Stability of Poiseuille flow in the presence of a longitudinal magnetic field

Proskurin, Alexander V.; Sagalakov, A. M.

doi:10.1007/s10808-008-0053-z

Cited by 11 publications

(6 citation statements)

References 10 publications

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“…The critical value

c_{c}

and the corresponding critical values of

R e_{c}

and

α_{c}

are found for various values of

R m

and

A

following the usual procedure 10 . There are many numerical methods available to solve the generalized eigenvalue problem 9–12 and traveling wave solution 23–26 …”

Section: Numerical Solutionmentioning

confidence: 99%

“…Makinde and Mhone 11 have investigated the role of the small magnetic Reynolds number in the stability of MHD Jeffery–Hamel flow. Later, Proskurin and Sagalakov 12 discussed the role of parallel magnetic field strength in the stability of plane Poiseuille flow using the different sweep method. They also studied in detail the dependence of magnetic Prandtl number on the flow control parameter and temporal stability analysis against small disturbances on the base flow in a horizontal porous medium.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

MHD instability of the pressure‐driven plane laminar flow in the presence of the uniform coplanar magnetic field: Linear stability analysis

Basavaraj¹,

Aruna²,

Kumar³

et al. 2021

Heat Trans

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The influence of the uniform longitudinal magnetic field on the stability against small disturbances of an electrically conducting Newtonian fluid flow between two parallel horizontal plates is investigated. The sixth‐order system of disturbance equations is solved by the Chebyshev collocation method, and the critical Reynolds number R e c , the critical wave number α c , and the critical wave speed c c are computed for a wide range of the magnetic Reynolds number R m and Alfven number A. Curves of wave number against Reynolds number for neutral stability are presented for different values of the parameters. The onset of instability is also discussed in detail using the growth rate curves for various parameters of the problem. It is observed that the effect of both conductivity of the fluid and the strength of the magnetic field is to decay the onset of instability. A comprehensive study is carried out at the critical state of the fluid using the graph of R e c , α c , and c c with respect to R m for various values of A. The critical values at the onset of instability are also presented for both the Galerkin method and the Chebyshev collocation method.

show abstract

“…The critical value

c_{c}

and the corresponding critical values of

R e_{c}

and

α_{c}

are found for various values of

R m

and

A

following the usual procedure 10 . There are many numerical methods available to solve the generalized eigenvalue problem 9–12 and traveling wave solution 23–26 …”

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

MHD instability of the pressure‐driven plane laminar flow in the presence of the uniform coplanar magnetic field: Linear stability analysis

Basavaraj¹,

Aruna²,

Kumar³

et al. 2021

Heat Trans

View full text Add to dashboard Cite

show abstract

“…However, unstable 3D perturbations exist in these sta bility windows. Therefore, it can be stated that the sta bility windows relative to 2D perturbations, which are formed upon an increase in the Reynolds number, are "covered" by the instability domains of 3D perturba tions, and no stabilization of flows takes place upon an increase in the Reynolds number (see also [8,9]). …”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Experimental verification of the results and con cepts of the linear theory of hydrodynamic stability is also a complicated problem (especially for large mag netic Prandtl numbers). The stability of the Poiseuille MHD flow of a conducting fluid in a longitudinal magnetic field was studied in [8,9].…”

Section: Introductionmentioning

confidence: 99%

Stability of the poiseuille flow in a longitudinal magnetic field

Proskurin

Sagalakov

2012

Tech. Phys.

Self Cite

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The stability to small perturbations of a 2D flow of a conducting viscous fluid with large Reynolds numbers in a longitudinal magnetic field is investigated. A complete linearized system of magnetohydrody namics equations is considered using the method of collocations and the differential sweep method. The dependences of the critical Reynolds numbers on the electrical conductivity are analyzed in detail. A new instability branch for large Reynolds numbers and a jumpwise variation of the critical Reynolds numbers are discovered.

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“…Using the multi-deck asymptotic approach, the effect of transverse magnetic field on the stability of Poiseuille flow at high Reynolds number was investigated by Makinde [6]. Proskurin and Sagalakov [7] analyzed the effect of longitudinal magnetic field on the stability of Poiseuille flow. Later, Makinde and Mhone [8] extended the work of Takashima [4] to an isotropic porous domain case and subsequently to an anisotropic porous domain by Shankar and Shivakumara [9].…”

Section: Introductionmentioning

confidence: 99%

MHD instability of pressure-driven flow of a non-Newtonian fluid

et al. 2019

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The effect of a uniform vertical magnetic field on the stability of pressure-driven flow of an electrically conducting non-Newtonian fluid in an isothermal channel is numerically investigated using the Chebyshev collocation method. The non-Newtonian fluid is modeled by the couple stress fluid theory, which permits for polar effects and encountered regularly in liquids with very large molecules. It is established that Squire's theorem is valid and the modified Orr-Sommerfeld equation is derived by considering the fact that the magnetic Prandtl number P m , for recognized electrically conducting liquids is too small. The triplets (R c , α c , c c), where R c is the critical Reynolds number, α c is the critical wave number and c c is the critical wave speed, are obtained for different values of couple stress parameter Λ and the Hartman number M. It is found that increasing M has a stabilizing effect on the system while an increase in the couple stress parameter shows twofold deeds. Individual aspects of the kinetic energy spectrum are observed and presented for different parametric values to obtain comprehensive information at the critical state of fluid flow.

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Stability of Poiseuille flow in the presence of a longitudinal magnetic field

Cited by 11 publications

References 10 publications

MHD instability of the pressure‐driven plane laminar flow in the presence of the uniform coplanar magnetic field: Linear stability analysis

MHD instability of the pressure‐driven plane laminar flow in the presence of the uniform coplanar magnetic field: Linear stability analysis

Stability of the poiseuille flow in a longitudinal magnetic field

MHD instability of pressure-driven flow of a non-Newtonian fluid

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