Abstract
Abstract The present work involves the study of penetrative convection in an incompressible fluid-saturated porous media with local thermal non-equilibrium. The onset of convection evaluated linearly and nonlinearly for the system influenced by heat extraction and heat generation. Darcy-Brinkman law is employed to model the momentum equation and four type of internal heat generating function are considered which leads to thermo-convective instability within the fluid layer. Linear analysis carried out by using normal mode technique and nonlinear stability analysis has been done by energy method. Due to heat generation within the fluid layer and heat extraction through boundary, the subcritical instability may exist with higher possibility. Effects of various parameters as: inter-phase heat transfer parameter, Darcy-Brinkman number, porosity-modified conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form.
Highlights
Penetrative convection is a phenomenon which occurs due to convective instability arises by unstable equilibrium
E ects of various parameters as: inter-phase heat transfer parameter, DarcyBrinkman number, porosity-modi ed conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form
Very recently e ect of a variety of internal heat generating source is observed by Nandal & Mahajan (2017) for a uid-saturated DarcyBrinkman porous media, to examine the e ect of heat generation on the stability of the system
Summary
Penetrative convection is a phenomenon which occurs due to convective instability arises by unstable equilibrium. Amit Mahajan and Reena Nandal, Penetrative convection in a fluid saturated Darcy-Brinkman porous media edge of this topic. For the study of uid ow behavior in porous media Darcy’s law is employed but it has limitations in several aspects. It is valid essentially for creeping ow through a long and uniform porous medium of low hydraulic conductivity. In many technological problems, the uid ow is very fast and Darcy’s law is not enough to describe the behavior of uid ow For such situation, Brinkman (1947) suggested that the classical fractional term must be added to model the momentum equation, and this model known as Brinkman’s model. Very recently e ect of a variety of internal heat generating source is observed by Nandal & Mahajan (2017) for a uid-saturated DarcyBrinkman porous media, to examine the e ect of heat generation on the stability of the system
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