Darcy Brinkman Number Research Articles

EFFECT OF VARIABLE GRAVITY ON THERMAL CONVECTION IN ROTATING JEFFREY NANOFLUID: DARCY-BRINKMAN MODEL

In this study, we explore the influence of varying gravity on the beginning of thermal instability in a rotating layer of Jeffrey nanofluid with Darcy-Brinkman porous media. The solution of the fluid layer retained between two free-free barriers is determined using linear stability analysis based on the normal mode approach. In this study, we used the Galerkin approach to find the eigenvalue. The influence of exponential and cubic variable gravity on the start of stationary and oscillatory convection is calculated analytically and graphically. The graphs are made with the help of MATLAB R2021b software. For both stationary and oscillatory convection, we've examined how variations in gravity affect the Jeffrey parameter, rotation (Taylor number), Darcy-Brinkman number, Lewis number, moderated diffusivity ratio, porosity of porous media, and nanoparticle Rayleigh number. It is discovered that stationary as well as oscillatory convections are more stabilized by negative exponential variable gravity parameter.

The onset of anisotropic Darcy–Brinkman penetrative convection with local thermal nonequilibrium due to heat generation and extraction

AbstractAn anisotropic, fluid‐saturated porous medium with local thermal nonequilibrium is the subject of this paper's analysis of the stability of the commencement of convection caused by internal heat generation. The classical Darcy's momentum equation is applied with the Brinkman model. To observe the thermal instabilities in the fluid layer, it is assumed that there is steady heat extraction through the bottom boundary and constant heat generation inside the fluid layer. The critical internal Darcy Rayleigh and associated wave numbers are computed using linear instability and energy approaches using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. The fluid layer becomes unstratified as a result of heat generation inside the fluid, which encourages the occurrence of any subcritical instability. The critical Darcy–Rayleigh number has been found to be significantly influenced by a number of parameters, including the anisotropy parameter, internal heat parameter, porosity‐modified conductivity ratio, inter‐phase heat transfer parameter, and Darcy–Brinkman number.

Impact of rotation on thermal instability of Darcy–Brinkman porous layer filled with a Jeffrey nanofluid

The novelty of this research lies in its investigation of the initiation of thermal instability within a Darcy–Brinkman porous layer containing a Jeffrey nanofluid under the influence of rotation. While non-Newtonian fluids complex flow patterns and heat transfer enhancements due to thermal gradients are known, this study addresses a specific and previously unexplored aspect, the impact of rotation on Darcy–Brinkman porous layer containing a Jeffrey nanofluid. When a fluid is subjected to rotation, it can induce additional forces and flow patterns within the fluid. The linear stability theory and normal mode analysis method are used to analyze the stability of the system analytically and are computed numerically using the software Mathematica version 11.3. The investigation focuses on understanding the influence of various factors, namely, the Taylor number, the Lewis number, the Jeffrey parameter, the modified diffusivity ratio, nanoparticles Rayleigh number, the Darcy–Brinkman number, and medium porosity on the onset of thermal instability in the physical system. This novel perspective can contribute to a deeper understanding of heat transfer processes in non-Newtonian fluids and has potential applications in improving the efficiency of industrial systems, such as cooling systems, heat exchangers, and microfluidic devices where efficient heat transfer is crucial for performance improvement.

Effect of variable gravity on thermal convection in Jeffrey nanofluid: Darcy-Brinkman model

The subject under consideration in this research has various geophysical and astrophysical applications. Specifically, we investigate the impact of variable gravity on the onset of thermal instability within a layer of Jeffrey nanofluid confined in a Darcy-Brinkman porous medium. The solution of the fluid layer, which is positioned between two free-free boundaries, is determined using a linear stability analysis employing the normal mode technique. The Rayleigh number on the onset of convection is derived by using the Galerkin method. For stationary convection, the effects of different variable gravity parameters on the Jeffrey parameter, Darcy-Brinkman number, Lewis number, moderated diffusivity ratio, porosity of porous media and nanoparticle Rayleigh number are analyzed and presented graphically. The choices of using Jeffrey nanofluid as the base fluid for the study add novelty. Non-Newtonian fluids encompass a diverse range of substances, such as engine oils, oil extraction, wallpaper paste, and various biological liquids like blood etc.

Penetrative convection in a fluid saturated Darcy-Brinkman porous media with LTNE via internal heat source

Abstract The present work involves the study of penetrative convection in an incompressible fluid-saturated porous media with local thermal non-equilibrium. The onset of convection evaluated linearly and nonlinearly for the system influenced by heat extraction and heat generation. Darcy-Brinkman law is employed to model the momentum equation and four type of internal heat generating function are considered which leads to thermo-convective instability within the fluid layer. Linear analysis carried out by using normal mode technique and nonlinear stability analysis has been done by energy method. Due to heat generation within the fluid layer and heat extraction through boundary, the subcritical instability may exist with higher possibility. Effects of various parameters as: inter-phase heat transfer parameter, Darcy-Brinkman number, porosity-modified conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form.

Stability analysis of a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model

A nonlinear stability threshold for convection in a couple stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple stress fluid parameter (F), temperature and pressure dependent viscosity (Γ), interface heat transfer coefficient (H), Darcy–Brinkman number (D˜a) and porosity modified conductivity ratio (γ) on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient (H) is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.

Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity

A nonlinear stability threshold for rotation in a couple-stress fluid heated from below saturating a porous medium with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The effects of couple-stress parameter, variable dependent viscosity, medium permeability, Taylor number and Darcy–Brinkman number on the onset of convection are also analysed.

Global Stability for Thermal Convection in a Couple Stress Fluid Saturating a Porous Medium with Temperature-pressure Dependent Viscosity: Galerkin Method

Couple-stress Fluid Porous Medium Global Stability Temperature-pressure Dependent Viscosity Different Conducting Boundaries (Free-free, Rigid-free, Rigi d-rigid) AB S T R ACT A g lobal nonlinear stability analysis is performed for a cou ple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is imp ortant because it shows that linearized instability theory has captured completely the physics of the onset of convection. The eigenvalue problems for different conducting boundary systems are solved by using Galerkin method. The effects of couple-stress parameter F , Darcy-Brinkman number Da and variable viscosity parameter Γ on the onset of convection are also analyzed. The use of Darcy-Brinkman model makes the system thermally more stable than the Darcy model for all the different conducting boundary systems, couple-stress parameter and medium permeability promotes stabilization, and the variable viscosity destabilizes the system.

Onset of Darcy–Brinkman Ferroconvection in a Rotating Porous Layer Using a Thermal Non-Equilibrium Model: A Nonlinear Stability Analysis

This article presents a nonlinear stability analysis of a rotating thermoconvective magnetized ferrofluid layer confined between stress-free boundaries using a thermal non-equilibrium model by the energy method. The effect of interface heat transfer coefficient \({( {{\mathcal H}^{\prime}})}\), magnetic parameter (M3), Darcy–Brinkman number \({( {\hat{{\rm D}}{\rm a}})}\), and porosity modified conductivity ratio (γ′) on the onset of convection in the presence of rotation \({({T_{{\rm A}_1}})}\) have been analyzed. The critical Rayleigh numbers predicted by energy method are smaller than those calculated by linear stability analysis and thus indicate the possibility of existence of subcritical instability region for ferrofluids. However, for non-ferrofluids stability and instability boundaries coincide. Asymptotic analysis for both small and large values of interface heat transfer coefficient \({({{\mathcal H}^{\prime}})}\) is also presented. A good agreement is found between the exact solutions and asymptotic solutions.

Onset of Darcy–Brinkman double-diffusive convection in a magnetized ferrofluid layer using a thermal non-equilibrium model: a nonlinear stability analysis

This paper presents a nonlinear stability analysis of a double-diffusive convection in a magnetized ferrofluid layer confined between stress-free boundaries using a thermal non-equilibrium model by the energy method. A Darcy–Brinkman model is used for the momentum equation and a two-field model is used for the energy equation, each representing the solid and fluid phases separately. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. The effects of the interface heat transfer coefficient , magnetic parameter (M3), Darcy–Brinkman number and porosity-modified conductivity ratio (γ') on the onset of ferroconvection in the presence of solute (S') have been analysed. For all the cases studied, it is found that solute gradient enhances the stability of the system. A comparison with linear instability theory shows that there is a difference between the critical Rayleigh numbers and thus indicates the possibility of the existence of a subcritical instability region for ferrofluids. However, for non-ferrofluids stability and instability boundaries coincide.