Numerical study of convection near the stability threshold in a square box with internal heat generation

Kolmychkov, V V; Мажорова, О. С.; Щерица, О. В.

doi:10.1016/j.physleta.2013.06.013

Cited by 15 publications

(10 citation statements)

References 27 publications

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“…Here we cite studies of both types but focus on quantitative findings, and we restrict ourselves to experiments that closely resemble one of the IH configurations defined in figure 1.1. Convection with internal heating has been studied also with various complications that we do not confront, such as cooled side walls [128,8,5,96,35,3,4,60,121,89,22,44], non-uniform heating [111,132,138,82], self-gravitating spheres [112,114,11,13,66,110], and hybrid configurations driven both internally and by the boundary conditions [125,77,75,95,135,30,19,61,2,124,145,55,9,81]. Section 3.1 addresses IH3, the last of the three IH configurations defined in figure 1.1.…”

Section: Similarities Between Rb and Ih Boundsmentioning

confidence: 99%

Internally Heated Convection and Rayleigh-Bénard Convection

Goluskin¹

2016

SpringerBriefs in Applied Sciences and Technology

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PrefaceThe purpose of this SpringerBrief is to review heat transfer in layers of convective fluid. Six different configurations are considered-three that are versions of Rayleigh-Bénard (RB) convection, which is driven by differential heating at the boundaries, and three that are driven by uniform internal heating. The essential features of all six models are derived mathematically. The experimental literature is reviewed in depth for the models of internally heated (IH) convection, which are much less studied than their RB counterparts. Experiments on RB convection are treated in less depth, as they have been thoroughly reviewed elsewhere.Along with placing the various convective models within a conceptual framework that brings out their similarities, we give some minor results not published elsewhere. For instance, a few of the linear instability and energy stability thresholds given in tables 2.2 and 2.3 either have not been reported before or have been reported with less precision. One of the bounds proven in §2.3 is also new, as are the visualizations of simulations included as figure 1.2.Chapter 1 provides background and then defines the six configurations under study, the governing equations of our models, and their basic features. Chapter 2 presents results that can be derived mathematically from the governing equations: linear and nonlinear stability thresholds of static states, along with proven bounds on mean temperatures and heat fluxes. For the IH cases only, chapter 3 gives a quantitative survey of heat transport in both laboratory experiments and numerical simulations, followed by suggestions for future work.

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Section: Similarities Between Rb and Ih Boundsmentioning

confidence: 99%

Internally Heated Convection and Rayleigh-Bénard Convection

Goluskin¹

2016

SpringerBriefs in Applied Sciences and Technology

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“…Аппроксимация конвективных членов не вносит вклад в баланс кинетической энергии и тепла [5]. Метод успешно использовался для исследования конвекции Рэлея-Бенара [6][7][8][9].…”

Section: численный методunclassified

“…За счет внутренних источников тепла кон-векция возможна при более широком классе краевых условий для температуры по сравнению с выше разобранными задачами. Из работ [12] и [2], [8] известно, что при малых значения числа Прандтля должны наблюдаться ячейки, при средних -валы, при больших -ячейки противоположного типа. Рассмотрим влияние краевых условий на типы наблюдаемых конвективных структур и обмен устойчивостью между ними.…”

Section: внутренние источники теплаunclassified

“…В области больших значений числа Прандтля задача изучалась теоретически и экспериментально Р. Кришнамурти [13], [14]. Исследования Кришнамурти демонстрируют, что при значениях числа Рэлея ниже критического возможно движение в фоме шестиугольных ячеек, тип которых зависит от знака q. В области малых значений числа Прандтля ситуация неопределенная, и приходится проводить параллели с задачами с другими граничными условиями [15] или использовать численный эксперимент [8], [9]. (a) Pr = 0.1, t = 80t ν (b) Pr = 0.25, t = 42t ν (с) Pr = 10, t = 500t ν Рис.…”

Section: идеально проводящие горизонтальные границы; T Bot >T Topunclassified

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Investigation of convective structures near the stability threshold in non-Bousssinesq fluid. Part two — numerical simulation

Kolmychkov

Мажорова

2018

KIAM Prepr.

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“…The results show the strong effects of thermo-capillary force at the interface on the time-dependent oscillations at the onset of instability convection. Kolmychkov [17] presented a numerical simulation RB convection including a homogenous internal heat generation and investigated transitions between the conducting state, hexagonal, and roll flows for a Prandtl number range of 0.1-100 and Rayleigh number from subcritical values up to 1.5 times of its critical value. Ouertatani [18] applied finite volume method and full multi-grid acceleration on RB convection problem.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study of Antisymmetric-Symmetric Mode of RB Convection through on Time Evolution

Benarab¹,

Tariq²

2017

World Congress on Momentum, Heat and Mass Transfer

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-The purpose of this work is to study a specific case of Rayleigh-Benard convection. Convection undergoes transition timedependent regime on a sufficiently high Rayleigh Number. The critical Rayleigh value is calculated where antisymmetric-symmetric mode switches. This mode exhibits an odd number of rolls along x and an even number of cells in the perpendicular direction. It is clearly shown that this oscillatory convection is perfectly physical and periodic. Random probes are chosen to follow the timeevolution of the different parameters of the fluid such as dimensionless horizontal and vertical velocities, along with that temperature evolution is calculated too. These parameters are compared and discussed. Streamlines and Isotherm lines are presented at different times for one cycle of oscillation and are presented to show and understand the perfect mirror symmetry which is an important parameter of the studied case. The variation in Nusselt number is tracked from the hot and cold sides during time evolution. Nusselt Number curves show the intervals between the hot and cold flow in the same interval of values. The results shown in this paper are in good agreement with the precedent works. The study is done in a square cavity for a Rayleigh number varying between 10 5 and 10 6 , the Prandtl number equal to 0.71 and a 10 K difference in the temperature. Governing equations of the phenomenon are numerically solved using FINITE VOLUME METHOD and the pressure-velocity coupling is matched by SIMPLER Algorithm.

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Numerical study of convection near the stability threshold in a square box with internal heat generation

Cited by 15 publications

References 27 publications

Internally Heated Convection and Rayleigh-Bénard Convection

Internally Heated Convection and Rayleigh-Bénard Convection

Investigation of convective structures near the stability threshold in non-Bousssinesq fluid. Part two — numerical simulation

A Numerical Study of Antisymmetric-Symmetric Mode of RB Convection through on Time Evolution

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