The onset of Darcy‐Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects

2020

WJE

Self Cite

Purpose The purpose of this study is to examine the influence of rotation and varying gravitational strength on the onset of thermal convection in a porous medium layer numerically. The porous layer is acted to uniform rotation and inconsistent downward gravitational field which changing with depth from the layer. The authors presented three categories of gravitational strength deviancy, namely, linear, parabolic and exponential. Design/methodology/approach The higher-terms Galerkin weighted residual procedure is applied to get the eigenvalue of the problem. Findings The results illustrate that both rotation parameter and gravity variation parameter suspend the arrival of convection. The measurement of the convection cells decreases on enhancing the rotation parameter and gravity variation parameter. Originality/value It is also found that the scheme is more stable for category exponential, whereas it is more unstable for category parabolic.

“…4. Numerical procedure Equations ( 16)-( 18) are cracked numerically by using the Galerkin process (Yadav, 2020c;Yadav et al, 2020). Thus, the variables as:…”

Section: Perturbed Statementioning

confidence: 99%

Effects of rotation and varying gravity on the onset of convection in a porous medium layer: a numerical study

2020

WJE

Self Cite

“…Examining the disturbances into the normal modes and considering that the perturbed variables as 59,62–68

([],,,, w, {normalΩ}_{normalz}, T, ϕ) = ([],,,, normalW ((), z), G ((), z), normalΘ ((), z), normalΦ ((), z)) e^{({ik}_{normalx} x + {ik}_{normaly} y + n t)},

…”

Section: Normal Mode Investigationmentioning

confidence: 99%

Thermal convection in a layer of micropolar nanofluid

Chand¹,

Asia-Pacific J Chem Eng

Bhattacharyya

et al. 2021

Self Cite

The theoretical investigation of thermal convection in a horizontal layer of micropolar nanofluid is examined within the rule of linear stability hypothesis. The model applied for nanofluid integrates the impact of Brownian and thermophoresis diffusions. The flux of the volumetric fraction of nanoparticles is considered to be nil on the boundaries. The critical eigenvalues are achieved using the Galerkin approach, and the results are discussed and illustrated graphically. The results show that the Lewis number, the modified diffusivity ratio, the nanoparticle Rayleigh number, and the coefficient of coupling amid spin and heat flux accelerate the onset of convective motion, whereas the micropolar parameter and the coefficient of coupling amid vorticity and spin delay the onset of convective motion in the system.

“…We now use the Galerkin weighted residuals technique to solve the system of equations (24) and (25). 54–57 Consequently, the unknown variables w∧ and θ∧ are approximated as …”

Section: The Linear Stability Theorymentioning

confidence: 99%

The effect of viscosity and Darcy number on the start of convective motion in a rotating porous medium layer saturated by a couple-stress fluid

Proceedings of the Institution of Mechanical Engineers, Part C:

2020

Self Cite

In chemical process industry, food process industry, centrifugal filtration processes, and rotating machinery, convective flows are characterized by rotation, where couple-stress fluid (a type of non-Newtonian fluid) with variable viscosity in a porous medium can act as a working fluid. In the present work, the combined effect of the temperature-dependent viscosity, the Darcy number and the uniform rotation on the arrival of convective motion in a couple-stress fluid saturated porous layer is examined applying linear stability concept. The outcome of the viscosity variation parameter Q, the rotation parameter [Formula: see text], the couple-stress parameter [Formula: see text], and the Darcy number [Formula: see text] on both stationary and oscillatory convections is investigated analytically and presented graphically in terms of the critical thermal Darcy–Rayleigh number [Formula: see text]. Below the critical value [Formula: see text], no convective motion arises in the considered system. It is recognized that the arrival of convective motion is oscillatory only if the rotation parameter [Formula: see text] surpasses a threshold value which in turn depends on other physical parameters. The impact of the viscosity variation parameter Q has a destabilizing influence, while the couple-stress parameter [Formula: see text], rotation parameter [Formula: see text], the Darcy number [Formula: see text], the Prandtl number ⪻, and the heat capacity ratio γ show stabilizing influences on the stability of arrangement.