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This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).

The numerical method is based on the FVM and multigrid acceleration.

Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.

The bifurcations between steady and unsteady states are investigated.

The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid‐driven flow in a three‐dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two‐dimensional (2D) cavity.

The second‐order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25‐4) and Reynolds numbers (0.01‐1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier‐Stokes (NS) equations and with available experimental data.

The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side‐walls in transverse direction (in 3D), due to which the vorticity in the core‐region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry‐plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid‐motion are observed; these are weak at low Reynolds numbers, but become quite strong at high Reynolds numbers.

The findings will be useful in the study of variety of enclosed fluid flows.

The present work is devoted to the numerical study of the stability of shallow jet. The effects of important parameters on the stability behavior for large scale shallow jets are considered and investigated. Connections between the stability theory and observed features reported in the literature are emphasized. The paper aims to discuss these issues.

A linear stability analysis of shallow jet incorporating the effects of bottom topography, bed friction and viscosity has been carried out by using the shallow water stability equation derived from the depth averaged shallow water equations in conjunction with both Chézy and Manning resistance formulae. Effects of the following main factors on the stability of shallow water jets are examined: Rossby number, bottom friction number, Reynolds number, topographic parameters, base velocity profile and resistance model. Special attention has been paid to the Coriolis effects on the jet stability by limiting the rotation number in the range of Ro∈[0, 1.0].

It is found that the Rossby number may either amplify or attenuate the growth of the flow instability depending on the values of the topographic parameters. There is a regime where the near cancellation of Coriolis effects due to other relevant parameters influences is responsible for enhancement of stability. The instability can be suppressed by the bottom friction when the bottom friction number is large enough. The amplification rate may become sensitive to the relatively small Reynolds number. The stability region using the Manning formula is larger than that using the Chézy formula. The combination of these effects may stabilize or destabilize the shallow jet flow. These results of the stability analysis are compared with those from the literature.

Results of linear stability analysis on shallow jets along roughness bottom bed are presented. Different from the previous studies, this paper includes the effects of bottom topography, Rossby number, Reynolds number, resistance formula and bed friction. It is found that the influence of Reynolds number on the stability of the jet is notable for relative small value. Therefore, it is important to experimental investigators that the viscosity should be considered with comparison to the results from inviscid assumption. In contrast with the classical analysis, the use of multi-parameters of the base velocity and topographic profile gives an extension to the jet stability analysis. To characterize the large scale motion, besides the bottom friction as proposed in the related literature, the Reynolds number Re, Rossby number Ro, the topographic parameters and parameters controlling base velocity profile may also be important to the stability analysis of shallow jet flows.

This research aims to investigate the effects of manipulation of a torpedo’s geometries to attain higher terminal velocity. The parameters of interest include geometric changes of the original design, as well as sea water properties that reflect water depth in South China Sea.

The research make use of computational fluid dynamics (CFD) software, FLUENT, to solve viscous incompressible Navier–Stokes equations with two equations k-epsilon turbulent model. The calculated drag coefficient is subsequently used to calculate the maximum attainable terminal velocity of the torpedo.

It was found that the terminal velocity can be improved by sharper tip angle, greater aspect ratio, greater diameter ratio and optimum rear angle at 30°. Sensitivity of drag coefficient toward each of the parameters is established in this paper.

The paper, in addition to verifying the importance of aspect ratio, has also established the tip angle, diameter ratio and rear angle of the torpedo as important geometric aspects that could be tuned to improve its terminal velocity.

Natural convection heat transfer combined with radiation heat transfer is used in electronic cooling. The purpose of this paper is to investigate the thermal loading characteristics of an enclosure.

The goal is to investigate the effect of thermal radiation on thermal and flow characteristics of the cavity. The enclosure lower wall is at constant temperature and the upper wall is adiabatic while there are several discrete heat sources inside the cavity. In addition the effect of parameters such as heating number (Nr), aspect ratio (A), the number of heaters (N), and thermal radiation on the maximum and mean temperature of system, thermal loading characteristics of the system, Nusselt number, and the maximum stream function rate is performed. To solve the governing nonlinear differential equations (mass, momentum, and energy), a finite‐volume code based on Patankar's SIMPLE method is utilized.

Heat transfer by natural convection solely and it's conjugation with thermal radiation on the thermal and flow characteristics of the system is studied. Also a parametric study illustrating the influence of the heating number, aspect ratio, the number of heaters, and thermal radiation on the maximum and mean temperature of system, thermal loading characteristics of the system, Nusselt number, and the maximum stream function rate is investigated. The results have revealed that the thermal radiation have an important effect on the thermal characteristics of system at low heating numbers.

The relevant governing parameters were: the heating number, Nr from 0.05 to 500, the cavity aspect ratio, A=H/L from 0.1 to 1 and the number of heaters, N, is an odd number ranging from 1 to 19

This work is numerical investigation only but can have engineering application such as electronic cooling, transformers, fusion reactors technology, hot structures, fuel cells, fibrous insulations and solar‐energy drying systems.

The effect of radiation in enclosure with discrete heaters within fluid has not been addressed in the literature.

Presents a numerical study on heat transfer by natural convection in porous media in vertical enclosures with side wall heating. The model for porous media includes inertia terms and also the Brinkman extension in addition to the Darcy resistance term. A semi‐implicit finite element scheme based on operator splitting method is adopted for solving the time‐dependent system of equations. The first half of the investigations is confined to the low permeability regime where Darcy law holds good. Presents the results for annular and rectangular cavities and proposes correlations for two types of boundary conditions, namely constant wall temperature case and uniform wall heat flux case. In the second half of the investigations, the scheme is applied in a high permeability regime, where the validity of Darcy law becomes questionable. Employs plane rectangular cavities with the two types of boundary conditions mentioned earlier. Highlights the influence of Rayleigh number (Ra) and Darcy number (Da) as separate parameters and proposes correlations for a square cavity for the first time in terms of Ra and Da as separate parameters. Discusses a qualitative study of the effect of aspect ratio on heat transfer as the permeability changes.

To investigate the large amplitude free flexural vibration of doubly curved shallow shells in the presence of cutouts.

Finite element model using an eight‐noded C⁰ continuity, isoparametric quadrilateral element is employed. Nonlinear strains of von Karman type are incorporated into the first‐order shear deformation theory.

Cylindrical shell shows mostly hard spring behavior whereas spherical shell shows both hard spring and soft spring behavior with the increase of amplitude ratios for different cutout sizes, radii of curvature and thickness parameters. At a particular value of the amplitude ratio, the frequency ratio of shells is governed by the interactive effects of stiffness and mass.

Aircraft, spacecraft and many other structures where shell panels are used, undergo large amplitude nonlinear vibrations.

The paper will assist researchers of vibration behavior of elastic systems.

Analytical and numerical studies are conducted for two‐dimensional steady‐state coupled Marangoni and buoyancy convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The results obtained by combining the two basic mechanisms (thermocapillarity and buoyancy) depend on whether their effects are aiding or opposite. The effect of the non‐Newtonian behavior on the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.

The purpose of this paper is to consider flow over heat generating bodies in an open‐ends cavity, which finds applications in electronics cooling and industrial processing. Heat transfer rates depend on the flow situation in the cavity, which is influenced by the cavity inlet and exit port locations, heat transferring body size and its orientation in the cavity, and the cavity size. Consequently, modeling of flow over heat transferring bodies in an open‐ends cavity and examination of the effect of the aspect ratio and orientation of the heat transferring bodies on the flow field and heat transfer rates becomes essential.

The flow over heat generating solid blocks situated in an open‐ends cavity is considered and the effects of blocks' orientations and aspect ratios on flow field as well as heat transfer rates are examined. A numerical scheme using a control volume approach is introduced to predict flow field in the cavity and heat transfer rates from the blocks.

It is found that complex flow structure is generated in the cavity due to the aspect ratios and orientations of the blocks. This, in turn, influences significantly heat transfer rates from the blocks in the cavity.

Surface areas of blocks are kept the same and aspect ratio is varied such that the surface area of each block remains the same in the simulations. In addition, Steady flow situation is considered for governing equations of flow and heat transfer in the cavity. However, for the future study transient heating and flow situations can be considered while varying the surface araes of the blocks. This will provide useful information on the circulations in the cavity and the enhancement of heat transfer due to the complex flow structure.

In practice, cooling effectiveness can be improved through changing the aspects ratio of the heat generating bodies in the cavity.

The findings are original and will be useful for the scientists and the design engineers working the specific area of heat transfer and fluid flow.

Analytical and numerical studies are conducted for two‐dimensional steady‐state Marangoni convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The effect of the non‐Newtonian behavior on the hydrodynamic stability, the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.