Study of Influence of Combustion on Darcy–Bénard Convection with Inherent Local Thermal Non-equilibrium Between Phases

Nandal, Reena; Siddheshwar, P. G.; Neela, Deepika

doi:10.1007/s11242-022-01886-1

Transp Porous Med

2022

DOI: 10.1007/s11242-022-01886-1

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Study of Influence of Combustion on Darcy–Bénard Convection with Inherent Local Thermal Non-equilibrium Between Phases

Reena Nandal

P. G. Siddheshwar

Deepika Neela

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2024

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Cited by 4 publications

References 43 publications

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Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

Franchi,

Nibbi,

Straughan

2023

Transp Porous Med

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We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise. Article Highlights A two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem. The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven. Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

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Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

Franchi,

Nibbi,

Straughan

2023

Transp Porous Med

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Thermohaline convection of a Casson fluid in a porous layer: Linear and non-linear stability analyses

Reddy,

Ragoju,

Shekhar

2023

Physics of Fluids

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The study investigates the thermosolutal convection of a Casson fluid in a horizontal layer that is heated and salted from below. Both linear and non-linear analyses are performed using the method of normal modes to solve the governing equations. Interestingly, the study demonstrates that the linear and non-linear stability thresholds coincide. To solve the differential eigenvalue problem for linear theory, a one-term Galerkin approach is employed. Meanwhile, for the eigenvalue problem of non-linear instability, a numerical solution is obtained using the bvp4c routine in MATLAB. The results reveal some important findings. First, the Casson parameter is shown to destabilize the flow, leading to instability. However, the Darcy number and solutal Rayleigh number are found to have a stabilizing effect on the system. Furthermore, the study develops a weakly non-linear theory using multiple scale analysis to investigate heat and mass transport, offering valuable insight into these transport phenomena within the context of the system under consideration.

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Linear and energy stability analyses of onset of Darcy-Bénard convection due to combustion

Siddheshwar,

Nandal

2024

HFF

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Purpose This paper aims to perform a linear and nonlinear analysis of the stability of a chemically reacting Newtonian fluid in a Darcy porous medium. The purpose of selecting both analyses is to investigate the probability of subcritical instability resulting from combustion. Design/methodology/approach The chemical reaction problem in a Darcy porous medium with Arrhenius kinetics is considered. The effect of the Frank-Kamenetskii number on the linear and nonlinear stability is analysed. The critical eigenvalue is obtained numerically by the Chebyshev pseudospectral method for both analyses. Findings The inference from the two analyses is that in the presence of combustion, the situation in the Darcy−Bénard convection problem can lead to subcritical instability. It is found that the value of the critical Frank-Kamenetskii number keeps on changing as the lower boundary temperature changes, beyond the critical value of the Frank-Kamenetskii number where the system splits, going from a steady condition to an explosive state. Originality/value The Chebyshev pseudospectral approach has been applied to address the combustion problem in this research. The normal mode methodology and energy method are used for linear and nonlinear analyses, and the effects of nonlinear factors are examined by comparing the outcomes.

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Study of Influence of Combustion on Darcy–Bénard Convection with Inherent Local Thermal Non-equilibrium Between Phases

Cited by 4 publications

References 43 publications

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

Thermohaline convection of a Casson fluid in a porous layer: Linear and non-linear stability analyses

Linear and energy stability analyses of onset of Darcy-Bénard convection due to combustion

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