scholarly journals Inherent thermal convection in a granular gas inside a box under a gravity field

2018 ◽  
Vol 859 ◽  
pp. 160-173
Author(s):  
Francisco Vega Reyes ◽  
Andrea Puglisi ◽  
Giorgio Pontuale ◽  
Andrea Gnoli
Keyword(s):  
Gravity Field ◽  
Thermal Convection ◽  
Numerical Solutions ◽  
Boussinesq Approximation ◽  
Hard Disks ◽  
Particle Collisions ◽  
Granular Gas ◽  
Combined Action ◽  
Vertical Walls ◽  
Lateral Walls

We theoretically prove the existence in granular fluids of a thermal convection that is inherent in the sense that it is always present and has no thermal gradient threshold (convection occurs for all finite values of the Rayleigh number). More specifically, we study a gas of inelastic smooth hard disks enclosed in a rectangular region under a constant gravity field. The vertical walls act as energy sinks (i.e. inelastic walls that are parallel to gravity), whereas the other two walls are perpendicular to gravity and act as energy sources. We show that this convection is due to the combined action of dissipative lateral walls and a volume force (in this case, gravitation). Hence, we call it dissipative lateral walls convection (DLWC). Our theory, which also describes the limit case of elastic collisions, shows that inelastic particle collisions enhance the DLWC. We perform our study via numerical solutions (volume-element method) of the corresponding hydrodynamic equations in an extended Boussinesq approximation. We show that our theory describes the essentials of the results for similar (but more complex) laboratory experiments.

scholarly journals Thermal Convection in Granular Gases with Dissipative Lateral Walls

2016 ◽  
Vol 117 (9) ◽  
Author(s):  
Giorgio Pontuale ◽  
Andrea Gnoli ◽  
Francisco Vega Reyes ◽  
Andrea Puglisi
Keyword(s):  
Thermal Convection ◽  
Granular Gases ◽  
Lateral Walls

Numerical Study of Thermal Convection in Boussinesq-Stokes Suspension Occupying a Rectangular Box

2011 ◽  
Author(s):  
S. Manjunath ◽  
N. P. Chandrashekara
Keyword(s):  
Aspect Ratio ◽  
Thermal Convection ◽  
Couple Stress ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Heat Conducting ◽  
Linear Temperature ◽  
Vertical Walls ◽  
Vertical Cavity

This paper is a Fourier–series assisted numerical study of two-dimensional thermal convection in Boussinesq–Stokes suspensions occupying a cavity. The suspension is modeled as a couple stress liquid. The horizontal walls of the cavity are assumed to be perfectly heat conducting and the vertical walls are non-uniformly heated to establish a linear temperature in the vertical direction. The critical Rayleigh number is obtained numerically as a function of couple stress parameter and aspect ratio, and the same is plotted graphically. The results of slender vertical cavity, classical Rayleigh-Be´nard convection, rectangular and square cavities of finite aspect-ratio heated from below are obtained as limiting cases of the study.

Analytic solution of angle-ply laminated plates under extension, bending, and torsion

2019 ◽  
Vol 54 (8) ◽  
pp. 1093-1106
Author(s):  
Shen-Haw Ju ◽  
Wen-Yu Liang ◽  
Hsin-Hsiang Hsu ◽  
Jiann-Quo Tarn
Keyword(s):  
Numerical Solutions ◽  
Anisotropic Elasticity ◽  
Laminated Plates ◽  
Rectangular Section ◽  
State Space Approach ◽  
Present Solution ◽  
End Conditions ◽  
Combined Action ◽  
Space Approach

This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

Existence and uniqueness of a complex fractional system with delay

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Rabha Ibrahim ◽  
Hamid Jalab
Keyword(s):  
Time Delay ◽  
Complex Systems ◽  
Fractional Order ◽  
Thermal Convection ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
System With Delay ◽  
Fractional System ◽  
Liquid Flows ◽  
Liu System

AbstractChaotic complex systems are utilized to characterize thermal convection of liquid flows and emulate the physics of lasers. This paper deals with the time-delay of a complex fractional-order Liu system. We have examined its chaos, computed numerical solutions and established the existence and uniqueness of those solutions. Ultimately, we have presented some examples.

scholarly journals Mixed thermal convection: fundamental issues and analysis of the planar case

2015 ◽  
Vol 87 (3) ◽  
pp. 1865-1885 ◽  
Author(s):  
JACQUES PADET ◽  
RENATO M. COTTA ◽  
EMILIA C. MLADIN ◽  
COLETTE PADET
Keyword(s):  
Free Convection ◽  
Mixed Convection ◽  
Forced Convection ◽  
Analytical Solutions ◽  
Thermal Convection ◽  
Boussinesq Approximation ◽  
Reference Temperature ◽  
Clear Definition ◽  
Planar Case ◽  
Definition Of

This paper aims to renew interest on mixed thermal convection research and to emphasize three issues that arise from the present analysis: (i) a clear definition of the reference temperature in the Boussinesq approximation; (ii) a practical delimitation of the three convective modes, which are the forced convection (FC), mixed convection (MC) and natural (or free) convection (NC); (iii) and, finally, a uniform description of the set FC/MC/NC in the similarity framework. The planar case, for which analytical solutions are available, allows a detailed illustration of the answers here advanced to the above issues.

scholarly journals Laminar and weakly turbulent oceanic gravity currents performing inertial oscillations

2011 ◽  
Vol 8 (5) ◽  
pp. 2001-2045
Author(s):  
A. Wirth
Keyword(s):  
Mathematical Models ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Gravity Current ◽  
Boussinesq Approximation ◽  
Turbulent Fluxes ◽  
Navier Stokes ◽  
Small Scale ◽  
Mean Flow ◽  
Inertial Oscillations

Abstract. The small scale dynamics of a weakly turbulent oceanic gravity current is determined. The gravity current considered is initially at rest and adjusts by performing inertial oscillations to a geostrophic mean flow. The dynamics is explored with a hierarchy of mathematical models. The most involved are the fully 3-D Navier-Stokes equations subject to the Boussinesq approximation. A 1-D and 0-D mathematical model of the same gravity current dynamics are systematically derived. Using this hierarchy and the numerical solutions of the mathematical models, the turbulent dynamics at the bottom and the interface is explored and their interaction investigated. Three different regimes of the small scale dynamics of the gravity current are identified, they are characterised by laminar flow, coherent roll vortices and turbulent dynamics with coherent streaks and bursts. The problem of the rectification of the turbulent fluxes, that is how to average out the fluctuations and calculate their average influence on the flow is considered. It is shown that two different regimes of friction are superposed, an Ekman friction applies to the average geostrophic flow and a linear friction, not influenced by rotation, to the inertial oscillations. The combination of the two makes the bulk friction non-local in time for the 0-D model. The implications of the results for parametrisations of the Ekman dynamics and the small scale turbulent fluxes in the planetary boundary layer are discussed.

An analytical solution for natural convective gas microflow in a tall vertical enclosure

2010 ◽  
Vol 225 (1) ◽  
pp. 145-154 ◽  
Author(s):  
H S Panda ◽  
S Ghosh Moulic
Keyword(s):  
Nusselt Number ◽  
Analytical Solution ◽  
Stokes System ◽  
Slip Flow ◽  
Velocity Slip ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
First Order ◽  
Vertical Walls ◽  
Slip Flow Regime

An analytical solution for buoyancy-induced gas microflow in a tall differentially heated enclosure with isothermal vertical walls is presented. The Navier—Stokes system has been solved. The Boussinesq approximation has been employed. Wall—fluid interactions are modelled by first-order velocity slip and temperature jump conditions. The analysis presented covers continuum to slip-flow regime. A functional form for the Nusselt number has been derived analytically. The results indicate that as the Knudsen number increases, the Nusselt number decreases.

A Model of Rayleigh-Bénard Convection

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Gravity Waves ◽  
Thermal Convection ◽  
Fluid Flows ◽  
Boussinesq Approximation ◽  
Internal Gravity Waves ◽  
Bénard Convection ◽  
Benard Convection ◽  
Key Characteristics ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, focusing on thermal convection and internal gravity waves. Thermal convection and internal gravity waves are the two basic types of fluid flows within planets and stars that are driven by thermally produced buoyancy forces. The chapter then reviews the equations that govern fluid dynamics based on conservation of mass, momentum, and energy. It also examines the conditions under which the Boussinesq approximation simplifies conservation equations to a form very similar to that of an incompressible fluid. Finally, it discusses the key characteristics of the model of Rayleigh–Bénard convection.

Sign in / Sign up

Export Citation Format

Share Document