NDLI: Stability of natural convection in a vertical layer of Brinkman porous medium

Content Provider	Springer Nature Link
Author	Shankar, B. M. Kumar, Jai Shivakumara, I. S.
Copyright Year	2016
Abstract	A classical linear stability theory is applied to emphasize the effect of inertia on the stability of buoyancy-driven parallel shear flow in a vertical layer of porous medium. The Lapwood–Brinkman model with fluid viscosity different from effective viscosity is used to describe the flow in a porous medium. The resulting eigenvalue problem is solved numerically using the Chebyshev collocation method. The critical Darcy–Rayleigh number $$R_\mathrm{Dc} $$ , the critical wave number $$a_\mathrm{c}$$ and the critical wave speed $$c_\mathrm{c}$$ are computed over a wide range of values of the Darcy–Prandtl number $$Pr_\mathrm{D}$$ and the Darcy number $${\tilde{D}}a$$ . Depending on the choice of physical parameters, instability occurs due to the presence of inertia. The value of $$Pr_\mathrm{D}$$ at which the transition from stationary to traveling-wave mode instability takes place increases with decreasing $${\tilde{D}}a$$ . Besides, the effect of decreasing $${\tilde{D}}a$$ shows destabilizing effect if the instability is via stationary mode, and on the contrary, it exhibits a dual behavior if the instability is through traveling-wave mode. The streamlines and isotherms presented herein demonstrate the development of complex dynamics at the critical state. In the energy spectrum, transition of instability from one type to another is found to take place as a function of $$Pr_\mathrm{D}$$ . The disturbance kinetic energy due to surface drag and viscous force plays no significant role in the stability of flow throughout the domain of $$Pr_\mathrm{D}$$ considered.
Starting Page	1
Ending Page	19
Page Count	19
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	228
Issue Number	1
e-ISSN	16196937
Language	English
Publisher	Springer Vienna
Publisher Date	2016-07-21
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical and Applied Mechanics Classical and Continuum Physics Continuum Mechanics and Mechanics of Materials Structural Mechanics Vibration, Dynamical Systems, Control Engineering Thermodynamics, Heat and Mass Transfer
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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