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The purpose of this chapter is to determine the essence of stagnating socio-economic systems through the prism of the theory of economic conflicts.

Comparative analysis of conceptual approaches to treatment of stagnation of socio-economic systems – the theory of cycles, the theory of economic growth, and the theory of economic conflicts – is performed. According to the theory of economic conflicts, signs of stagnation of socio-economic systems are determined with the help of methods of horizontal and trend analysis. The research objects are leading developed countries (major advanced economies – G7), which, according to the existing scientific and economic paradigm, should not stagnate, and countries of the Commonwealth of Independent States (CIS), which, in the contrary, may show signs of stagnation. The analyzed indicators are growth rate of GDP in constant prices, growth rate of GDP per capita in constant prices, and the level of unemployment rate. The research is performed in the period of post-crisis restoration of modern socio-economic systems, including the forecast period (2010–2022) based on the data of the International Monetary Fund.

As a result of the research, the essence of stagnation of socio-economic systems is determined, and the following characteristics are given: emergence after crisis, negative influence on economy, universal nature, and manageability.

The obtained conclusions show opposition of stagnation and sustainable development. Stagnation is absence of economic growth and development, regardless of social and ecological costs of economic activities. Contrary to it, sustainable development means stable economic growth with low social and ecological costs of economic activities. That’s why stagnation of economy is a negative phenomenon. Unlike crises, stagnation could and should be avoided with the help of the corresponding (anti-stagnation) measures of crisis management.

The aim of the study is to demonstrate evidence that societal ageing and poor economic growth are linked in the advanced economies. It challenges the claim however that secular stagnation represents a serious problem for future prosperity.

This paper critically reviews recent formulations of the secular stagnation hypothesis concerning stalled economic growth in the advanced economies and the links between demographic ageing and economic slowdown. It outlines both trends (of ageing and stalled growth) and reviews some of the key empirical studies that have sought to determine the role played by demographic change in accounting for the relative lack of growth in the advanced economies.

The advanced economies are ageing and their economic growth is slowing, although a causal link between these two phenomena remains unproven. However, even if no direct causal link can be drawn between these two processes the focus upon the impact of societal ageing serves as a stimulus to re-think the nature of future growth in our increasingly ageing and unequal societies.

While the measurement of demographic trends is relatively straightforward, there are more problems in specifying the exact parameters of macroeconomic growth. This makes empirical studies in the area difficult to interpret. However studies in this area have value in widening thinking about the role of ageing and the nature of growth in the future.

Rather than fearing the prospect of an age related slowdown in the rate of growth in the advanced economies, these developments offer opportunities to focus upon redistribution more than growth, while supporting a programme of growth with equity in the world's developing economies.

While a demographically over-determined model of the secular stagnation hypothesis is dubious, the future ageing of the advanced economies is certainly a challenge. It is also an opportunity for rethinking ideas about ageing, growth and development. Adopting such a more nuanced perspective offers a counter-narrative to the demographic catastrophising that is often evident when discussing 'societal ageing'. It also suggests the value of shifting the perspective of seeking ever increasing growth toward a greater focus upon redistribution, between and within the generations.

There has been very little engagement with the secular stagnation hypothesis outside economics. Behind its macroeconomic formulation, however, lie assumptions about the ageing of society that can easily become examples of unwarranted demographic catastrophising. By bringing this topic to the attention of the social sciences, the paper can serve as a stimulus for rethinking both ageing and growth.

The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge.

Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks.

First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

The purpose of this paper is to study theoretically the steady two‐dimensional mixed convection flow of a micropolar fluid impinging obliquely on a stretching vertical sheet. The flow consists of a stagnation‐point flow and a uniform shear flow parallel to the surface of the sheet. The sheet is stretching with a velocity proportional to the distance from the stagnation point while the surface temperature is assumed to vary linearly. The paper attempts also to show that a similarity solution of this problem can be obtained.

Using a similarity transformation, the basic partial differential equations are first reduced to ordinary differential equations which are then solved numerically using the Keller box method for some values of the governing parameters. Both assisting and opposing flows are considered. The results are also obtained for both strong and weak concentration cases.

These results provide information about the effect of a/c (ratio of the stagnation point velocity and the stretching velocity), σ (shear flow parameter) and K (material parameter) on the flow and heat transfer characteristics in mixed convection flow near a non‐orthogonal stagnation‐point on a vertical stretching surface. The results show that the shear stress increases as K increases, while the heat flux from the surface of the sheet decreases with an increase in K.

The results in this paper are valid only in the small region around the stagnation‐point on the vertical sheet. It is found that for smaller Prandtl number, there are difficulties in the numerical computation due to the occurrence of reversed flow for opposing flow. An extension of this work could be performed for the unsteady case.

The present results are original and new for the micropolar fluids. They are important in many practical applications in manufacturing processes in industry.

This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point.

The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB.

An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters.

The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

This paper aims to provide improvements to the newest version of the k‐ ω turbulence model of Wilcox for convective heat transfer prediction in turbulent axisymmetric jets impinging onto a flat plate.

Improvements to the heat transfer prediction in the impingement zone are obtained using the stagnation flow parameter of Goldberg and the vortex stretching parameter of Wilcox. The third invariant of the strain rate tensor in the form of Shih et al. and the blending function of Menter are applied in order make negligible the influence of the impingement modifications in the benchmark flows for turbulence models. Further, it is demonstrated that for two‐dimensional jets impinging onto a flat plate the stagnation region Nusselt number predicted by the original k‐ ω model is in good agreement with direct numerical simulation (DNS) and experimental data. Also for two‐dimensional jets, the proposed modification is deactivated.

The proposed modification has been applied to improve the convective heat transfer predictions in the stagnation flow regions of axisymmetric jets impinging onto a flat plate with nozzle‐plate distances H/D = 2, 6, 10 and Reynolds numbers Re = 23,000 and 70,000. Comparison of the predicted and experimental mean and fluctuating velocity profiles is performed. The heat transfer rates along a flat plate are compared to experimental data. Significant improvements are obtained with respect to the original k‐ ω model.

The proposed modification is simple and can be added to the k‐ ω model without causing stability problems in the computations.

Pratt & Whitney Aircraft's F100 augmented turbofan is the most advanced military engine in service today. It powers two of the U.S. Air Force's front‐line fighters: the twin‐engine McDonnell Douglas F‐15 and the newly introduced single‐engine General Dynamics F‐16. The F100 is a 25,000‐pound‐thrust class engine. Yet it weighs only 3,020 pounds. No other military aircraft engine can match its remarkable 8‐to‐1 thrust‐to‐weight ratio. But the F100's unparalleled performance was marred by an unexpected problem: early production models were susceptible to a curious phenomenon called stagnation. When an F100 stagnates, it won't respond to its throttle. Thrust drops sharply, and the engine's turbine stages may overheat. The only way out of stagnation is to shut down the engine and restart it. Recently, P&WA engineers — working with technical investigators from the U.S. Air Force and McDonnell Douglas — unlocked the mystery of stagnation. Their success represents a significant advance in the technology of high‐performance turbofan engines.

The purpose of this paper is to study the unsteady boundary layer flow of a micropolar fluid past a circular cylinder which is started impulsively from rest.

The nonlinear partial differential equations consisting of three independent variables are solved numerically using the 3D Keller‐box method.

Numerical solutions for the velocity profiles, wall skin friction and microrotation profiles are obtained and presented for various values of time t and material parameter K with the boundary condition for microrotation n=0 (strong concentration of microelements) and n=1/2 (weak concentration of microelements). The results are presented along the points on the cylinder surface, starting from the forward to the rear stagnation point, for small time up to the time when the boundary layer flow separates from the cylinder.

It is believed that this is the first paper that uses the 3D Keller‐box method to study the unsteady boundary layer flow of micropolar fluids. In the last four decades, there has been overhelming interest shown by researchers in micropolar fluids and still many problems are unsolved. The paper shows not only the fundamental importance of this problem, but also the implications for situations of practical interest.

The purpose of this paper is to do a comprehensive study on the unsteady general three-dimensional stagnation-point flow and heat transfer of a nanofluid by Buongiorno’s model.

In this study, the convective transport equations include the effects of Brownian motion and thermophoresis. By introducing new similarity transformations for velocity, temperature and nanoparticle volume fraction, the basic equations governing the flow, heat and mass transfer are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved both analytically and numerically.

The analysis shows that velocity, temperature and nanoparticle concentration profiles in the respective boundary layers depend on five parameters, namely unsteadiness parameter A, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr and Lewis number Le. It is found that the thermal boundary layer thickens with a rise in both of the Brownian motion and the thermophoresis effects. Therefore, similar to the earlier reported results, the Nusselt number decreases as the Brownian motion and thermophoresis effects become stronger. A correlation for the Nusselt number has been developed based on a regression analysis of the data. This correlation predicts the numerical results with a maximum error of 9 percent for a usual domain of the physical parameters.

The stagnation point flow toward a wavy cylinder (with nodal and saddle stagnation points) that a little attention has been given to it up to now. The examination of unsteadiness effect on the general three-dimensional stagnation-point flow. The application of an interesting and global model (Boungiorno’s model) for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. The study of the effects of Brownian motion and thermophoresis on the nanofluid flow, heat and mass transfer characteristics. The prediction of correlation for the Nusselt number based on a regression analysis of the data. General speaking, we can tell the problem with this geometry, characteristics, the applied model, and comprehensive results, was Not studied and analyzed in literature up to now.

This paper aims to discuss the stagnation-point flow and heat transfer for power-law fluid pass through a stretching surface with heat generation effect. Unlike the previous considerations about the research on stagnation-point flow, the process of heat transfer and the convective heat transfer boundary condition use the modified Fourier’s law in which the heat flux is power-law-dependent on velocity gradient.

The similarly transformation is used to convert the governing partial differential equations into a series of ordinary differential equations which are solved analytically by using the differential transform method and the base function method.

The variations of the velocity and temperature fields for different specific related parameters are graphically discussed and analyzed. There is a special phenomenon that all the velocity profiles converge from the initial value of velocity to stagnation parameter values. And the larger power-law index enhancesthe momentum diffusion. A significant phenomenon can be observed that the larger power-law index causes a decline in the heat flux. This influence indicates that the higher viscosity restricts the heat transfer. Furthermore, both velocity gradient and temperature gradient play an indispensable role in the processes of heat transfer.

This paper researches the process of heat transfer of stagnation-point flow ofpower-law magneto-hydro-dynamical fluid over a stretching surface with modified convective heat transfer boundary condition.