Stationary Convection in the Electrohydrodynamic Thermal Instability of Jeffrey Nanofluid Layer Saturating a Porous Medium: Free-Free, Rigid-Free, and Rigid-Rigid Boundary Conditions

Proceedings of the Institution of Mechanical Engineers, Part E:

Mohamad

Awasthi

2021

In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

“…In equation ( 2), we used the linear Jeffrey's model to model the non-Newtonian behavior of the Jeffrey fluid. 46,49 This model is valid for slowly varying Jeffrey fluid flow.…”

Section: Mathematical Modelmentioning

confidence: 97%

Section: Mathematical Modelmentioning

confidence: 99%

See 1 more Smart Citation

The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field

Proceedings of the Institution of Mechanical Engineers, Part E:

Mohamad

Awasthi

2021

“…The Darcy law is adjusted to comprise the Jeffery parameter and Coriolis force terms, whereas the Boussinesq assessment is used for density deviations. The relevant governing equations are as follows 9,32–36 :

\nabla \cdot boldv = 0,

\frac{μ {\overset{bold˜}{boldK}}_{m}^{- 1}}{false(1 + γ false)} boldv = - \nabla P + ρ_{0} false[1 - β_{θ} false(θ - θ_{0} false) false] boldg + \frac{2 ρ_{0} normalΩ}{ε} false(boldv \times {\overset{boldˆ}{bolde}}_{y} false),

σ \frac{\partial θ}{\partial t} + (boldv \cdot \nabla) θ = \nabla \cdot ({\overset{bold~}{boldα}}_{m} . \nabla θ),

θ = θ_{0} + normalΔ θ at y = 0, θ = θ_{0} at y = H and v = 0 at y = 0, H,

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Santhosh et al 31 determined the movement of a Jeffrey fluid in thin porous tubes and found that for given values of Jeffrey parameter, the effective viscosity improves by escalating tube radius. Very recently, Gautam et al 32 checked the strength of electric force on the stationary mode of convection in a porous layer saturated by a nanofluid using the Jeffrey fluid model. They established that the Jeffrey parameter increases in the formation of stationary instability.…”

Section: Introductionmentioning

confidence: 99%

Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer

2021

Heat Trans

Stability analysis of thermal convection for a Jeffrey fluid with rotation in an anisotropic porous medium is examined utilizing a modified Jeffrey–Darcy model. The linear stability theory is applied to examine how the Jeffrey parameter, rotation parameter, and anisotropic parameters affect the convective motion. It is observed that the rotation and the anisotropic in the thermal diffusivity act to delay the start of Jeffery fluid convection, while the Jeffery parameter and the anisotropic in the permeability show a dual effect in the presence of rotation. The extent of the convection cell diminishes with rotation and Jeffery parameters, while it augments with the thermal anisotropy parameter. Also, some previous outcomes are regained as special cases of the current analysis.

Convective flow of ethylene glycol‐silver Jeffery nanofluid in a Hele‐Shaw cell with an influence of external magnetic field

Asia-Pacific J Chem Eng

Al‐Balushi

Awasthi

et al. 2023

This effort investigates the arrival of magnetothermal convection of ethylene glycol‐silver Jeffrey nanofluid in a Hele‐Shaw cell utilizing the linear stability concept. The model practiced for the Jeffrey nanofluid includes the impacts of Brownian movement and thermophoresis. The norms for both marginal and overstable modes of convections are developed analytically. The impact of magnetic Chandrasekhar number QM, magnetic Prandtl number Prm, Jeffrey parameter δ, Hele‐Shaw number HS, and a variety of nanofluid parameters such as the volumetric fraction of nanoparticles ϕ, nanoparticle Rayleigh number Rp, adjusted diffusive ratio NA, and Lewis number italicLe on the beginning of convective motion are investigated, and results are illustrated graphically. It is observed that the overstable approach of convection is probable below the certain threshold estimate of the magnetic Prandtl number Prm. This threshold estimate of the magnetic Prandtl number Prm upturns with a rise in the rate of QM, HS, and δ, while it drops with a surge in the nanofluid parameters. The system was found to be more stable by decreasing the Hele‐Shaw number HS, the Jeffery parameter δ, and nanofluid parameters, while it was unstable by decreasing the magnetic Chandrasekhar number QM and the magnetic Prandtl number Prm.