scholarly journals EXTENDED BOUSSINESQ EQUATIONS FOR WAVES IN POROUS MEDIA: DERIVATION OF GOVERNING EQUATIONS AND GENERATION OF WAVES INTERNALLY

2014 ◽  
Vol 1 (34) ◽  
pp. 57 ◽  
Author(s):  
Changhoon Lee ◽  
Nghi Van Vu ◽  
Tae-Hwa Jung
Keyword(s):  
Porous Media ◽  
Boussinesq Equations ◽  
Governing Equations

scholarly journals A Framework and Numerical Solution of the Drying Process in Porous Media by Using a Continuous Model

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Hong Thai Vu ◽  
Evangelos Tsotsas
Keyword(s):  
Porous Media ◽  
Control Volume ◽  
Continuous Model ◽  
Control Volume Method ◽  
Drying Process ◽  
Transport Parameters ◽  
Governing Equations ◽  
Numerical Tools ◽  
Volume Method ◽  
The Continuum

The modelling and numerical simulation of the drying process in porous media are discussed in this work with the objective of presenting the drying problem as the system of governing equations, which is ready to be solved by many of the now widely available control-volume-based numerical tools. By reviewing the connection between the transport equations at the pore level and their up-scaled ones at the continuum level and then by transforming these equations into a format that can be solved by the control volume method, we would like to present an easy-to-use framework for studying the drying process in porous media. In order to take into account the microstructure of porous media in the format of pore-size distribution, the concept of bundle of capillaries is used to derive the needed transport parameters. Some numerical examples are presented to demonstrate the use of the presented formulas.

Extended Boussinesq equations for waves in porous media

2018 ◽  
Vol 139 ◽  
pp. 85-97 ◽  
Author(s):  
Van Nghi Vu ◽  
Changhoon Lee ◽  
Tae-Hwa Jung
Keyword(s):  
Porous Media ◽  
Boussinesq Equations

The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Porous Media ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Critical Rayleigh Number ◽  
Nanoparticle Volume Fraction ◽  
Governing Equations ◽  
Medium Layer ◽  
Vertical Throughflow

The model developed in our previous paper (Nield and Kuznetsov, 2011, “The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid,” Transp. Porous Media, 87(3), pp. 765–775) is now revised to accommodate a more realistic boundary condition on the nanoparticle volume fraction. The new boundary condition postulates zero nanoparticle flux through the boundaries. We established that in the new model, oscillatory instability is impossible. We also established that the critical Rayleigh number depends on three dimensionless parameters, and we derived these three parameters from the governing equations. We also briefly investigated the major trends.

Dispersion and nonlinearity of multi-layer non-hydrostatic free-surface flow

2013 ◽  
Vol 726 ◽  
pp. 226-260 ◽  
Author(s):  
Yefei Bai ◽  
Kwok Fai Cheung
Keyword(s):  
Deep Water ◽  
Surf Zone ◽  
Perturbation Expansion ◽  
Boussinesq Equations ◽  
Surface Flow ◽  
Second Order ◽  
Superior Performance ◽  
Wave Transformation ◽  
Intermediate Water ◽  
Governing Equations

AbstractNon-hydrostatic multi-layer models have become a popular tool in describing wave transformation from deep water to the surf zone, but the numerical approach lacks a theoretical framework to guide implementation and assist interpretation of the results. In this paper, we formulate a non-hydrostatic model in an analytical form for the derivation and examination of dispersive and nonlinear properties. Depth integration of the dimensionless continuity and Euler equations over each layer yields the conventional multi-layer formulation. A variable transformation converts the conventional form into an integrated series form, which provides separate descriptions of flux- and dispersion-dominated processes. Substitution of the non-hydrostatic pressure and vertical velocity in the governing equations by high-order derivatives of the horizontal velocity and surface elevation provides a direct comparison with the Boussinesq equations published in the literature. Implementation of a perturbation expansion extracts the first- and second-order governing equations with respect to the nonlinear parameter. Based on that, we derive analytical solutions of the linear dispersion and the second-order super- and sub-harmonics for up to three layers and optimize the solutions in terms of the layer arrangement. In relation to the Boussinesq equations at comparable orders of expansion, the two- and three-layer models provide slightly higher errors in shallow and intermediate water in terms of dispersion and super-harmonics, but show superior performance in describing sub-harmonics in deep water.

Statistics of Mathematical Two-Scale Closure of Momentum, Heat and Charge Transport Problems With Stochastic Orientation of Porous Medium Capillaries

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Volume Averaging ◽  
Governing Equations ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Model Flow ◽  
History Of ◽  
Transport Problems

Abstract The history of stochastic capillary porous media transport problem treatments almost corresponds to the history of porous media transport developments. Volume Averaging Theory (VAT), shown to be an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in capillary porous media. VAT based modeling of pore level transport in stochastic capillaries results in two sets of scale governing equations. This work shows how the two scale equations could be solved and how the results could be presented using statistical analysis. We demonstrate that stochastic orientation and diameter of the pores are incorporated in the upper scale simulation procedures. We are treating this problem with conditions of Bi for each pore is in a range when Bi ≳ 0.1 which allows even greater distinction in assessing an each additional differential, integral, or integral-differential term in the VAT equations.

Radiation Heat Transport in Porous Media

1999 ◽  
Author(s):  
V. S. Travkin ◽  
I. Catton
Keyword(s):  
Porous Media ◽  
Heterogeneous Media ◽  
Radiation Transport ◽  
Homogeneous Medium ◽  
Radiative Transport ◽  
Governing Equations ◽  
Radiation Heat ◽  
Heat And Mass Transport ◽  
First Time ◽  
Medium Heterogeneity

Abstract At present most work treats radiative transport in heterogeneous media as if it were a homogeneous medium, then relies on different methods to simulate the medium heterogeneity or uses similar governing equations with assigned distributions for coefficients. This approach is widely used although almost never found in other fields of heat and mass transport. The lack of generality in present theoretical treatments of radiative transport in heterogeneous media is addressed by rigorous development of a set of governing equations. The new rigorous equations for radiation transport in heterogeneous media are presented for the first time. As part of the development of the new set of equations for electromagnetic and spectral intensity fields, the diffusion approximation is explored.

Extended Boussinesq Equations for Water-Wave Propagation in Porous Media

2010 ◽  
Vol 136 (5) ◽  
pp. 625-640 ◽  
Author(s):  
Shih-Chun Hsiao ◽  
Kai-Cheng Hu ◽  
Hwung-Hweng Hwung
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Water Wave ◽  
Boussinesq Equations
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