Nonlinear stability analysis of a fluid saturated anisotropic Darcy–Brinkman medium with internal heat source

2019 ◽  
Vol 358 ◽  
pp. 216-231 ◽  
Author(s):  
Reena Nandal ◽  
Amit Mahajan
Keyword(s):  
Stability Analysis ◽  
Heat Source ◽  
Nonlinear Stability ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Nonlinear Stability Analysis ◽  
Brinkman Medium

POROUS PENETRATIVE CONVECTION WITH A SALT FIELD AND INTERNAL HEAT SOURCE

1992 ◽  
Vol 02 (04) ◽  
pp. 407-421
Author(s):  
LORNA RICHARDSON
Keyword(s):  
Porous Medium ◽  
Temperature Gradient ◽  
Heat Source ◽  
Nonlinear Stability ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Penetrative Convection ◽  
Weighted Energy ◽  
The Stability ◽  
Unconditional Nonlinear Stability

We investigate the stability of convection in a porous medium containing a heat source in which a destabilizing salt field and stabilizing temperature gradient are present. Both conditional and unconditional nonlinear stability thresholds are calculated and we note that RaE(conditional)>RaE(unconditional). The unconditional nonlinear analysis requires the use of a “weighted” energy.

scholarly journals Nonlinear stability analysis of Darcy’s flow with viscous heating

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160036 ◽  
Author(s):  
Michele Celli ◽  
Leonardo S. de B. Alves ◽  
Antonio Barletta
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Nonlinear Stability ◽  
Linear Stability Analysis ◽  
Integral Transform ◽  
Internal Heat ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Rate Analysis

The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.

scholarly journals An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients

2011 ◽  
Vol 468 (2138) ◽  
pp. 323-336 ◽  
Author(s):  
Antony A. Hill ◽  
M. S. Malashetty
Keyword(s):  
Heat Source ◽  
Nonlinear Stability ◽  
Operative Technique ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Linear Instability ◽  
Operative Method ◽  
Stability Analyses ◽  
Double Diffusive ◽  
Sharp Thresholds

This paper explores an operative technique for deriving nonlinear stability by studying double-diffusive porous convection with a concentration-based internal heat source. Previous stability analyses on this problem have yielded regions of potential subcritical instabilities where the linear instability and nonlinear stability thresholds do not coincide. It is shown in this paper that the operative technique yields sharp conditional nonlinear stability in regions where the instability is found to be monotonic. This is the first instance, in the present literature, where this technique has been shown to generate sharp thresholds for a system with spatially dependent coefficients, which strongly advocates its wider use.

Effect of Internal Heat Source on the Onset of Convection in a Nanofluid Layer

2011 ◽  
Vol 110-116 ◽  
pp. 1827-1832
Author(s):  
Dhananjay ◽  
G.S. Agrawal ◽  
R. Bhargava
Keyword(s):  
Brownian Motion ◽  
Stability Analysis ◽  
Rayleigh Number ◽  
Heat Source ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Onset Of Convection ◽  
Diffusivity Ratio ◽  
Upper Boundary

Effect of internal heat source on the onset of convection in nanofluid layer heated from below is studied. The lower boundary and upper boundary are assumed to be rigid and free respectively. The two important effects namely the Brownian motion and thermophoresis have been included in the model of nanofluid. Linear stability analysis has been made to investigate the effect of internal heat source on the onset of convection. Galerkin method is used to obtain the analytical expression for Rayleigh number in the non-oscillatory mode and result are depicted graphically. It has been shown that the internal heat source, nanoparticle Rayleigh number and modified diffusivity ratio have a destabilizing effect depending upon the values of various nanofluid parameters.

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