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1

A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer

Alharbi Ozwah S., Abdullah Abdullah A.

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

488--499

EN

A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode.

2

Konwekcja naturalna w modelowym pomieszczeniu z zastosowaniem aproksymacji Bussinesq’a

Radzikowska-Juś W., Owczarek S.

Biuletyn Wojskowej Akademii Technicznej

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2017

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Vol. 66, nr 3

75--82

PL

Artykuł przedstawia analizę numeryczną przepływu ciepła w czasie w modelowym pomieszczeniu w wyniku umieszczenia w nim obiektu o podwyższonej temperaturze. W wyniku różnicy temperatur pomiędzy obiektem a otoczeniem w pomieszczeniu następuje zjawisko konwekcji naturalnej. Obliczenia wykonywano z wykorzystaniem oprogramowania ELMER bazującego na metodzie elementów skończonych. W celu zmniejszenia ich złożoności w symulacji wykorzystano aproksymację Bussinesqa. Rozpatrywany przypadek jest zbliżony do konwekcji Rayleigha-Benarda, która stanowi punkt wyjścia dla przeprowadzonej analizy.

EN

The paper presents numerical analysis of heat transfer inside a model chamber in time after entering an object of elevated temperature therein. As a result of the temperature difference between the object and the environment in the room, natural convection has occurred. Numerical simulations were performed using ELMER software based on the Finite Element Method. In order to reduce the complexity of the simulation, the Bussinesq approximation was used. The relevant case is similar to Rayleigh-Benard convection, which was starting point to the conducted analysis.

3

The Rayleigh-Benard Convection Analysis by the Lorenz Dynamical System

Jopek H., Strek T.

Vibrations in Physical Systems

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2004

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Vol. 21

183--186

4

Effect of homogeneous chemical reaction on solutal analog of Rayleigh-Benard convection in a micropolar fluid

Siddheshwar P. G., Desseaux A.

International Journal of Applied Mechanics and Engineering

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2002

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Vol. 7, no 2

513-525

EN

The solutal analog of the Rayleigh-Benard convection in a reactive micropolar fluid is studied numerically using the Rayleigh-Ritz method. The solute concentration is assumed to disappear at a rate which is linearly proportional to the concentration. It is observed that the critical solutal Rayleigh number for this fluid system with homogeneous kinetics is greater than that of a non-reactive fluid system. The results have possible industrial applications.