Transitions and bifurcations in couple stress fluid saturated porous media using a thermal non-equilibrium model

Pan, Zhigang; Jia, Lan; Mao, Yiqiu; Wang, Quan

doi:10.1016/j.amc.2021.126727

Cited by 10 publications

(6 citation statements)

References 21 publications

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“…In this case, the system can be reduced as We need to find g 1 . Similarly, we can write the following equation where B is obtained as in (15).…”

Section: Periodic Boundary Condition With Zero Mean Casementioning

confidence: 99%

See 1 more Smart Citation

Dynamic transitions and bifurcations of 1D reaction-diffusion equations: The non-self-adjoint case

Şengül

Tiryakioglu

2023

Journal of Mathematical Analysis and Applications

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“…In this case, the system can be reduced as We need to find g 1 . Similarly, we can write the following equation where B is obtained as in (15).…”

Section: Periodic Boundary Condition With Zero Mean Casementioning

confidence: 99%

“…In recent years there have been a growing interest on the first dynamic transitions of nonlinear phenomena [6,9,18,13,15]. Thus it is a growing need to classify the first transitions of partial differential equations depending on the nonlinear terms appearing as well as on the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Dynamic transitions and bifurcations of 1D reaction-diffusion equations: The non-self-adjoint case

Şengül

Tiryakioglu

2023

Journal of Mathematical Analysis and Applications

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“…Convective instability of a doubly diffusive incompressible couple stress fluid layer was investigated by Kumar et al [33]. On account of phase transition, Pan et al [34] considered stability and transition of a couple stress fluid in saturated porous media.…”

Section: Introductionmentioning

confidence: 99%

On dynamics of double‐diffusive magneto‐convection in a non‐Newtonian fluid layer

Fan

Pan

et al. 2023

Math Methods in App Sciences

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This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case.

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“…Convective instability of a doubly diffusive incompressible couple stress fluid layer was investigated by Kumar et al [32]. On account of phase transition, Pan et al [33] considered stability and transition of a couple stress fluid in saturated porous media.…”

Section: Introductionmentioning

confidence: 99%

On Dynamics of Double-Diffusive Magnetoconvection in a Non-Newtonian Fluid Layer

Pan

Fan

et al. 2022

Preprint

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This article concerns the dynamic transitions of a non-Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is done by deriving the principle of exchange of stability condition, which shows the system loses stability when thermal Rayleigh number exceeds a critical threshold. Second, we considered the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transitions, as well as the stable convection patterns. Our results show that when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, both continuous and jump transitions can occur for certain parameters; and if the diffusivities from big to small is the inverse of the previous case, only continuous transition induced by real eigenvalues are observed, which indicate a stationary convection.

show abstract

Transitions and bifurcations in couple stress fluid saturated porous media using a thermal non-equilibrium model

Cited by 10 publications

References 21 publications

Dynamic transitions and bifurcations of 1D reaction-diffusion equations: The non-self-adjoint case

Dynamic transitions and bifurcations of 1D reaction-diffusion equations: The non-self-adjoint case

On dynamics of double‐diffusive magneto‐convection in a non‐Newtonian fluid layer

On Dynamics of Double-Diffusive Magnetoconvection in a Non-Newtonian Fluid Layer

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