Выходит 12 номеров в год
ISSN Печать: 1091-028X
ISSN Онлайн: 1934-0508
Indexed in
The Stability of a Developing Thermal Front in a Porous Medium. I Linear Theory
Краткое описание
In this paper, we analyze the stability of the developing thermal boundary layer that is induced by suddenly raising the temperature of the lower horizontal boundary of a uniformly cold semi-infinite porous domain. A full linear stability analysis is developed, and it is shown that disturbances are governed by a parabolic system of equations. Numerical solutions of this system are compared with the neutral stability curve obtained by approximating the system as an ordinary differential eigenvalue problem. Different criteria are used to mark the onset of convection of an evolving disturbance, namely, the maximum disturbance temperature, the surface rate of heat transfer, and the disturbance energy. It is found that these different measures yield different neutral curves. We also show that the disturbances have a favoured evolutionary path in the sense that disturbances introduced at different times or with different initial profiles eventually tend toward that common path.
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Hong Joung Sook, Kim Min Chan, Effect of anisotropy of porous media on the onset of buoyancy-driven convection, Transport in Porous Media, 72, 2, 2008. Crossref
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Rees D. A. S., The Onset and Nonlinear Development of Vortex Instabilities in a Horizontal Forced Convection Boundary Layer With Uniform Surface Suction, Transport in Porous Media, 77, 2, 2009. Crossref
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HIDALGO JUAN J., CARRERA JESÚS, Effect of dispersion on the onset of convection during CO2 sequestration, Journal of Fluid Mechanics, 640, 2009. Crossref
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Wessel-Berg Dag, On a Linear Stability Problem Related to Underground CO$_2$ Storage, SIAM Journal on Applied Mathematics, 70, 4, 2009. Crossref
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Kim Min Chan, Song Kwang Ho, Choi Chang Kyun, Yeo Jong-Kee, Onset of buoyancy-driven convection in a liquid-saturated cylindrical porous layer supported by a gas layer, Physics of Fluids, 20, 5, 2008. Crossref
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Nield D. A., Kuznetsov A. V., The Onset of Convection in a Heterogeneous Porous Medium with Transient Temperature Profile, Transport in Porous Media, 85, 3, 2010. Crossref
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Chan Kim Min, Kyun Choi Chang, Linear stability analysis on the onset of buoyancy-driven convection in liquid-saturated porous medium, Physics of Fluids, 24, 4, 2012. Crossref
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Behroozi A., Hatamipour M.S., Rahimi A., Mathematical modeling and parametric study of coke-burning process in a hydrocracker reactor, Computers & Chemical Engineering, 38, 2012. Crossref
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Daniel Don, Tilton Nils, Riaz Amir, Optimal perturbations of gravitationally unstable, transient boundary layers in porous media, Journal of Fluid Mechanics, 727, 2013. Crossref
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Kim Min Chan, Choi Chang Kyun, Analysis on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated uniformly from below, Chemical Engineering Science, 98, 2013. Crossref
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Emami Meybodi Hamid, Hassanzadeh Hassan, Stability analysis of two-phase buoyancy-driven flow in the presence of a capillary transition zone, Physical Review E, 87, 3, 2013. Crossref
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Tilton Nils, Daniel Don, Riaz Amir, The initial transient period of gravitationally unstable diffusive boundary layers developing in porous media, Physics of Fluids, 25, 9, 2013. Crossref
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Noghrehabadi Aminreza, Rees D. Andrew S., Bassom Andrew P., Linear Stability of a Developing Thermal Front Induced by a Constant Heat Flux, Transport in Porous Media, 99, 3, 2013. Crossref
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Myint Philip C., Firoozabadi Abbas, Onset of buoyancy-driven convection in Cartesian and cylindrical geometries, Physics of Fluids, 25, 4, 2013. Crossref
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Kim Min Chan, Analysis of onset of buoyancy-driven convection in a fluid layer saturated in anisotropic porous media by the relaxed energy method, Korean Journal of Chemical Engineering, 30, 6, 2013. Crossref
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Kim Min Chan, Yadav Dhananjay, Linear and Nonlinear Analyses of the Onset of Buoyancy-Induced Instability in an Unbounded Porous Medium Saturated by Miscible Fluids, Transport in Porous Media, 104, 2, 2014. Crossref
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Rees D. Andrew S., Bassom Andrew P., Unsteady thermal boundary layer flows of a Bingham fluid in a porous medium, International Journal of Heat and Mass Transfer, 82, 2015. Crossref
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Kim Min Chan, Choi Chang Kyun, Effect of first-order chemical reaction on gravitational instability in a porous medium, Physical Review E, 90, 5, 2014. Crossref
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Kim Min Chan, The Effect of Boundary Conditions on the Onset of Buoyancy-Driven Convection in a Brine-Saturated Porous Medium, Transport in Porous Media, 107, 2, 2015. Crossref
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Kim Min Chan, Numerical simulation of the Rayleigh–Taylor instability of a miscible slice in a porous medium, Journal of Engineering Mathematics, 100, 1, 2016. Crossref
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Emami-Meybodi Hamid, Hassanzadeh Hassan, Green Christopher P., Ennis-King Jonathan, Convective dissolution of CO2 in saline aquifers: Progress in modeling and experiments, International Journal of Greenhouse Gas Control, 40, 2015. Crossref
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Taheri Amir , Wessel-Berg Dag , Torsæter Ole , Prediction of the Minimum Onset Time for Convection in a Gravitationally Unstable Diffusive Boundary Layer Using a Finite Difference Pressure Solver, All Days, 2015. Crossref
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Rabiei Faradonbeh M., Harding T. G., Abedi J., Hassanzadeh H., Stability Analysis of Coupled Heat and Mass Transfer Boundary Layers During Steam–Solvent Oil Recovery Process, Transport in Porous Media, 108, 3, 2015. Crossref
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Hattori T., Patterson J.C., Lei C., Characterization of linear and oscillatory behaviours of radiation-induced natural convection boundary layer in response to constant and time-varying thermal forcing, International Journal of Heat and Mass Transfer, 87, 2015. Crossref
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Kim Min Chan, Choi Chang Kyun, Some theoretical aspects on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated impulsively from below, Korean Journal of Chemical Engineering, 32, 12, 2015. Crossref
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Kim Min Chan, Magnetic field effect on the onset of Soret-driven convection of a nanofluid confined within a Hele-Shaw cell, Korean Journal of Chemical Engineering, 34, 1, 2017. Crossref
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Lyubimova Tatyana, Zubova Nadezhda, Onset and nonlinear regimes of convection of binary fluid with negative separation ratio in square cavity heated from above, International Journal of Heat and Mass Transfer, 106, 2017. Crossref
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Emami-Meybodi Hamid, Stability analysis of dissolution-driven convection in porous media, Physics of Fluids, 29, 1, 2017. Crossref
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Bidin Biliana, Rees D., The Onset of Convection in an Unsteady Thermal Boundary Layer in a Porous Medium, Fluids, 1, 4, 2016. Crossref
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Ghorbani Zohreh, Riaz Amir, Daniel Don, Convective mixing in vertically-layered porous media: The linear regime and the onset of convection, Physics of Fluids, 29, 8, 2017. Crossref
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Lyubimova T., Zubova N., Shevtsova V., Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above, The European Physical Journal E, 40, 3, 2017. Crossref
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Taheri Amir, Lindeberg Erik, Torsæter Ole, Wessel-Berg Dag, Qualitative and quantitative experimental study of convective mixing process during storage of CO 2 in homogeneous saline aquifers, International Journal of Greenhouse Gas Control, 66, 2017. Crossref
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Ryoo Won Sun, Kim Min Chan, Effect of vertically varying permeability on the onset of convection in a porous medium, Korean Journal of Chemical Engineering, 35, 6, 2018. Crossref
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Rees D.A.S., Selim A., Ennis-King J.P., The Instability of Unsteady Boundary Layers in Porous Media, in Emerging Topics in Heat and Mass Transfer in Porous Media, 22, 2008. Crossref
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Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2013. Crossref
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Emami-Meybodi Hamid, Zhang Fengyuan, Buoyancy-driven instabilities of partially miscible fluids in inclined porous media, Journal of Fluid Mechanics, 926, 2021. Crossref
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Kim Min Chan, Song Kwang Ho, Gravitational instability and its scaling relation of a partially miscible two‐component system in a porous medium, International Journal of Heat and Mass Transfer, 169, 2021. Crossref
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Kim Min Chan, Choi Chang Kyun, Density maximum effects on the onset of buoyancy-driven convection in a porous medium saturated with cold water, International Journal of Heat and Mass Transfer, 71, 2014. Crossref
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Kim Min Chan, Linear and nonlinear analyses on the onset of gravitational instabilities in a fluid saturated within a vertical Hele-Shaw cell, Chemical Engineering Science, 126, 2015. Crossref
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Dhar J., Meunier P., Nadal F., Méheust Y., Convective dissolution of carbon dioxide in two- and three-dimensional porous media: The impact of hydrodynamic dispersion, Physics of Fluids, 34, 6, 2022. Crossref
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Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2017. Crossref