Natural Convection in Enclosed Porous Media With Rectangular Boundaries

1970 ◽  
Vol 92 (1) ◽  
pp. 21-27 ◽  
Author(s):  
B. K. C. Chan ◽  
C. M. Ivey ◽  
J. M. Barry
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Natural Convection ◽  
Transfer Rate ◽  
Darcy Number ◽  
Field Equations ◽  
Geometric Aspect ◽  
Lumped Parameter ◽  
Different Temperatures

Numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures. The results are presented in terms of theoretical streamlines and isotherms. From these the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of three-dimensionless parameters: the Darcy number Da, the Rayleigh number Ra, and a geometric aspect ratio L/D. A possible correlation using the lumped parameter Da Ra is proposed for Da Ra greater than about 40.

Natural Convection Inside a Bidisperse Porous Medium Enclosure

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Arunn Narasimhan ◽  
B. V. K. Reddy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Solid Phase ◽  
Darcy Number ◽  
The Core ◽  
Side Walls ◽  
Porous Blocks ◽  
Rayleigh Numbers

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks (N2), macropore volume fraction (ϕE), and internal Darcy number (DaI) for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both DaI and DaE. At low Ra values, Nu is strongly affected by both DaI and ϕE. When N2 is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of Raϕ, DaE, DaI, and N2. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, RaϕDaE.

Heat transfer analysis of a ventilated room with a porous partition: LB-MRT simulations

2020 ◽  
Vol 91 (2) ◽  
pp. 20904
Author(s):  
Zouhira Hireche ◽  
Lyes Nasseri ◽  
Djamel Eddine Ameziani
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Natural Convection ◽  
Reynolds Numbers ◽  
Darcy Number ◽  
The Other ◽  
Flow In Porous Media ◽  
Heat Transfer Analysis ◽  
Maximum Deviation ◽  
Important Conclusion

This article presents the hydrodynamic and thermal characteristics of transfers by forced, mixed and natural convection in a room ventilated by air displacement. The main objective is to study the effect of a porous partition on the heat transfer and therefore the thermal comfort in the room. The fluid flow future in the cavity and the heat transfer rate on the active wall have been analyzed for different permeabilities: 10−6 ≤ Da ≤ 10. The other control parameters are obviously, the Rayleigh number and the Reynolds number varied in the rows: 10 ≤ Ra ≤ 106 and 50 ≤ Re ≤ 500 respectively. The transfer equations write were solved by the Lattice Boltzmann Multiple Relaxation Time method. For flow in porous media an additional term is added in the standard LB equations, to consider the effect of the porous media, based on the generalized model, the Brinkman-Forchheimer-extended Darcy model. The most important conclusion is that the Darcian regime start for small Darcy number Da < 10−4. Spatial competition between natural convection cell and forced convection movement is observed as Ra and Re rise. The effect of Darcy number values and the height of the porous layer is barely visible with a maximum deviation less than 7% over the ranges considered. Note that the natural convection regime is never reached for low Reynolds numbers. For this Re values the cooperating natural convection only improves transfers by around 10% while, for the other Reynolds numbers the improvement in transfers due to natural and forced convections cooperation is more significant.

Natural convection of nanofluids in a wavy porous cavity

2021 ◽  
pp. 095440622110426
Author(s):  
Prabir Barman ◽  
PS Rao
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Natural Convection ◽  
Volume Fraction ◽  
Unit Length ◽  
Vertical Wall ◽  
Darcy Number ◽  
Heat Transfer Process ◽  
Wide Range ◽  
Wavy Cavity

In this piece of work, a numerical investigation of natural convection is carried out on the buoyancy-driven flow of nanofluids and heat transfer through porous media packed inside a wavy cavity. The cavity is placed horizontal, and its right vertical wall is of wavy nature, the bottom and top walls of the cavity are adiabatic, and there is a temperature difference between the left and right vertical wall. The dimensionless governing equations for the flow of nanofluids through the Darcian porous media are solved iteratively by using finite difference method. The study is conducted for wide range of governing parameters, such as Rayleigh-Darcy number [Formula: see text], nanoparticle volume fraction [Formula: see text] for three types of nanofluids [Formula: see text]-[Formula: see text], Cu-[Formula: see text], TiO2-[Formula: see text], the waviness of the vertical wall controlled by dimensionless length of amplitude of the wave [Formula: see text] and number of undulations per unit length ( N = 1, 3, 5). The simulated results reveals that the presence of nanoparticles enhances the convective heat transfer process at low Ra, and the wall affects the local convection rate and it also controls the overall heat transfer rate. For a cavity with N = 3, [Formula: see text] is increased by 33% at Ra = 10, and at [Formula: see text] has a drop by 10% as the a is increased from 0.05 to 0.25 having 20% of nanoparticles.

Numerical study of laminar mixed convection flow in a lid-driven square cavity filled with porous media

2018 ◽  
Vol 28 (4) ◽  
pp. 857-877 ◽  
Author(s):  
Najib Hdhiri ◽  
Brahim Ben Beya
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Mixed Convection ◽  
Transfer Rate ◽  
Richardson Number ◽  
Convection Flow ◽  
Brinkman Model ◽  
Mixed Convection Flow ◽  
Content Type

Purpose The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure. Design/methodology/approach The authors used the finite volume method. Findings The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium. Originality/value A comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

Natural Convection Experiments in a Stratified Liquid-Saturated Porous Medium

1986 ◽  
Vol 108 (3) ◽  
pp. 660-666 ◽  
Author(s):  
D. C. Reda
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
High Permeability ◽  
Transfer Rates ◽  
Variable Porosity ◽  
Radial Extent

Natural convection heat transfer from a constant-flux cylinder, immersed vertically through a stratified (two-layer) liquid-saturated porous medium, was investigated experimentally. Measured radial temperature profiles and heat transfer rates agreed well with numerical predictions based on the work of Hickox and Gartling. The 1:6 permeability-ratio interface existing between the two layers was found to effectively trap buoyancy-driven fluid motion within the high-permeability region, beneath the interface. Within this high-permeability region, Nusselt number versus Rayleigh number data were found to correlate with previously measured results, obtained for the same basic geometry, but with a fully permeable upper-surface hydrodynamic boundary condition. In both cases, the vertical and radial extent of the region under study were large compared to the radius of the heat source. Combined results indicate that, for a given Rayleigh number in the Darcy-flow regime, heat transfer rates from cylinders immersed vertically in uniform liquid-saturated porous media of large vertical and radial extent potentially approach limiting values. Variable-porosity effects which occur in unconsolidated porous media adjacent to solid boundaries were investigated numerically for cases where the particle-to-heater diameter ratio was small (≈ 10−2). Results showed variable-porosity effects to have a negligible influence on the thermal field adjacent to such boundaries under conditions of Darcy flow.

Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference

1978 ◽  
Vol 100 (2) ◽  
pp. 191-198 ◽  
Author(s):  
A. Bejan ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Temperature Difference ◽  
Transfer Rate ◽  
Horizontal Cylinder ◽  
Horizontal Layer ◽  
Parallel Plates ◽  
End To End

Natural convection in a porous medium filling a slender horizontal space with an end-to-end temperature difference is studied analytically. The end-to-end temperature difference gives rise to a horizontal counterflow pattern augmenting the heat transfer rate through the porous medium. Two basic geometries are considered: horizontal layer confined between two adiabatic and impermeable parallel plates, and horizontal cylinder surrounded by an adiabatic and impermeable cylindrical surface. Nusselt number relations are derived in terms of the Rayleigh number and the cavity aspect ratio. The end-wall permeability is shown to affect the heat transfer rate through the medium.

scholarly journals NATURAL CONVECTIVE HEAT TRANSFER IN A POROUS MEDIUM WITHIN A TWO DIMENSIONAL ENCLOSURE

2017 ◽  
Vol 18 (2) ◽  
pp. 196-211 ◽  
Author(s):  
Mehdi Ahmadi
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Solid Phase ◽  
Fluid Motion ◽  
Darcy Number ◽  
Large Share ◽  
Porous Media Model

In this paper, to achievement the effect of increase number of heating components arrangement on the rate of heat transfer of natural convection, that others have been less noticed. Therefore, in each stage increase the number of heating components so much the space occupied by them remains constant. Then by calculating the amount of heat transfer in different Rayleigh number became clear that minify and distributing heating solid phase in the enclosure increases the total Nusselt number and heat transfer, One reason could be high intensity of fluid motion in corners and near walls of the enclosure. In the next section with the solid phases on the enclosure can be made porous media model. As the results showed an increase in average Rayleigh number, Nusselt number has increased. Also be seen in the lower Darcy numbers, speed of increase in Nusselt number with increase in average Rayleigh number is higher. It can be said that in enclosure by any number of solid pieces with certain Darcy number, with an increase in average Rayleigh number, circular flow inside the enclosure becomes more intense and isothermal lines near walls with constant temperature are so dense, that represents an increase in rate of heat transfer. Also by increasing the Darcy number, rate of heat transfer from the porous media has decreased, as regards that a large share of heat transfer in porous media is done by conduction, although increasing Darcy number increases heat transfer of natural convection but decrease a heat transfer of conduction, therefore decrease total of heat transfer.

Analysis of Darcy Flow in Confined Porous Media Including Wall Effect

2011 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Heat Exchange ◽  
Velocity Field ◽  
Darcy Number ◽  
Momentum Transport ◽  
Mean Velocity ◽  
Viscous Shear ◽  
The Mean

Effective cooling lies at the heart of reactor design and safe operation. Materials for cooling systems include solid porous media (e.g. metal foam). This is due to the large surface area per unit volume and the random internal structure of such porous medium. The former promotes heat exchange rates by providing large surface area, while the latter enhances it by providing vigorous mixing of the working fluid, which gives rise to what is called dispersion (an added mechanism of heat transfer). Hence, momentum transport in porous media is critical for heat transfer analysis, computation and design. Porous media are also used as storage of nuclear waste. In such applications, the porous medium is confined by solid boundaries. These impermeable boundaries give rise to shear stress and boundary layers, which strongly influence the velocity field and the pressure drop inside the porous medium. The velocity field directly influence the heat transfer rate, while the pressure drop determines the required pumping power. The Brinkman-extended Darcy equation describes the momentum transport due to fully developed Newtonian fluid flow in confined porous media. This equation is an extension of the famous Darcy equation, and it contains the viscous shear at the boundaries as well as the viscous shear on the internal surface of the porous medium. The equation is solved analytically inside and outside the boundary layer in a cylindrical porous-media system. As, expected, the volume-averaged velocity decays as the distance from the boundary increases. The mean and maximum velocities are obtained and their behavior is investigated in terms of the Darcy number and the ratio of the effective to the actual fluid viscosity. The friction factor is defined based on the mean velocity and is found to be inversely proportional to the Reynolds number, the Darcy number and the mean velocity. The analytical velocity can be directly substituted in the governing convection heat transfer equation to assess the heat transfer performance of confined cylindrical heat exchange systems.

Effect of Microscopic Vortices Caused by Flow Interaction With Solid Obstacles on Heat Transfer in Turbulent Porous Media Flows

2019 ◽  
Author(s):  
Ching-Wei Huang ◽  
Vishal Srikanth ◽  
Haodong Li ◽  
Andrey V. Kuznetsov
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Porous Medium ◽  
Porous Media ◽  
Heat Transfer Rate ◽  
Contact Area ◽  
Transfer Rate ◽  
Porous Media Flow ◽  
Pore Scale ◽  
Solid Obstacles

Abstract Turbulent flow in a homogeneous porous medium was investigated through the use of numerical methods by employing the Reynolds Averaged Navier-Stokes (RANS) modeling technique. The focus of our research was to study how microscopic vortices in porous media flow influence the heat transfer from the solid obstacles comprising the porous medium to the fluid. A Representative Elementary Volume (REV) with 4 × 4 cylindrical obstacles and periodic boundary conditions was used to represent the infinite porous medium structure. Our hypothesis is that the rate of heat transfer between the obstacle surface and the fluid (qavg) is strongly influenced by the size of the contact area between the vortices and the solid obstacles in the porous medium (Avc). This is because vortices are regions with low velocity that form an insulating layer on the surface of the obstacles. Factors such as the porosity (φ), Pore Scale Reynolds number (Rep), and obstacle shape of the porous medium were investigated. All three of these factors have different influences on the contact area Avc, and, by extension, the overall heat transfer rate qavg. Under the same Pore Scale Reynolds number (Rep), our results suggest that a higher overall heat transfer rate is exhibited for smaller contact areas between the vortices and the obstacle surface. Although the size of the contact area, Avc, is affected by Rep, the direct influence of Rep on the overall heat transfer rate qavg is much stronger, and exceeds the effect of Avc on qavg. The Pore Scale Reynolds number, Rep, and the mean Nusselt number, Num, have a seemingly logarithmic relationship.

Convective Heat Transfer of Al2O3 Nanofluids in Porous Media

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Navid O. Ghaziani ◽  
Fatemeh Hassanipour
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Porous Media ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Particle Concentration ◽  
Metal Foam ◽  
Volume Fraction ◽  
Constant Heat Flux

In this study, the performance of a heat sink embedded with a porous medium and nanofluids as coolants is analyzed experimentally. The nanofluid is a mixture of de-ionized water and nanoscale Al2O3 particles with three different volumetric concentrations: ζ = 0.41%, 0.58%, and 0.83%. The experimental test section is a rectangular minichannel filled with metal foam, which is electrically heated to provide a constant heat flux. The porous medium is assumed to be homogeneous and the flow regime is laminar. The result of heat transfer enhancement by slurry of Al2O3 nanofluid in porous media is studied under various flow velocities, heat flux, porous media structure, and particle concentration of nanofluid. The effect of particles volume fraction on heat transfer coefficient is also studied. This experimental study discovers and/or confirms the following hypotheses: (1) nanoparticle slurry in conjunction with metal foam has a significant effect on heat transfer rate; (2) there is an optimum permeability for the foam resulting in maximal heat transfer rate; (3) for a fixed particle concentration, smaller particles are more effective in enhancing heat transfer; and (4) increasing particle concentration results in some gains, but this trend weakens after a threshold.

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