Three-Dimensional Simulations for Convection Problem in Anisotropic Porous Media with Nonhomogeneous Porosity, Thermal Diffusivity, and Variable Gravity Effects

2013 ◽  
Vol 102 (1) ◽  
pp. 43-57 ◽  
Author(s):  
A. J. Harfash
Keyword(s):  
Porous Media ◽  
Thermal Diffusivity ◽  
Three Dimensional ◽  
Anisotropic Porous Media ◽  
Gravity Effects ◽  
Convection Problem ◽  
Variable Gravity ◽  
Three Dimensional Simulations

Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media

2016 ◽  
Vol 17 (5) ◽  
pp. 205-220 ◽  
Author(s):  
Akil J. Harfash
Keyword(s):  
Porous Media ◽  
Thermal Diffusivity ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Double Diffusive Convection ◽  
Anisotropic Porous Media ◽  
Onset Of Convection ◽  
Diffusive Convection ◽  
Dimensional Simulation ◽  
Double Diffusive

AbstractA model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as${R_c}$increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as$Rc$increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

scholarly journals Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 1-6 ◽  
Author(s):  
Wei Cai ◽  
Wen Chen ◽  
Fajie Wang
Keyword(s):  
Porous Media ◽  
Fundamental Solution ◽  
Diffusion Equation ◽  
Diffusion Model ◽  
Anomalous Diffusion ◽  
Three Dimensional ◽  
Fractal Structures ◽  
Anisotropic Porous Media ◽  
Convection Diffusion Equation ◽  
Time Space

The anomalous diffusion in fractal isotropic/anisotropic porous media is characterized by the Hausdorff derivative diffusion model with the varying fractal orders representing the fractal structures in different directions. This paper presents a comprehensive understanding of the Hausdorff derivative diffusion model on the basis of the physical interpretation, the Hausdorff fractal distance and the fundamental solution. The concept of the Hausdorff fractal distance is introduced, which converges to the classical Euclidean distance with the varying orders tending to 1. The fundamental solution of the 3-D Hausdorff fractal derivative diffusion equation is proposed on the basis of the Hausdorff fractal distance. With the help of the properties of the Hausdorff derivative, the Huasdorff diffusion model is also found to be a kind of time-space dependent convection-diffusion equation underlying the anomalous diffusion behavior.

Three-dimensional simulations of biofilm growth in porous media

AIChE Journal ◽  
2009 ◽  
Vol 55 (2) ◽  
pp. 494-504 ◽  
Author(s):  
D. A. Graf von der Schulenburg ◽  
T. R. R. Pintelon ◽  
C. Picioreanu ◽  
M. C. M. Van Loosdrecht ◽  
M. L. Johns
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Biofilm Growth ◽  
Three Dimensional Simulations
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