Onset of Darcy-Brinkman convection with a uniform internal heat source and vertical throughflow

Abstract

The problem of thermal convection in a horizontal uid-saturated porous layer is examined, where the ow is governed by the Brinkman extension of Darcy's law. A uniform internal heat source and vertical through ow are also considered. The linear and nonlinear stability analyses are performed in order to determine the stability characteristics of the system. The linear and nonlinear thresholds give good agreement in the absence of vertical through ow. However, it is shown that there are potential regions of sub-critical instabilities for increasing values of internal heat source parameter Q, Péclet number P e and Darcy number Da.

The onset of Darcy‐Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects

“…k k (17) such that w ˆk and θ ˆk satisfy the Equation (15). Application of Equation ( 16) into Equations ( 13) and ( 14) and applying the orthogonal property, we got…”

“…An asymptotic study of the beginning of Darcy‐Brinkman convection in a porous layer was made by Rees 14 . Deepika et al 15 studied the vertical throughflow and internal heating effects on the start of Brinkman convection in a porous layer. Yadav et al 16 studied the impact of rotation on the start of Darcy‐Brinkman convection in a porous layer made solely by internal heating.…”

Effect of Coriolis force on Rayleigh-Bénard convection with internal heat generation

“…Riahi [5] studied the inertial and rotational effects on an oscillatory flow in a horizontal layer and the study showed that the Coriolis effect is able to enhance the physical domain for an oscillatory flow as opposed to the inertial force. Another study made by Deepika et al [6] shows that there are potential regions of sub-critical instabilities for increasing values of internal heat source parameter Q in the problem of thermal convection in a horizontal fluidsaturated porous layer where the flow is governed by the Brinkman extension of Darcy's law. The onset of convection with a parabolic basic temperature profile was first studied by Roberts [7] in the study of convection in a horizontal layer with internal heat generation.…”

“…Figures 5,6,7 are the plot of Ta , positive and negative internal Rayleigh number respectively in case of rigid-free isothermal boundary conditions. Figures8,9,10 are the plot of Ta , and negative internal Rayleigh number respectively in case of rigid-free adiabatic boundary conditions.…”

Continuous dependence for the Brinkman–Darcy–Kelvin–Voigt equations backward in time

“…The Brinkman–Darcy equations have been employed extensively to study flow of a Newtonian fluid in a porous medium when the porosity is not too small. In particular, studies of thermal convection have been prominent, see, for example, Rees, 28 Postelnicu and Rees, 29 Deepika et al, 30 Mahajan and Nandal, 31 and Nandal and Mahajan 32 . A review of the range of validity of the Brinkman ‐ Darcy equations in terms of the porosity is given in Gentile and Straughan 33 .…”