Stability of natural convection in a vertical non-Newtonian fluid layer with an imposed magnetic field

Shankar, B. M.; Kumar, Jai; Shivakumara, I. S.; Raghunatha, K. R.

doi:10.1007/s11012-017-0770-6

Cited by 7 publications

(9 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fluid layer is permeated by a uniform vertical magnetic induction ⃗ B 0 = (0, 0, B 0 ) . Following Stokes [22], Takashima [4] and Shankar et al [27], the governing linear stability equations in the dimensionless form are…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The velocity stream function ϕ(x, z, t)and the magnetic stream function ψ(x, z, t)are introduced through (neglect the tilde in the subsequent analysis) and eliminate P from the Eqs. (26) and (27) to obtain It is well known that P m for the liquid sodium is of the order 10 −5 and for mercury it is of the order 10 −7 and hence terms in Eqs. (33) and (34) concerning B b , and u b − c in Eq.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Shankar et al [27] to discretize the stability equation, which yields with the corresponding boundary conditions where (Canuto et al [40]…”

Section: Numerical Solutionmentioning

confidence: 99%

“…In a slit channel with metrically astringent walls, the hydromagnetic flow of a couple stress fluid was investigated by Mekheimer [25]. The stability of free (natural) convection in a vertical couple stress fluid layer was investigated by Shankar et al [18] while later this study was extended by Shankar et al [26] and Shankar et al [27] to include a uniform AC electric field and magnetic field, respectively. In addition, many researchers investigated the effect of couple stresses on fluid flows in different contexts (Rudraiah et al [28], Shivakumar et al [29], Turkyilmazoglu [30], Shivakumara and Naveen Kumar [31], Srinivasacharya and Rao [32], Ramesh [33], Tripathi et al [34], Mahabaleshwar et al [35], Layek and Pati [36], Nandal and Mahajan [37], Reddy et al [38], Naveen Kumar et al [39]).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

“…Shankar et al [27] to discretize the stability equation, which yields with the corresponding boundary conditions where (Canuto et al [40]…”

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…To avoid such side effects, there is a need to understand the growth rate of RTI and suppresses the same. Shankar et al, [21] have contributed the applications of non-Newtonian fluid and the same researchers [22] were studied the MHD instability of pressure-driven flow of a non-Newtonian fluid. The linear and weakly nonlinear stability of a doubly diffusive electrically conducting non-Newtonian couple stress fluid layer in the presence of a uniform vertical magnetic field is investigated by Naveenkumar et al, [23].…”

Section: Introductionmentioning

confidence: 99%

The Influence of Boundary Roughness on Rayleigh-Taylor Instability at the Interface of Superposed Couple-Stress Fluids

Chavaraddi¹,

Gouder²,

Kudenatti³

2020

ARFMTS

View full text Add to dashboard Cite

The influence of boundary roughness on suppressing of Rayleigh-Taylor instability (RTI) at the interface between two superposed couples-stress fluids is investigated in the present paper. This is a theoretical study is based on fully developed approximations for deriving the growth rate of RTI at the interface between two fluids. Thus, it is found that the couple-stress parameter and boundary roughness have stabilization effect, whereas the buoyancy force (surface tension) has destabilize the system. Hence the study favors to control the growth rate of RTI.

show abstract

Natural convection laminar flow between two vertical walls with a nonlinear variation of density and viscosity with temperature

Nagaraja

Gireesha

2023

Heat Trans

View full text Add to dashboard Cite

Under the combined influence of buoyancy force and constant pressure gradient, the free convection flow and heat transmission inside a channel placed vertically and consisting of two parallel walls are examined. Through the application of the Runge–Kutta fourth‐order approach and the shooting procedure, the modeled equations of the problem including nonlinear density–temperature and quadratic viscosity–temperature change at constant but different wall temperatures are numerically solved. For distinct values of the embedded parameters, the fluctuations in fluid's velocity and temperature are examined. For various situations of linear, quadratic, and nonlinear dependence of density on temperature, numerical values for heat transmission rate, volume flow rate and skin friction are determined and tabulated. The fluctuations of the Nusselt number with the Grashof number corresponding to thermal expansion coefficients are depicted through graphical interpretations. It was found that the combined effect of thermal expansion coefficients raises the values of the physical entities, Nusselt number, volume flow rate, and heat transmission rate. For the lower Reynolds number values, the Nusselt number value stays around one, indicating the same impact of conduction and convection on heat transmission.

show abstract

Stability of natural convection in a vertical non-Newtonian fluid layer with an imposed magnetic field

Cited by 7 publications

References 25 publications

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

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

The Influence of Boundary Roughness on Rayleigh-Taylor Instability at the Interface of Superposed Couple-Stress Fluids

Natural convection laminar flow between two vertical walls with a nonlinear variation of density and viscosity with temperature

Contact Info

Product

Resources

About