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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.

This paper aims to examine the interaction effect of regulations (monetary and macro-prudential) in explaining the possible non-linear effect of bank risk exposures (credit risk and insolvency risk) on banking stability in Africa.

The study uses a two-step system generalized method of moments (GMM) estimator for a data set of banks across 54 African countries over the period 2006–2020.

The authors find that the relationships between bank credit risk–bank stability and bank insolvency risk–bank stability are non-linear and characterized by the presence of optimal thresholds, which are 5.3456 for credit risk and 2.3643 for insolvency. Contrary to their positive effects below these optimal thresholds, credit risk and insolvency risk become negatively linked to bank stability in Africa. The authors find that macro-prudential action and monetary policy both have a positive and significant relationship with bank stability. The authors provide evidence to support that the marginal effect of excessive credit risk and insolvency risk on bank stability is reduced when interacted with monetary and macro-prudential regulations, and the impact is significant in strong institutional environment.

Future research should extend data to include developing and emerging economies in the world. Also, policymakers, researchers and practitioners should consider different regulatory and institutional frameworks in explaining the relationship between the thresholds of bank risk exposures and bank stability in the world.

Regulatory authorities should have to deeply reform their financial systems, develop risk-based regulatory framework and effective supervision mechanism relating to appropriate techniques that maintain an optimal and desired level of bank risks and risk-taking behaviours required to ensure a stable banking system.

To the best of the authors’ knowledge, this is the first study to examine how different regulatory frameworks shape the non-linear impact of bank risk exposures on bank stability in Africa.

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.

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.

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 Ra_L . Fourth, the authors find that the convection has three different interesting patterns.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.