The linear stability of a developing thermal front in a porous medium: The effect of local thermal non-equilibrium (original) (raw)
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Iraqi Journal of Science, 2022
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Journal of Non-Equilibrium Thermodynamics, 2022
The internal heat source and reaction effects on the onset of thermosolutal convection in a local thermal non-equilibrium porous medium are examined, where the temperature of the fluid and the solid skeleton may differ. The linear instability and nonlinear stability theories of Darcy-Brinkman type with fixed boundary condition are carried out where the layer is heated and salted from below. The D 2 Chebyshev tau technique is used to calculate the associated system of equations subject to the boundary conditions for both theories. Three different types of internal heat source function are considered, the first type increases across the layer, while the second decreases, and the third type heats and cools in a nonuniform way. The effect of different parameters on the Rayleigh number is depicted graphically. Moreover, the results detect that utilizing the internal heat source, reaction, and non-equilibrium have pronounced effects in determining the convection stability and instability thresholds.
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In this study, the linear stability of an unsteady thermal boundary layer in a semi-infinite porous medium is considered. This boundary layer is induced by varying the temperature of the horizontal boundary sinusoidally in time about the ambient temperature of the porous medium; this mimics diurnal heating and cooling from above in subsurface groundwater. Thus if instability occurs, this will happen in those regions where cold fluid lies above hot fluid, and this is not necessarily a region that includes the bounding surface. A linear stability analysis is performed using small-amplitude disturbances of the form of monochromatic cells with wavenumber, k. This yields a parabolic system describing the time-evolution of small-amplitude disturbances which are solved using the Keller box method. The critical Darcy-Rayleigh number as a function of the wavenumber is found by iterating on the Darcy-Rayleigh number so that no mean growth occurs over one forcing period. It is found that the most dangerous disturbance has a period which is twice that of the underlying basic state. Cells that rotate clockwise at first tend to rise upwards from the surface and weaken, but they induce an anticlockwise cell near the surface at the end of one forcing period, which is otherwise identical to the clockwise cell found at the start of that forcing period.
Transport in Porous Media, 2006
This paper considers the onset of free convection in a horizontal fluid-saturated porous layer with uniform heat generation. Attention is focused on cases where the fluid and solid phases are not in local thermal equilibrium, and where two energy equations describe the evolution of the temperature of each phase. Standard linearized stability theory is used to determine how the criterion for the onset of convection varies with the inter-phase heat transfer coefficient, H, and the porosity-modified thermal conductivity ratio, γ. We also present asymptotic solutions for small values of H. Excellent agreement is obtained between the asymptotic and the numerical results.
Global stability for thermal convection in a fluid overlying a highly porous material
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
This paper investigates the instability thresholds and global nonlinear stability bounds for thermal convection in a fluid overlying a highly porous material. A two-layer approach is adopted, where the Darcy–Brinkman equation is employed to describe the fluid flow in the porous medium. An excellent agreement is found between the linear instability and unconditional nonlinear stability thresholds, demonstrating that the linear theory accurately emulates the physics of the onset of convection.
American Journal of Scientific and Industrial Research, 2011
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Continuum Mechanics and Thermodynamics, 2006
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Transport in Porous Media, 2017
The onset of convection in a porous layer heated from below is considered, and we determine how the presence of two solid but heat-conducting bounding plates of finite thickness alters the manner in which convection ensues. Heat is generated by the lower plate (with an insulating lower boundary), but the upper one is passive with a fixed upper boundary temperature. It is shown that this composite layer may mimic in turn one of the three different types of classical single-layer onset problems which are well-known in the literature. The type which is selected (or indeed whether it corresponds to a transitional case) depends quite critically on the precise values of the relative thickness of the solid layers and their conductivity ratio. It is also shown that care needs to be taken over declaring that the solid plates are thin: extreme values of the conductivity ratio can yield a stability criterion which appears to be different from that suggested by the imposed boundary conditions.
On the evolution of thermal disturbances during natural convection in a porous medium
Journal of Fluid Mechanics, 1980
In natural convection in a porous medium heated from below, the convective flow in two dimensions becomes unsteady above a certain critical Rayleigh number and exhibits a fluctuating or oscillatory behaviour (depending on the confinement in the horizontal dimension). This fluctuating behaviour is due to a combination of the instability of the thermal boundary layers a t horizontal boundaries together with a 'triggering' effect of earlier disturbances. The point of the origin of the instability of the thermal boundary layer appears to play a dominant role in determining the regularity of the fluctuating flow. This numerical study investigates the importance of this point of evolution and concludes that there may exist more than one oscillatory mode of convection, depending on its position. The investigation focuses on the symmetry of the flow and demonstrates that with stable and accurate numerical schemes, an artificial symmetry may be imposed in trhe absence of realistic physical noise. If an initially symmetric perturbation is imposed the flow retains an essentially symmetric flow pattern with a high degree of regularity in the oscillatory behaviour. The imposition of an asymmetric perturbation results in a degradation of regularity. The appearance of the symmetric, regularly oscillatory flow is characterized by a symmetric (and stationary) arrangement of the points of origin of the instability of the upper and lower thermal boundary layers; in the case of the irregular oscillations the points of origin are not symmetric and their locations are not fixed.