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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.

To estimate mean droplet diameter (MDD) of a spray, three different numerical models were used in this paper. One of them is investigation of the surface instability of the liquid sheet producing from an injector.

First, the linear instability (LI) analysis introduced by Ibrahim (2006) is implemented. Second, the improved (ILI) analysis already introduced by the present authors is used. ILI analysis is different from the prior analysis, so that the instability of hollow-cone liquid sheet with different cone angles is investigated rather than a cylindrical liquid sheet. It means that besides the tangential and axial movements, radial movements of the liquid sheet and gas streams have been considered in the governing equations. Beside LI theory as a momentum-based approach, a new model as a theoretical energy-based (TEB) model based on the energy conservation law is proposed in this paper.

Based on the energy-based approach, atomization occurs because of kinetic energy loss. The resulting formulation reveals that the MDD is inversely proportional to the atomization efficiency and liquid Weber number.

The results of these three models are compared with the available experimental data. Prediction obtained by the proposed TEB model is in reasonable agreement with the result of experiment.

The results of these three models are compared with the available experimental data. Prediction of the proposed energy-based theoretical model is in very good agreement with experimental data.

Comparison between the results of new model, experimental data, other previous methods show that it can be used as a new simple and fast model to achieve good estimation of spray MDD.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The issue of export instability exerts an enduring fascination for economists with an interest in the area of economic development. Over several decades a voluminous literature has emerged embracing debates on the domestic consequences and on the causes of export instability. The purpose here is to examine these debates and an attempt is made to set out different theoretical stances, to classify and examine empirical findings, and to indicate the directions in which the debates have moved. Such a statement of a review article's purpose is, of course, incomplete without more specific delineation of the boundaries within which the general objectives are pursued. Here that delineation has three facets.

The purpose of this paper is to investigate a model for convection induced by the selective absorption of radiation in a fluid layer. The concentration based internal heat source is modelled quadratically. Both linear instability and global nonlinear energy stability analyses are tested using three dimensional simulations. The results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.

The author introduce the stability analysis of the problem of convection induced by absorption of radiation in fluid layer, then the author select a situations which have very big subcritical region. Then, the author develop a three dimensions simulation for the problem. To do this, first, the author transform the problem to velocity – vorticity formulation, then the author use a second order finite difference schemes. The author use implicit and explicit schemes to enforce the free divergence equation. The size of the Box is evaluated according to the normal modes representation. Moreover, the author adopt the periodic boundary conditions for velocity and temperature in the $x, y$ dimensions.

This paper explores a model for convection induced by the selective absorption of radiation in a fluid layer. The results demonstrate that the linear instability thresholds accurately predict the onset of instability. A three-dimensional numerical approach is adopted.

As the author believe, this paper is one of the first studies which deal with study of stability of convection using a three dimensional simulation. When the difference between the linear and nonlinear thresholds is very large, the comparison between these thresholds is very interesting and useful.

Changes frequently made to material delivery schedules (MDSs) accumulate upstream in the supply chain (SC), causing a bullwhip effect. This article seeks to elucidate how dynamic complexity generates MDS instability at OEMs in the automotive industry.

An exploratory multiple-case study methodology involved in-depth semistructured interviews with informants at three automotive original equipment manufacturers (OEMs).

Dynamic complexity destabilizes MDSs primarily via internal horizontal interactions between product and process complexities and demand and SC complexities. A network of complexity interactions causes and moderates such instability through complexity absorption and generation and complexity importation and exportation.

The multiple-case study contributes to empirical knowledge about the dynamics of MDS instability. Deductive research to validate the identified relationships remains for Future research.

In revealing antecedents of complexity’s effect on MDS instability, the findings imply the need to develop strategies, programs, and policies dedicated to improving capacity scalability, supplier flexibility, and the flexibility of material order fulfillment.

Building on complexity literature, the authors operationalize complexity transfer and develop a framework for analyzing dynamic complexity in SCs, focusing on complexity interactions. The identification and categorization of interactions provide a granular view of the dynamic complexity that generates MDS instability. The identified and proposed importance of readiness of the SC to absorb complexity challenges the literature focus on external factors for explaining complexity outcomes. The results can be used to operationalize such dynamic interactions by introducing new variables and networks of relationships. Moreover, the work showcases how a complexity perspective could be used to discern the root causes of a complex phenomenon driven by non-linear relationships.

A linear stability analysis has been employed to investigate the thermocapillary instability occurring in a nonisothermal liquid bridge. The steady, axisymmetric basic state was solved numerically using a finite difference method. A mixed finite difference‐spectral method, combining the advantages of both methods, was then used to reduce the linear disturbance equations to an eigenvalue problem. The critical Marangoni numbers for axisymmetric disturbances are predicted for small Prandtl numbers and various aspect ratios. The effect of surface heat transfer is also investigated. The present results are compared with energy‐theory results and with the results of other experiments.

In the present chapter, we explore how employee well-being changes over time, both linear and psychological during periods of economic instability. Moreover, we examine how employee job embeddedness (JE) buffers the effects of economic shocks on employee well-being, and how these buffering effects change employee perceptions of time. We theorize that employees with higher levels of JE psychologically experience economic shocks as occurring infrequently with the economically unstable period feeling quick, but employees with lower levels of JE psychologically experience economic shocks as occurring frequently with the economically unstable period feeling slow. Finally, we extend these relationships to account for the spread of employee well-being through social connections, both inside and outside of the work context. Because JE requires strong social connections, we theorize that the links component of embeddedness is responsible for economic shocks and employee well-being crossing over the work/nonwork boundary. We discuss the implications for our theoretical model.