A Numerical Solution of Variable Porosity Effects on Natural Convection in a Packed-Sphere Cavity

1991 ◽  
Vol 113 (2) ◽  
pp. 391-399 ◽  
Author(s):  
E. David ◽  
G. Lauriat ◽  
P. Cheng
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Particle Diameter ◽  
Fluid Phase ◽  
Momentum Equation ◽  
Spherical Particles ◽  
Porosity Variation ◽  
Nusselt Numbers ◽  
Variable Porosity ◽  
Prandtl Numbers

The problem of natural convection in differentially heated vertical cavities filled with spherical particles saturated with Newtonian fluids is investigated numerically. The Brinkman–Darcy–Ergun equation is used as the momentum equation, and the wall effect on porosity variation is approximated by an exponential function. The effect of variable stagnant thermal conductivities is taken into consideration in the energy equation. The formulation of the problem shows that the flow and heat transfer characteristics depend on six dimensionless parameters, namely, the Rayleigh and Prandtl numbers of the fluid phase, the dimensionless particle diameter, the conductivity ratio of the two phases, the bulk porosity, and the aspect ratio of the cavity. The influences of these parameters on the heat transfer rate are thoroughly investigated. The predicted Nusselt numbers are compared with existing experimental results. It is found that the computed Nusselt numbers based on the present model compare the best with experimental data.

Analysis of Transient Three-Dimensional Natural Convection in Porous Media

1981 ◽  
Vol 103 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Y. T. Chan ◽  
S. Banerjee
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Natural Convection ◽  
Thermophysical Properties ◽  
Fluid Phase ◽  
Spherical Particles ◽  
Solid Matrix ◽  
Time Step ◽  
Nusselt Numbers ◽  
Convection In Porous Media

Transient multidimensional natural convection in porous media has been studied using a numerical method based on the simplified marker and cell technique with local cancellation of low order, diffusional truncation errors. The conservation equations and boundary conditions were phrased in terms of the primitive variables, velocity and temperature. Differences in temperature between the fluid and the solid matrix are considered. Heat transfer between the solid and liquid phases was modelled by representing the porous medium as an assemblage of spherical particles, and solving the conduction problem within the spheres at every time step. Nusselt numbers at walls were calculated from the temperature and velocity profiles. Numerical results for heat transfer through fluid saturated porous media heated from below are in good agreement with published experiments. Consideration of heat transfer between the solid and fluid phase leads to Nusselt numbers that vary with the thermophysical properties of the solid material, even when the Rayleigh number and fluid thermophysical properties are kept constant. This is also observed in experiments. The calculations also show convective instabilities of the right period at high Rayleigh numbers.

Natural Convection in Cubic and Rhomb-Shaped Enclosures

2013 ◽  
Author(s):  
Milorad B. Dzodzo
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Fields ◽  
Nusselt Numbers ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Laminar Natural Convection ◽  
Velocity And Temperature Fields ◽  
Prandtl Numbers ◽  
Volume Method

Laminar natural convection in cubic and rhomb–shaped enclosures (rhomb angles 59°, 44° and 28.2°) with two opposite vertical walls kept at different temperatures was investigated experimentally and numerically. The enclosures were filled with glycerol and the Rayleigh (Ra) and Prandtl (Pr) numbers ranged from 2,000<Ra<369,000 and 2,680<Pr<7,000. The visualization of the velocity and temperature fields was obtained by using Plexiglass and liquid crystal particles as tracers. The finite volume method based on the finite difference approach was applied for numerical analysis. The velocity and temperature fields and average Nusselt numbers were found as a function of the Reyleigh and Prandtl numbers. Comparison of the average Nusselt numbers for cubic and rhomb-shaped enclosures indicates decrease of heat transfer for the cases when the lower and upper vertical walls of the rhomb-shaped enclosures are at lower and higher temperatures, respectively. This is due to the tendency of fluid stratification in the lower and upper corners.

Natural Convection From Horizontal Wires to Viscoelastic Fluids

1986 ◽  
Vol 108 (4) ◽  
pp. 790-795 ◽  
Author(s):  
M. L. Ng ◽  
J. P. Hartnett ◽  
E. Y. Kwack
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Shear Rate ◽  
Convection Heat Transfer ◽  
Viscoelastic Liquid ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Nusselt Numbers ◽  
Prandtl Numbers ◽  
Different Diameters

Natural convection heat transfer from horizontal wires of three different diameters (0.0254, 0.0508, and 0.0826 cm) to a pool of viscoelastic liquid was studied. Aqueous solutions of Natrosol and Polyox constituted the viscoelastic test fluids. The experimental Nusselt numbers were found to agree with the correlations recommended by Fand and Brucker for Newtonian fluids if the zero shear rate viscosity is used in the Rayleigh and Prandtl numbers.

scholarly journals Influence of Macroscopic Wall Structures on the Fluid Flow and Heat Transfer in Fixed Bed Reactors with Small Tube to Particle Diameter Ratio

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 689
Author(s):  
Thomas Eppinger ◽  
Nico Jurtz ◽  
Matthias Kraume
Keyword(s):  
Heat Transfer ◽  
Fixed Bed ◽  
Particle Diameter ◽  
Diameter Ratio ◽  
Spherical Particles ◽  
Reactor Wall ◽  
Entry Length ◽  
Fixed Bed Reactors ◽  
Wall Structures ◽  
Small Tube

Fixed bed reactors are widely used in the chemical, nuclear and process industry. Due to the solid particle arrangement and its resulting non-homogeneous radial void fraction distribution, the heat transfer of this reactor type is inhibited, especially for fixed bed reactors with a small tube to particle diameter ratio. This work shows that, based on three-dimensional particle-resolved discrete element method (DEM) computational fluid dynamics (CFD) simulations, it is possible to reduce the maldistribution of mono-dispersed spherical particles near the reactor wall by the use of macroscopic wall structures. As a result, the lateral convection is significantly increased leading to a better radial heat transfer. This is investigated for different macroscopic wall structures, different air flow rates (Reynolds number Re = 16 ...16,000) and a variation of tube to particle diameter ratios (2.8, 4.8, 6.8, 8.8). An increase of the radial velocity of up to 40%, a reduction of the thermal entry length of 66% and an overall heat transfer increase of up to 120% are found.

Effects of Insulated and Isothermal Baffles on Pseudosteady-State Natural Convection Inside Spherical Containers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Transfer Enhancement ◽  
Nusselt Numbers ◽  
Extended Surface ◽  
Parametric Studies ◽  
Thermal Layer

The effects of insulated and isothermal thin baffles on pseudosteady-state natural convection within spherical containers were studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106, and 107, baffles with three lengths positioned at five different locations were investigated (120 cases). The fluid that is heated adjacent to the sphere rises replacing the colder fluid, which sinks downward through the stratified stable thermal layer. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid, thus causing oscillations in the temperature and flow fields. Due to flow obstruction (blockage or confinement) effect of baffles and also because of the extra heating afforded by the isothermal baffle, multi-cell recirculating vortices are observed. This additional heat is directly linked to creation of another recirculating vortex next to the baffle. In effect, hot fluid is directed into the center of the sphere disrupting thermal stratified layers. For the majority of the baffles investigated, the Nusselt numbers were generally lower than the reference cases with no baffle. The extent of heat transfer modification depends on Ra, length, and location of the extended surface. With an insulated baffle, the lowest amount of absorbed heat corresponds to a baffle positioned horizontally. Placing a baffle near the top of the sphere for high Ra number cases can lead to heat transfer enhancement that is linked to disturbance of the thermal boundary layer. With isothermal baffles, heat transfer enhancement is achieved for a baffle placed near the bottom of the sphere due to interaction of the counterclockwise rotating vortex and the stratified layer. For some high Ra cases, strong fluctuations of the flow and thermal fields indicating departure from the pseudosteady-state were observed.

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103&lt;Ra&lt;4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

An Experimental Investigation on Forced Convection Heat Transfer From a Cylinder Embedded in a Packed Bed

1994 ◽  
Vol 116 (1) ◽  
pp. 73-80 ◽  
Author(s):  
K. Nasr ◽  
S. Ramadhyani ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Forced Convection ◽  
Convection Heat Transfer ◽  
Particle Diameter ◽  
Packed Bed ◽  
Spherical Particles ◽  
Theoretical Equation ◽  
Convection Heat ◽  
Forced Convection Heat Transfer

Forced convection heat transfer from a cylinder embedded in a packed bed of spherical particles was studied experimentally. With air as the working fluid, the effects of particle diameter and particle thermal conductivity were examined for a wide range of thermal conductivities (from 200 W/m K for aluminum to 0.23 W/m K for nylon) and three nominal particle sizes (3 mm, 6 mm, and 13 mm). In the presence of particles, the measured convective heat transfer coefficient was up to seven times higher than that for a bare tube in crossflow. It was found that higher heat transfer coefficients were obtained with smaller particles and higher thermal conductivity packing materials. The experimental data were compared against the predictions of a theory based on Darcy’s law and the boundary layer approximations. While the theoretical equation was moderately successful at predicting the data, improved correlating equations were developed by modifying the form of the theoretical equation to account better for particle diameter and conductivity variations.

A Numerical Study of Laminar Natural Convection in Shallow Cavities

1981 ◽  
Vol 103 (2) ◽  
pp. 226-231 ◽  
Author(s):  
G. S. Shiralkar ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Numerical Study ◽  
Aspect Ratios ◽  
Shallow Cavities ◽  
Horizontal Cavity ◽  
Side Walls ◽  
Prandtl Numbers

Heat transfer by natural convection in a horizontal cavity with adiabatic horizontal walls and isothermal side walls is investigated numerically for high aspect ratios (width/height). Comparison is made with existing analytical and experimental results. Agreement is generally good at moderate and high Prandtl numbers to which most previous works have been restricted. Improvements of the existing correlation have been proposed in regions of discrepancy. Extension to the low Prandtl number case, including the range of liquid metals, has been made on the basis of an analytical model for high Rayleigh numbers as well as by numerical solution of the full equations. The agreement between the two is found to be very good. A correlation for the heat transfer is proposed for each of the two different cases of high and low Prandtl number.

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