effect of the tapering ratio on the amplitude of oscillation is particularly analyzed. For tapered cylinders it is found that the amplitude of oscillation under flow decreases strongly when a critical tapering is reached. This is consistent with experimental data. A similar effect is found in wavy cylinders. A third system, consisting of a...