Berkovsky-Polevikov Correlations for Natural Convection in a Nonhomogeneous Enclosure Filled With a Fluid and Disconnected-Conducting Solid Particles

A well-known set of Berkovsky–Polevikov (BP) correlations have been extremely useful in predicting the wall-averaged Nusselt number of “wide” enclosures heated from the side and filled with a fluid undergoing natural convection. A generic form of these correlations, dependent on only two coefficients, is now proposed for predicting the Nusselt number of a heterogeneous (fluid–solid), porous enclosure, i.e., an enclosure filled not only with a fluid but also with uniformly distributed, disconnected and conducting, homogeneous solid particles. The final correlations, and their overall accuracies, are determined by curve fitting the numerical simulation results of the natural convection process inside the heterogeneous enclosure. Results for several Ra and Pr, and for 1, 4, 9, 16, and 36 solid particles, with the fluid volume-fraction (porosity) maintained constant, indicate the accuracy of these correlations to be detrimentally affected by the interference phenomenon caused by the solid particles onto the vertical boundary layers that develop along the hot and cold walls of the enclosure; the resulting correlations, in this case, present standard deviation varying between 6.5% and 19.7%. An analytical tool is then developed for predicting the interference phenomenon, using geometric parameters and scale analysis results. When used to identify and isolate the interference phenomenon, this tool is shown to yield correlations with much improved accuracies between 2.8% and 9.2%.

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Numerical Analysis of Laminar Natural Convection in Rectangular Enclosures of Different Aspect Ratios With and Without Aerosol Nanofluid

Volume 8C: Heat Transfer and Thermal Engineering ◽

10.1115/imece2013-65056 ◽

2013 ◽

Author(s):

Mosfequr Rahman ◽

Andrew Hudson ◽

Gustavo Molina ◽

Valentin Soloiu

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Heat Transfer Enhancement ◽

Computer Model ◽

Large Scale ◽

Solid Particles ◽

Process Equipment ◽

Air Cooling ◽

Transfer Enhancement ◽

Aspect Ratios

Natural convection heat transfer in rectangular enclosures is important in many real-world engineering applications. Included in these applications are the energy efficient design of buildings, operation and safety of nuclear reactors, solar collector design, passive energy storage, heat transfer across multi-pane windows, thermo-electric refrigeration and heating devices, and the design-for-mitigation of optical distortion in large-scale laser systems, environmental engineering and electronic packaging. A common industrial application of natural convection is free air cooling without the aid of fans and can happen on small scales such as computer chips to large scale process equipment. In addition to temperature gradient convection strength within the enclosure can vary due to the existence of nanoparticles with the base fluid. The field of nanofluid research has been expanding in recent years. Most of the research performed for the purpose of heat transfer using nanofluids has been conducted on liquid based nanofluids, leaving the aerosol-based nanofluid research lagging. There is also a deficit in the research previously performed to develop a computer model of heat transfer enhancement using nanofluid. The transport of solid particles and liquid droplets in a fluid has long been a subject of great interest. Understanding, measuring, and quantifying the deposition of aerosol on walls is important in various sectors of science and technology. Some examples are the deposition of drugs and harmful substances in the nasal and respiratory tracts in medical science and engineering; deposition of particles and droplets in gas and steam turbines in power plant engineering; the atmospheric dispersal of pollutants and the determination of indoor air quality in environmental science; the transport and sedimentation of various substances in rivers in civil engineering; fouling of process and heat transfer equipments in process industries; and the transport of chemical aerosols in chemical process engineering. In this research work the case of pure air was first solved for 6 different aspect ratios, then the nanofluid was introduced and the resulting heat transfer was observed. The aerosol nanofluid used was composed of air with copper nanoparticles suspended in an enclosure. This procedure was repeated for multiple aspect ratios. This research also develops a functional computer model for heat transfer enhancement using nanofluid.

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Natural Convection in Horizontal Porous Layers: Effects of Darcy and Prandtl Numbers

Journal of Heat Transfer ◽

10.1115/1.3250807 ◽

1989 ◽

Vol 111 (4) ◽

pp. 926-935 ◽

Cited By ~ 34

Author(s):

N. Kladias ◽

V. Prasad

Keyword(s):

Porous Medium ◽

Natural Convection ◽

Rayleigh Number ◽

Prandtl Number ◽

Numerical Solutions ◽

Fluid Layer ◽

Darcy Number ◽

Solid Particles ◽

Convection Regime ◽

Porous Layers

Natural convection in horizontal porous layers heated from below is studied by employing a formulation based on the Brinkman–Forchheimer–extended Darcy equation of motion. The numerical solutions show that the convective flow is initiated at lower fluid Rayleigh number Raf than that predicted by the linear stability analysis for the Darcy flow model. The effect is considerable, particularly at a Darcy number Da greater than 10−4. On the other hand, an increase in the thermal conductivity of solid particles has a stabilizing effect. Also, the Rayleigh number Raf required for the onset of convection increases as the fluid Prandtl number is decreased. In the stable convection regime, the heat transfer rate increases with the Rayleigh number, the Prandtl number, the Darcy number, and the ratio of the solid and fluid thermal conductivities. However, there exists an asymptotic convection regime where the porous media solutions are independent of the permeability of the porous matrix or Darcy number. In this regime, the temperature and flow fields are very similar to those obtained for a fluid layer heated from below. Indeed, the Nusselt numbers for a porous medium with kf = ks match with the fluid results. The effect of Prandtl number is observed to be significant for Prf < 10, and is strengthened with an increase in Raf, Da, and ks/kf. An interesting effect, that a porous medium can transport more energy than the saturating fluid alone, is also revealed.

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