Non-Darcian Effects in Open-Ended Cavities Filled With a Porous Medium

1991 ◽  
Vol 113 (3) ◽  
pp. 747-756 ◽  
Author(s):  
J. Ettefagh ◽  
K. Vafai ◽  
S. J. Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Saturated Porous Medium ◽  
Critical Value ◽  
Inertial Parameter ◽  
Flow Models ◽  
Flow And Heat Transfer ◽  
Buoyancy Driven Convection

The importance and relevance of non-Darcian effects associated with the buoyancy driven convection in open-ended cavities filled with fluid-saturated porous medium is analyzed in this work. Several different flow models for porous media, such as Brinkman-extended Darcy, Forchheimer-extended Darcy, and generalized flow models, are considered. The significance of inertia and boundary effects, and their crucial influence on the prediction of buouancy-induced flow and heat transfer in open-ended cavities, are investigated. Analysis is made on the proper choice of parameters that can fully determine the criteria for the range of validity of Darcy’s law in this type of configuration. Critical values of the inertial parameter, Λcrit, below which, for any given modified Rayleigh number, the Darcy flow model breaks down, have been investigated. It is shown that the critical value of the inertial parameter depends on the modified Rayleigh number and that this critical value increases as Ra* increases. It is also observed that for higher modified Rayleigh number, the deviation from a Darcian formulation appears at Darcy numbers greater than 1×10−4. The Prandtl number effects on convective flow and heat transfer are shown to be quite significant for small values of Pr. The Prandtl number effects are reduced significantly for higher values of the Prandtl number.

scholarly journals Mixed Convective Flow of Micropolar Nanofluid across a Horizontal Cylinder in Saturated Porous Medium

2019 ◽  
Vol 9 (23) ◽  
pp. 5241 ◽  
Author(s):  
Ahmed M. Rashad ◽  
Waqar A. Khan ◽  
Saber M. M. EL-Kabeir ◽  
Amal M. A. EL-Hakiem
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Convective Flow ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Titania Nanoparticles ◽  
Flow And Heat Transfer ◽  
Micropolar Nanofluid ◽  
Mixed Convective Flow ◽  
The Impact

The micropolar nanofluids are the potential liquids that enhance the thermophysical features and ability of heat transportation instead of base liquids. Alumina and Titania nanoparticles are mixed in a micropolar fluid. The impact of convective boundary condition is also examined with assisting and opposing flows of both nanofluids. The main objective of this study is to investigate mixed convective flow and heat transfer of micropolar nanofluids across a cylinder in a saturated porous medium. Non-similar variables are used to make the governing equations dimensionless. The local similar and non-similar solutions are obtained by using the Runge-Kutta-Fehlberg method of seventh order. The impacts of various embedded variables on the flow and heat transfer of micropolar nanofluids are investigated and interpreted graphically. It is demonstrated that the skin friction and heat transfer rates depend on solid volume fraction of nanoparticles, Biot number, mixed convection, and material parameters.

Natural convective heat transfer in a hemispherical cavity filled with ZnO–H2O nanofluid saturated porous medium

2018 ◽  
Vol 29 (10) ◽  
pp. 1850097 ◽  
Author(s):  
Abderrahmane Baïri ◽  
Najib Laraqi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Physical Parameters ◽  
Numerical Work

This three-dimensional (3D) numerical work based on the volume control method quantifies the convective heat transfer occurring in a hemispherical cavity filled with a ZnO–H2O nanofluid saturated porous medium. Its main objective is to improve the cooling of an electronic component contained in this enclosure. The volume fraction of the considered monophasic nanofluid varies between 0% (pure water) and 10%, while the cupola is maintained isothermal at cold temperature. During operation, the active device generates a heat flux leading to high Rayleigh number reaching [Formula: see text] and may be inclined with respect to the horizontal plane at an angle ranging from 0[Formula: see text] to 180[Formula: see text] (horizontal position with cupola facing upwards and downwards, respectively) by steps of 15[Formula: see text]. The natural convective heat transfer represented by the average Nusselt number has been quantified for many configurations obtained by combining the tilt angle, the Rayleigh number, the nanofluid volume fraction and the ratio between the thermal conductivity of the porous medium’s solid matrix and that of the base fluid. This ratio has a significant influence on the free convective heat transfer and ranges from 0 (without porous media) to 70 in this work. The influence of the four physical parameters is analyzed and commented. An empirical correlation between the Nusselt number and these parameters is proposed, allowing determination of the average natural convective heat transfer occurring in the hemispherical cavity.

scholarly journals Heat transfer for two types of viscoelastic fluid over an exponentially stretching sheet with variable thermal conductivity and radiation in porous medium

2014 ◽  
Vol 18 (4) ◽  
pp. 1079-1093 ◽  
Author(s):  
V. Singh ◽  
Shweta Agarwal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Wall Temperature ◽  
Stretching Sheet ◽  
Variable Thermal Conductivity ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

An Analysis has been carried out to study the boundary layer flow and heat transfer characteristics of second order fluid and second grade fluid with variable thermal conductivity and radiation over an exponentially stretching sheet in porous medium. The basic boundary layer equations governing the flow and heat transfer in prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformations. Numerical solutions of the resulting boundary value problem are solved by using the fourth order Runge-Kutta method with shooting technique for various values of the physical parameters. The effect of variable thermal conductivity, porosity, Prandtl number, radiation parameter and viscoelastic parameters on velocity and temperature profiles (in PST and PHF cases) are analyzed and discussed through graphs. Numerical values of wall temperature gradient in PST case and wall temperature in PHF case are obtained and tabulated for various values of the governing parameters. In this study Prandtl number also treated as variable inside the boundary layer because it depends on thermal conductivity. The results are also verified by using finite difference method.

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.

Experimental Study of Free Convection from a Vertical Flat Plate in Porous Media

2008 ◽  
Vol 273-276 ◽  
pp. 796-801
Author(s):  
L.B.Y. Aldabbagh ◽  
Mohsen Sharifpur ◽  
Mahdi Zamani
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Free Convection ◽  
Flat Plate ◽  
Saturated Porous Medium ◽  
Convection Heat Transfer ◽  
Steady State Condition ◽  
Free Convection Heat ◽  
Vertical Flat Plate

A set of experiments is done to study the phenomenon of free convection heat transfer from an isothermal vertical flat plate embedded in a saturated porous medium in steady state condition. The porous medium consisting of 0.8 cm spheres. The aspect ratio of the isothermal flat plate, H/W, is equal to 2. Where H is the height and W is the width of the vertical plate. The investigations were cared out for Darcy modified Rayleigh number between 100 and 500. The results indicate that heat transfer increases linearly with increasing the Darcy modified Rayleigh number. In addition, the present results are in good agreement with the higher-order boundary layer theory obtained by Cheng and Hsu [1].

Interacting convection modes in a saturated porous medium of nearly square planform: four modes

2017 ◽  
Vol 82 (3) ◽  
pp. 526-547 ◽  
Author(s):  
Brendan J. Florio ◽  
Andrew P. Bassom ◽  
Konstantinos Sakellariou ◽  
Thomas Stemler
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Critical Value ◽  
Basins Of Attraction ◽  
Stable States ◽  
Pitchfork Bifurcations ◽  
Multiple Stable States ◽  
Box Dimensions

Abstract Convection can occur in a confined saturated porous box when the associated Rayleigh number exceeds a threshold critical value: the identity of the preferred onset convection mode depends sensitively on the geometry of the box. Here we discuss examples for which the box dimensions are such that four modes share a common critical Rayleigh number. Perturbation theory is used to derive a system of coupled ordinary differential equations that governs the nonlinear interaction of the four modes and an analysis of this set is undertaken. In particular, it is demonstrated that as the Rayleigh number is increased beyond critical so a series of pitchfork bifurcations occur and multiple stable states are identified that correspond to the survival of just one of the four modes. The basins of attraction for each mode in the 4D phase space are described by a reduction to a suitable 3D counterpart.

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