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.

scholarly journals Study of Thermal Convection in Micropolar Fluids Occupying a Rectangular Box

2012 ◽  
Vol 11 (3) ◽  
pp. 129-142
Author(s):  
S Manjunath ◽  
N P Chandrashekara
Keyword(s):  
Aspect Ratio ◽  
Thermal Convection ◽  
Numerical Study ◽  
Coupling Parameter ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Linear Temperature ◽  
Micropolar Fluids ◽  
Vertical Walls ◽  
Square Box

This paper is a Fourier–series assisted numerical study of two–dimensional steady thermal convection in micropolar fluid occupying a rectangular box. The horizontal walls of the cavity are uniformly heated to establish a linear temperature in the vertical direction. The vertical walls are insulated. The critical Rayleigh number is obtained numerically as a function of coupling parameter, couple stress parameter and aspect ratio, and the same is plotted graphically. The results of slender vertical, rectangular and square box of finite aspect ratio are obtained as limiting cases of the study.

scholarly journals On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

2014 ◽  
Vol 7 (5) ◽  
pp. 2065-2076 ◽  
Author(s):  
P.-A Arrial ◽  
N. Flyer ◽  
G. B. Wright ◽  
L. H. Kellogg
Keyword(s):  
Rayleigh Number ◽  
Numerical Simulations ◽  
Spherical Harmonics ◽  
Thermal Convection ◽  
Mantle Convection ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Initial Condition ◽  
Numerical Discretization ◽  
The Impact

Abstract. Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how the discretization of the governing equations affects the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth's mantle, we consider isoviscous Rayleigh–Bénard convection at infinite Prandtl number, where the aspect ratio between the inner and outer shell is 0.55. We show that the subtleties involved in developing mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes – an established, community-developed, and benchmarked finite-element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBFs) – are compared. A full numerical study is investigated for the following three cases. The first case is based on the cubic (or octahedral) initial condition (spherical harmonics of degree ℓ = 4). How this pattern varies to perturbations in the initial condition and Rayleigh number is studied. The second case investigates the stability of the dodecahedral (or icosahedral) initial condition (spherical harmonics of degree ℓ = 6). Although both methods first converge to the same pattern, this structure is ultimately unstable and systematically degenerates to cubic or tetrahedral symmetries, depending on the code used. Lastly, a new steady-state pattern is presented as a combination of third- and fourth-order spherical harmonics leading to a five-cell or hexahedral pattern and stable up to 70 times the critical Rayleigh number. This pattern can provide the basis for a new accuracy benchmark for 3-D spherical mantle convection codes.

scholarly journals On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

2014 ◽  
Vol 7 (2) ◽  
pp. 2033-2064
Author(s):  
P.-A. Arrial ◽  
N. Flyer ◽  
G. B. Wright ◽  
L. H. Kellogg
Keyword(s):  
Rayleigh Number ◽  
Numerical Simulations ◽  
Spherical Harmonics ◽  
Thermal Convection ◽  
Mantle Convection ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Initial Condition ◽  
Numerical Discretization ◽  
The Impact

Abstract. Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how does the discretization of the governing equations affect the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth's mantle, we consider isoviscous Rayleigh-Bénard convection at infinite Prandtl number, where the aspect ratio between the inner and outer shell is 0.55. We show that the subtleties involved in development mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes: an established, community-developed, and benchmarked finite element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBF) are compared. A full numerical study is investigated for the following three cases. The first case is based on the cubic (or octahedral) initial condition (spherical harmonics of degree ℓ =4). How variations in the behavior of the cubic pattern to perturbations in the initial condition and Rayleigh number between the two numerical discrezations is studied. The second case investigates the stability of the dodecahedral (or icosahedral) initial condition (spherical harmonics of degree ℓ = 6). Although both methods converge first to the same pattern, this structure is ultimately unstable and systematically degenerates to cubic or tetrahedral symmetries, depending on the code used. Lastly, a new steady state pattern is presented as a combination of order 3 and 4 spherical harmonics leading to a five cell or a hexahedral pattern and stable up to 70 times the critical Rayleigh number. This pattern can provide the basis for a new accuracy benchmark for 3-D spherical mantle convection codes.

An Analytical Study on Natural Convection in Isotropic and Anisotropic Porous Channels

1990 ◽  
Vol 112 (2) ◽  
pp. 396-401 ◽  
Author(s):  
T. Nilsen ◽  
L. Storesletten
Keyword(s):  
Analytical Study ◽  
Vertical Direction ◽  
Flow Patterns ◽  
Heat Conducting ◽  
Two Dimensional ◽  
Anisotropic Porous Media ◽  
Onset Of Convection ◽  
Linear Temperature ◽  
Weakly Nonlinear ◽  
Rayleigh Numbers

This paper is an analytical study on natural two-dimensional convection in horizontal rectangular channels filled by isotropic and anisotropic porous media. The channel walls, assumed to be impermeable and perfectly heat conducting, are nonuniformly heated to establish a linear temperature distribution in the vertical direction. We derive the critical Rayleigh numbers for the onset of convection and examine the steady flow patterns at moderately supercritical Rayleigh numbers. The stability properties of these flow patterns are examined against two-dimensional perturbations using a weakly nonlinear theory.

scholarly journals Numerical Study on the Surface Plasmon Resonance Tunability of Spherical and Non-Spherical Core-Shell Dimer Nanostructures

Nanomaterials ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1728
Author(s):  
Joshua Fernandes ◽  
Sangmo Kang
Keyword(s):  
Refractive Index ◽  
Optical Properties ◽  
Surface Plasmon Resonance ◽  
Aspect Ratio ◽  
Surface Plasmon ◽  
Plasmon Resonance ◽  
Shell Thickness ◽  
Numerical Study ◽  
Field Enhancement ◽  
Core Shell

The near-field enhancement and localized surface plasmon resonance (LSPR) on the core-shell noble metal nanostructure surfaces are widely studied for various biomedical applications. However, the study of the optical properties of new plasmonic non-spherical nanostructures is less explored. This numerical study quantifies the optical properties of spherical and non-spherical (prolate and oblate) dimer nanostructures by introducing finite element modelling in COMSOL Multiphysics. The surface plasmon resonance peaks of gold nanostructures should be understood and controlled for use in biological applications such as photothermal therapy and drug delivery. In this study, we find that non-spherical prolate and oblate gold dimers give excellent tunability in a wide range of biological windows. The electromagnetic field enhancement and surface plasmon resonance peak can be tuned by varying the aspect ratio of non-spherical nanostructures, the refractive index of the surrounding medium, shell thickness, and the distance of separation between nanostructures. The absorption spectra exhibit considerably greater dependency on the aspect ratio and refractive index than the shell thickness and separation distance. These results may be essential for applying the spherical and non-spherical nanostructures to various absorption-based applications.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

Turbulent convection driven by surface cooling in shallow water

2002 ◽  
Vol 464 ◽  
pp. 81-111 ◽  
Author(s):  
OLEG ZIKANOV ◽  
DONALD N. SLINN ◽  
MANHAR R. DHANAK
Keyword(s):  
Thermal Convection ◽  
Large Scale ◽  
Fourier Method ◽  
Vertical Direction ◽  
Finite Depth ◽  
Turbulent Convection ◽  
Bottom Surface ◽  
Computational Domain ◽  
Surface Cooling ◽  
Adverse Weather

We present the results of large-eddy simulations (LES) of turbulent thermal convection generated by surface cooling in a finite-depth stably stratified horizontal layer with an isothermal bottom surface. The flow is a simplified model of turbulent convection occurring in the warm shallow ocean during adverse weather events. Simulations are performed in a 6 × 6 × 1 aspect ratio computational domain using the pseudo-spectral Fourier method in the horizontal plane and finite-difference discretization on a high-resolution clustered grid in the vertical direction. A moderate value of the Reynolds number and two different values of the Richardson number corresponding to a weak initial stratification are considered. A version of the dynamic model is applied as a subgrid-scale (SGS) closure. Its performance is evaluated based on comparison with the results of direct numerical simulations (DNS) and simulations using the Smagorinsky model. Comprehensive study of the spatial structure and statistical properties of the developed turbulent state shows some similarity to Rayleigh–Bénard convection and other types of turbulent thermal convection in horizontal layers, but also reveals distinctive features such as the dominance of a large-scale pattern of descending plumes and strong turbulent fluctuations near the surface.

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