Linear instability of concentric annular flow: Effect of Prandtl number and gap between cylinders

Khan, Arshan; Bera, P.

doi:10.1016/j.ijheatmasstransfer.2020.119530

Cited by 11 publications

(4 citation statements)

References 31 publications

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“…Further, we have also checked the impact of the Prandtl number and curvature parameter on the stability characteristics for a purely viscous medium. The results obtained were consistent with those of Khan & Bera [6]. Moreover, we have also reproduced the critical Reynolds number of 5772.22 × 4 3 at α c = 2 × 1.0205 (considering the scalings used) for high curvature parameters C = 100, which is the classical result of Orszag [18] for plane poisuille flow.…”

Section: Numerical Validationsupporting

confidence: 90%

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Linear Instability of Mixed Convection in a Vertical Annulus Filled With Porous Medium under LTNE Condition

Sharma,

Bera,

Khan

2024

Topical Problems of Fluid Mechanics 2024

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The stability of non-isothermal annular parallel flow through a highly permeable porous medium (such as metallic foam) is studied under a local thermal non-equilibrium (LTNE) state. An external pressure gradient and the linear varying temperature of the inner cylinder of the annulus govern the flow. The classical normal mode analysis has been considered to investigate the influence of the different controlling parameters such as Reynolds number (Re), interphase heat transfer coefficient (H), ratio of thermal conductivities (γ) and media permeability (Da) on the instability of the flow. It is found that irrespective of the other parameters, the critical instability boundary decreases sharply with Re in the range of 100 − 2000. An increment in the value of H contributes towards the stability of the basic flow. On the other hand, a destabilizing impact of γ has been observed in the present study.

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Section: Numerical Validationsupporting

confidence: 90%

“…The two mediums must be modelled via separate energy equations [5]. From the duct flow dynamics point of view, the mechanism of annular flow provides a general overview of the physics of wall-bounded convective flows [6]. Therefore, an understanding of the flow in such a configuration is essential.…”

Section: Introductionmentioning

confidence: 99%

Linear Instability of Mixed Convection in a Vertical Annulus Filled With Porous Medium under LTNE Condition

Sharma,

Bera,

Khan

2024

Topical Problems of Fluid Mechanics 2024

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“…The generalized eigenvalue problem is solved by the Chebyshev spectral collocation method [17]. The domain of the Chebyshev polynomials is [−1, 1] and in order to reconstruct in the required domain, the field variables in the fluid domain and porous domain are approximated [18] by ζ = 2z − 1 and ζ m = −2z m − 1 respectively. The eigenvalues are computed by using QZ algorithm [19] inbuilt in MATLAB software.…”

Section: Linearized Perturbed Equationsmentioning

confidence: 99%

Stability of Nonisothermal Poiseuille Flow in a Fluid Overlying a Highly Porous Domain

Anjali¹

2022

Topical Problems of Fluid Mechanics 2022

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The present article examines the stability of nonisothermal Poiseuille flow in a highly permeable porous domain underlying a fluid domain. A two domain approach with the Newtonian fluid’s flow being governed by Navier-Stokes equations in the fluid domain and Darcy- Brinkman model in the porous domain is adopted. The impact of depth ratio (ratio of fluid domain’s depth to porous domain’s depth), Darcy number, Reynolds number and Prandtl number are analyzed with the aid of linear stability analysis. The neutral stability curves characterize unimodal (either porous or fluid) or bimodal (both porous and fluid) behavior depending on the parametric variation. A decrease in depth ratio and increase in Darcy number, Reynolds number and Prandtl number instigates the instability in porous domain. A qualitative comparison with the existing results on Darcy’s law is also presented.

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“…In order to reconstruct the domain to , i.e. the domain of the Chebyshev polynomials, the field variables are mapped (Khan & Bera 2020 a ) by in the fluid domain whereas the same are mapped by in the porous domain. The linearized disturbance equations result in a generalized eigenvalue problem of the form where and are complex matrices and , are the eigenvalue and eigenvector, respectively.…”

Section: Problem Formulationmentioning

confidence: 99%

Stability of non-isothermal Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous domain

2022

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A two-domain approach is used to investigate the thermal convection of Poiseuille flow in an anisotropic and inhomogeneous porous domain underlying a fluid domain. The flow of the Newtonian fluid is regulated by Darcy's law in the porous domain with the implementation of the Beavers–Joseph condition at the interface. The impact of medium anisotropy and inhomogeneity is inspected by virtue of linear stability analysis along with other governing parameters such as depth ratio (ratio of depth of fluid domain to porous domain), Darcy number, Reynolds number and Prandtl number concerning the stability of the fluid–porous system. The neutral curves are found to be bimodal and unimodal in nature with the anisotropy and inhomogeneity leaving its imprint on parametric variation. An increase in anisotropy or decrease in the inhomogeneity parameter follows the modal change from unimodal (porous) to bimodal (both porous and fluid). Also, it has been identified that, irrespective of the considered variations in anisotropy and inhomogeneity, the least stable mode for the depth ratio ${<}0.05$ is porous and for the depth ratio ${>}0.16$ is fluid. Furthermore, energy budget analysis is carried out to classify the type of instability and validate the type of mode. The instability is found to be thermal–buoyant in nature with omission of low Reynolds numbers along with very low values of the ratio of permeability in the horizontal to vertical direction, where thermal–shear instability is witnessed. Likewise, secondary flow patterns in the context of the streamfunction and temperature contour are analysed to validate the least stable mode and the type of prevailing instability in the fluid–porous system. The presented numerical results find good experimental support from the results of Chen & Chen (J. Fluid Mech., vol. 207, 1989, pp. 311–321) in the limit of natural convection with an isotropic and homogeneous porous domain.

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Linear instability of concentric annular flow: Effect of Prandtl number and gap between cylinders

Cited by 11 publications

References 31 publications

Linear Instability of Mixed Convection in a Vertical Annulus Filled With Porous Medium under LTNE Condition

Linear Instability of Mixed Convection in a Vertical Annulus Filled With Porous Medium under LTNE Condition

Stability of Nonisothermal Poiseuille Flow in a Fluid Overlying a Highly Porous Domain

Stability of non-isothermal Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous domain

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