Pressure Effects on Natural Convection for Non-Boussinesq Fluid in a Rectangular Enclosure

Hung, Kuo Shu; Cheng, Chin‐Hsiang

doi:10.1080/104077802753570347

Cited by 30 publications

(8 citation statements)

References 11 publications

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“…Relevant and excellent examples along these lines are Chenoweth and Paolucci [40], Fröhlich and Gauthier [41], Crockera and Paranga [42], Cook and Riley [43], Nicoud [44], Hung and Cheng [45], Munz et al [14], Park and Munz [46], Weisman et al [47], Beccantini et al [15], Benteboula and Lauriat [48], Bouloumou et al [49]. Although the specifics of the techniques used by these authors vary, the basic idea is the same.…”

Section: The First Category Consists Of Variants Of Methods Originallmentioning

confidence: 99%

A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures

Lappa

2016

Journal of Computational Physics

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The relevance of non-equilibrium phenomena, nonlinear behavior, gravitational effects and fluid compressibility in a wide range of problems related to high-temperature gas-dynamics, especially in thermal, mechanical and nuclear engineering, calls for a concerted approach using the tools of the kinetic theory of gases, statistical physics, quantum mechanics, thermodynamics and mathematical modeling in synergy with advanced numerical strategies for the solution of the Navier-Stokes equations. The reason behind such a need is that in many instances of relevance in this field one witnesses a departure from canonical models and the resulting inadequacy of standard CFD approaches, especially those traditionally used to deal with thermal (buoyancy) convection problems. Starting from microscopic considerations and typical concepts of molecular dynamics, passing through the Boltzmann equation and its known solutions, we show how it is possible to remove past assumptions and elaborate an algorithm capable of targeting the broadest range of applications. Moving beyond the Boussinesq approximation, the Sutherland law and the principle of energy equipartition, the resulting method allows most of the fluid properties (density, viscosity, thermal conductivity, heat capacity and diffusivity, etc.) to be derived in a rational and natural way while keeping empirical contamination to the minimum. Special attention is deserved as well to the well-known pressure issue. With the application of the socalled multiple pressure variables concept and a projection-like numerical approach, difficulties with such a term in the momentum equation are circumvented by allowing the hydrodynamic pressure to decouple from its thermodynamic counterpart. The final result is a flexible and modular framework that on the one hand is able to account for all the molecule (translational, rotational and vibrational) degrees of freedom and their effective excitation, and on the other hand can guarantee adequate interplay between molecular and macroscopic-level entities and processes. Performances are demonstrated by computing some incompressible and compressible benchmark test cases for thermal (gravitational) convection, which are then extended to the high-temperature regime taking advantage of the newly developed features

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Section: The First Category Consists Of Variants Of Methods Originallmentioning

confidence: 99%

A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures

Lappa

2016

Journal of Computational Physics

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“…A survey of the literature shows that correlations for natural convection from vertical and horizontal plates, vertical and horizontal cylinders, spheres, vertical channels, and elliptic cylinders have been reported for different thermal boundary conditions. Furthermore, numerical studies on heat transfer inside horizontal ducts, cavities, and enclosures have been reported by many authors for various boundary conditions [1][2][3][4][5][6][7][8][9][10][11], and natural convection in inclined rectangular enclosures have been studied by Rahman and Sharif [12] and by Sharif and Liu [13] for different aspect ratios and angles of inclination, respectively. However, limited numbers of analytical and numerical studies have been concerned with heat transfer from the external surface of rectangular ducts, which motivated the current study.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Natural Convection Around Isothermal Horizontal Rectangular Ducts

Zeitoun

Ali

2006

Numerical Heat Transfer, Part A: Applications

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Two-dimensional laminar natural-convection heat transfer in air around horizontal ducts with rectangular and square cross sections is studied numerically. Different aspect ratios are used for wide ranges of Rayleigh numbers. Results are presented in the form of streamlines and isothermal plots around the circumference of the ducts. The computational procedure is based on the finite-element technique. Temperature and velocity profiles are obtained near each surface of the ducts. Reverse flow and circulations are observed at high aspect ratios. Heat transfer data are generated and presented in terms of Nusselt number versus Rayleigh number for different aspect ratios. Correlation covering the aspect ratios used is obtained in dimensionless form of Nusselt number, Rayleigh number, and aspect ratio.

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“…Figure 6 shows the variations in dimensionless input power (˙ W ) as a function of the phase angle ( ) at f = 15, l=H = 0:8, and T 1 − T 2 = 1:32, by showing the results associated with cases 1-12. The values of˙ W are calculated by Equation (15) and indicated with circles in this ÿgure. For the zero-phase-angle cases, both vertical walls move at the same speed and in the same direction, and therefore the volume of the enclosure is moving but not deforming.…”

Section: Resultsmentioning

confidence: 99%

Numerical predictions of flow and thermal fields in an enclosure with two periodically moving walls

Cheng

Hung

2006

Numerical Methods in Fluids

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SUMMARYNumerical predictions of transient ow and thermal ÿelds in a rectangular enclosure with two periodically moving vertical walls are presented. The combined in uence of the movement of the walls and the buoyancy as well on the ow pattern and heat transfer performance is evaluated. The compressibleow model is adopted, and governing equations are expressed in integral form and discretized on the moving grids, which deform in resonance with the walls to accommodate the variation in the volume of the enclosure. A two-stage pressure-correction scheme is applied for simultaneously determining the distributions of absolute pressure, density, temperature, and velocity of the compressible ow ÿeld in the enclosure during the periodically stable periods. E ects of the frequency, stroke, and the phase angle of the wall oscillations on the ow are of major concerns in this study. The frequency is ranged between 5 and 25 Hz and the dimensionless strokes (l=H ) of the wall are varied from 0.4 to 1.0. Results for Nusselt numbers on the walls as well as the dimensionless input work required to excite the wall oscillation are provided.

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Pressure Effects on Natural Convection for Non-Boussinesq Fluid in a Rectangular Enclosure

Cited by 30 publications

References 11 publications

A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures

A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures

Numerical Investigation of Natural Convection Around Isothermal Horizontal Rectangular Ducts

Numerical predictions of flow and thermal fields in an enclosure with two periodically moving walls

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