Darcy Brinkman Porous Medium Research Articles

Inertial and Darcy’s Terms Ratio in Boundary Layer at Fluid–Porous Medium Interface

The study considers the forced boundary-layer flow overlying the Darcy–Brinkman porous medium and gives a quantitative analysis of the nonlinear inertial terms in the Brinkman filtration equation. The inertial terms are shown to be larger than the Darcy’s drag near the porous medium interface. The applicability range of boundary-layer approach is determined. It is suitable in high-permeable media with moderate velocities of an external flow. If it is slow enough, the inertial terms can be omitted in spite of interface effect. On the other hand, fast external flow produces the filtration with large pore-scale Reynolds number; therefore, the Forchheimer’s drag should be taken into account. It is shown the Brinkman term as well as inertial terms have a significant role in boundary-layer formation within the porous medium.

Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling

The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.

Numerical analysis of the onset of longitudinal convective rolls in a porous medium saturated by an electrically conducting nanofluid in the presence of an external magnetic field

The effect of a uniform external magnetic field on the onset of convection in an electrically conducting nanofluid layer is examined numerically based on non-homogeneous two-phase model (i.e., classical Buongiorno’s mathematical model) which incorporates the effects of Brownian motion and thermophoresis of nanoparticles in the thermal transport mechanism of nanofluids. In this investigation, we consider that the nanofluid is Newtonian, heated from below and confined horizontally in a Darcy-Brinkman porous medium between two infinite rigid boundaries, with different nanoparticle configurations at the horizontal boundaries (i.e., top heavy and bottom heavy nanoparticle distributions). The linear stability theory has been wisely used to obtain a set of linear differential equations which are transformed to an eigenvalue problem, so that the thermal Rayleigh number Ra is the corresponding eigenvalue. The thermal Rayleigh number Ra and its corresponding wave number a are found numerically using the Chebyshev-Gauss-Lobatto collocation method for each set of fixed nanofluid parameters. The marginal instability threshold (Rac, ac) characterizing the onset of stationary convection is computed accurately for wide ranges of the modified magnetic Chandrasekhar number Q, the modified specific heat increment NB, the nanoparticle Rayleigh number RN, the modified Lewis number Le, the modified diffusivity ratio NA and the Darcy number Da. Based on these control parameters and the notions of streamlines, isotherms and iso-nanoconcentrations, the stability characteristics of the system and the development of complex dynamics at the critical state are discussed in detail for both nanoparticle distributions.

Multiple Solutions of an Unsteady Stagnation-Point Flow with Melting Heat Transfer in a Darcy–Brinkman Porous Medium

AbstractThe characteristics of the unsteady boundary layer flow with melting heat transfer near a stagnation-point towards a flat plate embedded in a DarcyBrinkman porous medium with thermal radiation are investigated. The governing partial differential equations are transformed into self-similar ordinary differential equations by similarity transformations. The transformed self-similar equations are solved numerically using bvp4c from Matlab for several values of the flow parameters. The study reveals that the multiple solutions exist for the decelerating (

ONSET OF THERMAL CONVECTION IN A ROTATING NANOFLUID LAYER SATURATING A DARCY-BRINKMAN POROUS MEDIUM: A MORE REALISTIC MODEL

In this paper, we investigate analytically the thermal convection in a rotating nanofluid layer saturating a Darcy-Brinkman porous medium by using a more realistic linear stability analysis model. In this model, we assume that the nanoparticle concentration flux is zero on the boundaries and we can put values of temperature at the boundaries. The assumed boundary conditions neutralize the possibility of oscillatory convection, and only stationary convection occurs in the absence of rotation. But in the presence of rotation, oscillatory convection occurs due to the Coriolis effect. This paper is the extension of our previous paper in which we put both temperature and nanoparticle volume fraction at the boundaries of the nanofluid layer.

Mixed Convection in a Darcy–Brinkman Porous Medium with a Constant Convective Thermal Boundary Condition

The characteristics of the boundary layer flow past a plane surface adjacent to a saturated Darcy–Brinkman porous medium are investigated in this paper. The flow is driven by an external free stream moving with constant velocity. The surface is heated with a convective boundary condition with constant heat transfer coefficient. The problem is non-similar and is investigated numerically by a finite difference method. The problem is governed by four non-dimensional parameters, that is, the convective Darcy number, the convective Grashof number, the Prandtl number, and the axial distance along the plate. The influence of these parameters on the results is investigated, and the results are presented in tables and figures. The Darcy term and the Grashof term in the momentum equation contradict each other and this contradiction makes the problem complicated. However, the wall shear stress and the wall temperature increase continuously along the plate and the wall temperature always tends to 1.

Wall-Driven Versus Pressure Gradient-Driven Flows in Porous Media

The heat transfer characteristics of two boundary layer flows past an isothermal plane surface adjacent to a saturated Darcy–Brinkman porous medium is compared to each other in this paper. The flows are driven either by a stretching of the adjacent plane boundary, or by an external pressure gradient. It is found that below a threshold value $$\tilde{P}r_{*} $$ of the modified Prandtl number $$\tilde{P}r$$ , the Nussselt number in case of the pressure gradient-driven flow is larger than in case of the wall- driven flow, while for $$\tilde{P}r>\tilde{P}r_{*} $$ the flow driven by the moving wall provides a more efficient heat transfer mechanism. The dependence of $$\tilde{P}r_{*} $$ on the Darcy number is also discussed in detail.

Combined Effect of Suspended Particles and Rotation on Double-Diffusive Convection in a Viscoelastic Fluid Saturated by a Darcy-Brinkman Porous Medium

In this paper, the combined effect of suspended (fine dust) particles and rotation on the onset of double-diffusive convection in a viscoelastic fluid in porous medium is studied. For the porous medium, the Brinkman model is employed and Walters' (model B′) model is used to characterize viscoelastic fluid. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, stable solute gradient, suspended particles, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the rotation, stable solute gradient have stabilizing effect and suspended particles have destabilizing effect on the system whereas Darcy number and medium permeability have stabilizing/destabilizing effects under certain conditions. The effects of rotation, stable solute gradient, suspended particles, Darcy number and medium permeability have also been investigated.

On the onset of thermal convection in rotating nanofluid layer saturating a Darcy–Brinkman porous medium

In this paper, the effect of rotation on the onset of thermal convection in a horizontal layer of nanofluid saturated by a Darcy–Brinkman porous medium is considered. A linear stability analysis based upon normal mode is used to find solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphically. The effects of the concentration Rayleigh number, Taylor number, Lewis number, Darcy number and modified diffusivity ratio on the stability of the system are investigated. The sufficient conditions for the non-existence of overstability are also derived.

Forced Convection Flow of Power-Law Fluids Over a Flat Plate Embedded in a Darcy-Brinkman Porous Medium

The steady forced convection flow of a power-law fluid over a horizontal plate embedded in a saturated Darcy-Brinkman porous medium is considered. The flow is driven by a constant pressure gradient. In addition to the convective inertia, also the “porous Forchheimer inertia” effects are taken into account. The pertinent boundary value problem is investigated analytically, as well as numerically by a finite difference method. It is found that far away from the leading edge, the velocity boundary layer always approaches an asymptotic state with identically vanishing transverse component. This holds for pseudoplastic (0 1) fluids as well. The asymptotic solution is given for several particular values of the power-law index n in an exact analytical form. The main flow characteristics of physical and engineering interest are discussed in the paper in some detail.

DARCY-BRINKMAN FLOW WITH SOLID INCLUSIONS

The slow viscous flow in a Darcy-Brinkman porous medium with solid inclusions is studied. The general separable solutions in spherical and cylindrical coordinates are applied to the flow over a sphere and a circular cylinder. The problem is governed by a parameter k representing the effect of the porous medium. As k approaches zero, the solutions approach the Stokes flow solution for the sphere, but singularly vanish for the cylinder, confirming the Stokes paradox. For large k, the influence of the sphere or cylinder is limited to its immediate surroundings. The pressure drop due to multiple inclusions is then predicted.

Flow Adjacent to a Stretching Permeable Sheet in a Darcy–Brinkman Porous Medium

In this article, we extend the work of Chakrabarti and Gupta (1979, Quart. Appl. Math., Vol. 37, pp. 73–78), and the work of Pop and Na (1998, Mechanics Research Communications, Vol. 25, pp. 263–269) to a Darcy–Brinkman porous medium.

Asymptotic Profiles for the Blasius and Sakiadis flows in a Darcy–Brinkman Isotropic Porous Medium Either with Uniform Suction or with Zero Transverse Velocity

The Blasius and Sakiadis flows with uniform suction or with zero transverse velocity, at the asymptotic state, in a Darcy–Brinkman porous medium are investigated in this note. Exact analytical solutions are derived for velocity as well as for the integral quantities. It is found that both the dimensional and non-dimensional displacement thickness, momentum thickness, energy thickness and the absolute wall shear stress are identical in both Blasius and Sakiadis flows at the asymptotic state.

Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium

A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical properties (ρ, μ and c p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and mixed convection. Temperature and velocity profiles are also presented.