Heat Transfer in Low-Prandtl Number Free Convection From Internally Heated Rectangular Enclosures (original) (raw)
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Low-Prandtl number natural convection in volumetrically heated rectangular enclosures
International Journal of Heat and Mass Transfer, 2000
Following previous studies for enclosures of aspect ratios 4 and 1, direct numerical two-dimensional simulations were conducted for the free convection¯ow of a low-Prandtl number¯uid with internal heat generation in a shallow cavity (AR 0.25) having adiabatic top and bottom walls and isothermal side walls. The Prandtl number was 0.0321 and the Grashof number, Gr, based on power density and cavity width, ranged from 10 6 to 10 11 . The¯ow was steady for Gr up to 3 Â 10 9 , time-periodic for Gr % 10 10 and chaotic for Gr P 3 Â 10 10 . In both the steady and the periodic regimes, the¯ow was instantaneously symmetric with respect to the vertical centreline of the enclosure; in the chaotic regime the instantaneous¯ow was asymmetric, but bilateral symmetry was recovered in the time-averaged velocity and temperature ®elds. For Grashof numbers above $10 7 , the Nusselt number (overall/conductive heat transfer) increased roughly as Gr 1=5 , i.e., slightly more markedly than for the previous aspect ratios and in agreement with the behaviour expected in the separated-boundary layer regime. Ó : S 0 0 1 7 -9 3 1 0 ( 0 0 ) 0 0 3 4 7 -1
Two-dimensional, time-dependent simulations of free convection in an internally heated square enclosure were conducted using a finite-volume code. The enclosure was cooled from the side walls while top and bottom walls were adiabatic. The Prandtl number was 0.0321 and the Grashof number Gr ranged from 105 to 109. Starting from still fluid, steady symmetric flow was predicted up to Gr=1.4×10 7 , and steady but spatially asymmetric flow for Gr=2×10 7 ~3×10 7 . Periodic and chaotic solutions were found for higher Gr. Starting from the solution for large Gr and reducing the power density, steady symmetric flow was predicted for Gr≥1.0×10 7 . In a narrow intermediate range Gr≈1.0×10 7 -1.4×10 7 , three distinct steady state solutions were obtained, one exhibiting bilateral symmetry and the other two asymmetric and mirror-images of each other. Any sufficiently slow periodic variation of power density over this range would give rise to a hysteresis cycle, characterized by two abrupt transi...
A Computational Study of Chaotic Flow and Heat Transfer within a Trapezoidal Cavity
Energies
Numerical findings of natural convection flows in a trapezoidal cavity are reported in this study. This study focuses on the shift from symmetric steady to chaotic flow within the cavity. This cavity has a heated bottom wall, a cooled top wall, and adiabatic inclined sidewalls. The unsteady natural convection flows occurring within the cavity are numerically simulated using the finite volume (FV) method. The fluid used in the study is air, and the calculations are performed for different dimensionless parameters, including the Prandtl number (Pr), which is kept constant at 0.71, while varying the Rayleigh numbers (Ra) from 100 to 108 and using a fixed aspect ratio (AR) of 0.5. This study focuses on the effect of the Rayleigh numbers on the transition to chaos. In the transition to chaos, a number of bifurcations occur. The first primary transition is found from the steady symmetric to the steady asymmetric stage, known as a pitchfork bifurcation. The second leading transition is fou...
Numerical study of free convection turbulent heat transfer in an enclosure
Energy Conversion and Management, 2004
The roll of melting heat transfer on magnetohydrodynamic natural convection in a square enclosure with heating of bottom wall is examined numerically in this article. The dimensionless governing partial differential equations are transformed into vorticity and stream function formulation and then solved using the finite difference method (FDM). The effects of thermal Rayleigh number (Ra), melting parameter (M) and Hartmann number (Ha) are graphically illustrated. As melting parameter and Rayleigh number increase, the rate of fluid flow and temperature gradients also increase. And in the presence of magnetic field, the temperature gradient reduces and hence, the conduction mechanism is dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameter in the both cases of heating of bottom wall.
Effect of Several Heated Interior Bodies on Turbulent Natural Convection in Enclosures
Scientia Iranica, 2018
In this study, turbulent natural convection in a square enclosure including one or four hot and cold bodies is numerically investigated in the range of Rayleigh numbers of 10 12 10 R 10 a. The shape of the internal bodies is square or rectangular with the same surface areas and different aspect ratios. In all cases, the horizontal walls of the enclosure are adiabatic and the vertical ones are isothermal. It is desired to investigate the influence of different shapes and arrangements of internal bodies on the heat transfer rate inside the enclosure with wideranging applications such as ventilation of buildings, electronic cooling and industrial coldbox packages. Governing equations including Reynolds-averaged-Navier-Stokes equations have been solved numerically with finite volume method and k turbulence model in a staggered grid. The boundary condition for turbulence model is based on the standard wall function approach. Strongly implicit method is employed to solve the discretized systems of algebraic equations with a remarkable rate of convergence. The effects of several parameters such as distance between the bodies, aspect ratio and Rayleigh number on heat transfer rate have been investigated. The most change in heat transfer rate at high values of Rayleigh numbers is associated with alteration in distance between square bodies. Moreover, the horizontal installation of rectangular bodies with h/w = 1/3 is accompanied by a maximum reduction of heat transfer at low Rayleigh numbers. The present results have been compared with previous experimental and numerical works regarding enclosures with or without internal bodies and reasonable agreement is observed.
Turbulent mixed convection in a shallow enclosure with a series of heat generating components
International Journal of Thermal Sciences, 2009
Turbulent mixed convection flow and heat transfer in a shallow enclosure with and without partitions and with a series of block-like heat generating components is studied numerically for a range of Reynolds and Grashof numbers with a time-dependent formulation. The flow and temperature distributions are taken to be two-dimensional. Regions with the same velocity and temperature distributions can be identified assuming repeated placement of the blocks and fluid entry and exit openings at regular distances, neglecting the end wall effects. One half of such module is chosen as the computational domain taking into account the symmetry about the vertical centreline. The mixed convection inlet velocity is treated as the sum of forced and natural convection components, with the individual components delineated based on pressure drop across the enclosure. The Reynolds number is based on forced convection velocity. Turbulence computations are performed using the standard k-model and the Launder-Sharma low-Reynolds number kmodel. The results show that higher Reynolds numbers tend to create a recirculation region of increasing strength in the core region and that the effect of buoyancy becomes insignificant beyond a Reynolds number of typically 5 × 10 5. The Euler number in turbulent flows is higher by about 30 per cent than that in the laminar regime. The dimensionless inlet velocity in pure natural convection varies as Gr 1/3. Results are also presented for a number of quantities of interest such as the flow and temperature distributions, Nusselt number, pressure drop and the maximum dimensionless temperature in the block, along with correlations.
Modeling of Natural Turbulent Convection in an Enclosure with Localized Heating
2019
Purpose: The purpose of the study was to model natural turbulent convection in an enclosure with localized heating. Methodology: The study considered the equations governing a free convection. Precisely, the equations governed a Newtonian fluid that experiences transfer of heat or mass. The governing equations were derived from the conservation principles namely the conservation of mass, the conservation of momentum, and the conservation of energy. These equations were decomposed using the Reynolds decomposition then the decomposed equations were non-dimensionalized and reduced using the Boussinesq assumptions. The k-e model was employed in the simulation of flow characteristics. Finally, the equations were solved numerically for the flow quantities. Results: The results were presented in form of isotherms and vector potentials in different sections of the enclosure. The results of the study indicated that the variation of the Rayleigh number affects the flow properties such as the ...
International Journal of Thermal Sciences, 2015
Unsteady natural convection process of a fluid inside an inner walled vessel caused by an external forced turbulent convective flow of air in a rectangular duct has been analyzed numerically for Re ¼ 5000; Re ¼ 22,000. Fluid mechanics and conjugate convective heat transfer, for both inner fluid (water) and outer fluid (air), described in terms of continuity, linear momentum, keε turbulence model and energy equations were predicted by using the finite-volume method (FVM). Results for the streamlines, isotherms, local Nusselt numbers along the cavity walls and the average friction factor are presented. A comparison between obtained results for both Reynolds number is made. In general, it was found that the cooling process is improved up to 79% when Re number is increased from 5000 to 22,000; and the fluid mechanics characteristics inside the vessel is not considerable affected by the velocity inlet of the cooling air.