Estimation of an effective Rayleigh number for convection in a vertically inhomogeneous porous medium or clear fluid

1994 ◽  
Vol 15 (4) ◽  
pp. 337-340 ◽  
Author(s):  
D.A. Nield
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Clear Fluid ◽  
Inhomogeneous Porous Medium

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

The equations of immiscible viscous displacement in a porous medium

1981 ◽  
Vol 59 (1) ◽  
pp. 45-56 ◽  
Author(s):  
T. J. T. Spanos
Keyword(s):  
Porous Medium ◽  
Statistical Theory ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Continuum Theory ◽  
Immiscible Displacement ◽  
Macroscopic Scale ◽  
Inertial Terms ◽  
Inhomogeneous Porous Medium ◽  
Relative Motions

A statistical theory for the construction of the equations of viscous displacement in a porous medium is considered. This yields a continuum theory for immiscible displacement which can be applied to either a homogeneous or inhomogeneous porous medium. The relative motions of the fluid are considered in terms of the motion of surfaces of constant saturation which are smoothed surfaces at the macroscopic scale considered. The boundary conditions and initial conditions at the injection boundary are considered as well as the boundary conditions and breakthrough conditions at the recovery boundary and the side boundary conditions. The inertial terms are included in the equations and shown to be of importance in describing these initial conditions and the breakthrough conditions.

Stability and Convection in Impulsively Heated Porous Layers

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristoffersen ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Temperature Fluctuations ◽  
Lower Surface ◽  
Onset Of Convection ◽  
Upward Moving ◽  
The Stability

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

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.

On steady convection in a porous medium

1972 ◽  
Vol 54 (1) ◽  
pp. 153-161 ◽  
Author(s):  
Enok Palm ◽  
Jan Erik Weber ◽  
Oddmund Kvernvold
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Transport ◽  
Abrupt Change ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Sixth Order ◽  
Steady Convection ◽  
Good Agreement

For convection in a porous medium the dependence of the Nusselt number on the Rayleigh number is examined to sixth order using an expansion for the Rayleigh number proposed by Kuo (1961). The results show very good agreement with experiment. Additionally, the abrupt change which is observed in the heat transport at a supercritical Rayleigh number may be explained by a breakdown of Darcy's law.

Thermal Convective Instabilities in a Porous Medium

1984 ◽  
Vol 106 (1) ◽  
pp. 137-142 ◽  
Author(s):  
M. Kaviany
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Temperature Distribution ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Onset Of Convection ◽  
Long Time ◽  
Nonlinear Temperature

The onset of convection due to a nonlinear and time-dependent temperature stratification in a saturated porous medium with upper and lower free surfaces is considered. The initial parabolic temperature distribution is due to uniform internal heating. The medium is then cooled by decreasing the upper surface temperature linearly with time. Linear stability theory is applied to the more formally developed governing equations. In order to obtain an asymptotic solution for transient problems involving very long time scales, the critical Rayleigh number for steady-state, nonlinear temperature distribution is also obtained. The effects of porosity, permeability, and Prandtl number on the time of the onset of convection are examined. The steady-state results show that the critical Rayleigh number depends only on the ratio of porosity to permeability and when this ratio exceeds a value of one thousand, the critical Rayleigh number is directly proportional to this ratio.

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