Darcy Brinkman Porous Medium Research Articles

Radiative flow of clay nanoparticles on the lubricity of Williamson drilling fluids across a vertical surface in a Darcy-Brinkman porous medium

Drilling fluids are essential for extracting gases and oils from rocks and soil. To increase drilling fluid efficiency, clay nanoparticles are crucial. The use of clay particles in drilling fluids increases their thermal conductivity, viscosity, and boiling point, hence giving resilience to high temperatures and controlling fluid costs. Therefore, this research examines the convection radiative flow and heat transfer incorporated in the Williamson nanofluid with a heat source/sink. The effective thermophysical properties of clay nanofluid are represented quantitatively by using Maxwell-Garnett and Brinkman's formulas. The leading PDEs with physical boundary conditions that control the flow phenomena are predetermined. These PDEs are converted into ODEs using the similarity method, and dual solutions are then found by using an effective bvp4c solver. The effects of mixed convective, permeability, Williamson constraint, heat source/sink, nanoparticle volume fraction, and radiation parameters were all thoroughly studied quantitatively and theoretically. The Nusselt number and skin friction are calculated and displayed in tabular form as well as graphical form along with the velocity and temperature profiles. Multiple solutions are observed in the shrinkable sheet as well as the buoyancy assisting flow. The findings demonstrate that the Nusselt number rises noticeably when volume concentration increases. In addition, the permeability parameter expands the boundary layer thickness in the lower solution, while the contrary behavior is observed in the upper solution.

External velocity and dissipative flow of clay nanoparticles on the lubricity of drilling fluids across a vertical surface in a Darcy-Brinkman porous medium with thermal radiation

Drilling fluids are important in the extraction of oils and gases through rocks and soil. Clay nanoparticles are essential for enhancing drilling fluid efficiency. The thermal conductivity, viscosity, and boiling point of drilling fluids increase when clay nanoparticles are incorporated, providing resistance to high temperatures and regulating fluid costs. This article illustrates the convection heat transfer in drilling nanofluid while taking into account the significant presence of clay nanoparticles in the fluid with viscous dissipation, thermal radiation, and heat source/sink. The efficient thermophysical characteristics of clay nanofluid are expressed mathematically using Maxwell-Garnett and Brinkman’s formulas. The partial differential equations (PDEs) with physical boundary conditions that control the flow phenomena are predetermined. The similarity technique is employed to transmute these PDEs into ordinary differential equations (ODEs) and then an efficient boundary value problem fourth-order (bvp4c) solver is utilized to find dual solutions. The Nusselt number and skin friction are calculated and displayed in tabular form as well as graphical form along with the velocity and temperature profiles. Multiple solutions are observed in the shrinking sheet as well as the buoyancy assisting flow. The findings demonstrate that when volume concentration increases, the Nusselt number rises noticeably. In addition, the permeability parameter expands the boundary layer thickness in the lower solution, while the contrary behavior is observed in the upper solution.

Numerical simulation of Darcy–Brinkman oscillatory flow of dissipative fluid: Utilization of finite difference method

This study investigates viscous flow behavior in a Darcy–Brinkman porous medium, considering the effects of porous dissipation and frictional heating. The fluid is flowing over a flat plate, oscillating in its plane. The velocity and temperature profiles are simulated using a mathematical model that includes linear convection and considers the effects of porous and viscous dissipation. After performing mathematical transformations, the governing equations are modified into coupled and nonlinear dimensionless PDEs. The forward time centered space method numerically solves the modeled dimensionless equations. The acquired results are explicitly validated against the findings of the literature in a situation where limits are considered. The numerical results are presented graphically, providing a comprehensive analysis of the variables impacting fluid characteristics, including temperature and velocity. Interestingly, this work shows that a rise in the porosity parameter causes temperature profiles to rise and velocity to decrease. Moreover, a drop in velocity is linked to a rise in the Prandtl number. Furthermore, the influence of surface friction is diminished by including the porosity parameter. Moreover, a rise in the heat transmission rate at the surface can be observed.

Stability of penetrative convective currents in local thermal non-equilibrium

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

Coupled instability modes at a solvent/non-solvent interface to decorate cellulose acetate flowers

Dispensing a water drop on the thin film of a solution composed of cellulose acetate (CA) in dimethyl formamide (DMF) forms a thin and porous CA layer at the water–DMF interface. While a denser water drop on a rarer CA–DMF film manifests a Rayleigh–Taylor instability—RTI, the dynamically forming porous layer at the water–DMF interface triggers a Saffman–Taylor instability—STI. The combined effects of RTI and STI enable the formation, growth, coalescence, and branching of an array of periodic finger patterns to finally develop into a flower-like morphology. A general linear stability analysis (GLSA) of a thin bilayer composed of a Newtonian and incompressible water layer resting on a Darcy–Brinkman porous medium could predict the length and the time scales of such a finger formation phenomenon. The GLSA uncovers the crucial roles of pressure gradients originating from the gravitational effects, osmotic forces, the Marangoni effect, and capillary forces on the dynamics of the finger formation. While the density difference between water and CA–DMF layer plays a crucial role in deciding the initial finger spacing, the osmotic pressure dictates the formation, growth, branching, and coalescence of fingers. The length-FL and number-Navg of fingers are found to scale as FL∼We0.33Re−0.25 and Navg∼We0.33Re0.25. Further, an inverse relationship of the concentration of CA (C) with ∼We−0.3 and ∼Re−0.7 highlights its role in the formation and growth of fingers. The loading of CA in DMF, the viscosity and density of the CA–DMF film, and the curvature of the fingers are found to be other parameters that decide morphologies.

ON THERMAL CONVECTION IN ROTATING CASSON NANOFLUID PERMEATED WITH SUSPENDED PARTICLES IN A DARCY-BRINKMAN POROUS MEDIUM

The present paper investigates the effect of suspended particles on thermal convection in rotating Casson nanofluids saturating a Darcy-Brinkman porous medium which has various applications in different sectors, including those that process food, paint, water generators, electricity generators, hydrology, and geophysics, heavily rely on rotation in thermal convection. With the aid of the Galerkin 1st approximation technique, the numerical examination is carried out. The Darcy-Brinkman porous media and particles suspension are taken into consideration throughout the conduct of this study. The non-Newtonian Casson nanofluid, Darcy-Brinkman porous medium, particle suspension and rotation parameter, and their impact on thermal convection have been analyzed and presented graphically for free-free, rigid-rigid, and rigid-free boundaries. It is found that for all boundary conditions the Casson nanofluid and suspended particle parameters have destabilizing impact on the stationary convection, whereas the parameter which occurred due to presence of rotation, i.e., Taylor number and Brinkman porous medium parameters, both delayed the stationary convection. In addition, we have discovered that for realistic rigid-rigid boundary condition, the system is determined to be more stable than for the other two boundary conditions. Also, on the basis of several approximations on the Taylor number and other parameters, the critical wave number and value for stationary convection are determined.

IMPACT OF POROUS AND MAGNETIC DISSIPATION ON DISSIPATIVE FLUID FLOW AND HEAT TRANSFER IN THE PRESENCE OF DARCY-BRINKMAN POROUS MEDIUM

In this article, the boundary layer flow of an electrically-conducting fluid through a porous medium attached with a radiative permeable stretching sheet is analyzed. Following the Brinkman theory, an extended Darcy model (Darcy-Brinkman model) is utilized for the model momentum equation. Heat transfer analysis is also performed in the presence of viscous and Joule dissipation. Moreover, in the modeling of the energy equation, the effects of internal heating resulting from the mechanical effort required to squeeze out the fluid through the porous medium are also included in porous dissipation. Suitable dimensionless variables are introduced to convert the governing boundary layer equations into a dimensionless form, which are then converted into self-similar, nonlinear ordinary differential equations by utilizing similarity transformations. The exact solution of the nonlinear self-similar momentum equation is obtained in the form of the exponential function. In contrast, the solution of the energy equation is computed through the Laplace transform technique in the form of Kummer confluent hypergeometric functions. Effects of involved physical parameters on the momentum boundary layer (MBL), thermal boundary layer (TBL), wall shear stress, and local Nusselt number are explored through graphs and tables. Moreover, the slope linear regression (SLR) technique is used to calculate the rate of decrease/increase in shear stress and the rate of heat transfer at the boundary. The velocity and momentum boundary layer decreases for large values of porosity parameter and increases by increasing the viscosity ratio. The shear stress increases by increasing the porosity parameter, Hartman number, and suction parameter, while the opposite effect is examined with increasing values of viscosity ratio parameter. Heat transfer rate also enhances by increasing the Brinkman viscosity ratio parameter and wall suction velocity.

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.

Thermal performance of hydromagnetic nanofluid flow within an asymmetric channel with arbitrarily conductive walls filled with Darcy-Brinkman porous medium

The primary purpose of the investigation is to explore the thermal performance of steady hydromagnetic flow of Ti6Al4V-H2O nanofluid within two arbitrarily electrically conductive walls enclosing Darcy-Brinkman porous medium. The energy dissipations and Hall effect on flow performance are also examined. The equations of the flow model are derived from the field and constitutive equations connecting electric and magnetic fields. The flow model is solved by an analytical approach, and the mathematical expressions for flow field such as velocity field, motional generated magnetic field, and temperature field are derived in two particular cases, i.e., (i) in the case of the Hartmann flow (c=0) and (ii) Hartmann-Couette flow (c=1). The quantities of physical interests like wall shear stress, the critical value of the Grashof number, mass flux, and heat transport rate are also derived. The governing parameters for the numerical computation are chosen for the range of hc=0.25≤hc≤hc=0.75, Da=0.02≤Da≤Da=2, ψl,ψu=0.01≤ψl,ψu≤ψl,ψu=100, Pr=0.03≤Pr≤Pr=7.0 and Er=0.05≤Er≤Er=2.0. An interesting outcome of the study is the appearance of flow reversal in the direction of normal flow when c=1. It is further confirmed from the numerical results that the Darcy-Brinkman drags and upper wall conductivity significantly raise the normal flow near the lower wall. At the same time, while this substantially reduces the normal flow in the area nearby the upper wall.

Darcy–Brinkman porous medium for dusty fluid flow with steady boundary layer flow in the presence of slip effect

This study looks at the Darcy–Brinkman flow across a stretched sheet of porous dissipation and frictional heating. The geometry of a steady flow of dust particles fluid through a porous material in the existence of slip effect and porous dissipation is the subject of this study. The equations that govern the system are shown and summarized as boundary layer assumptions, and then modified into framework of first-order DEs using the similarity approach. By using similarity transformation, a two-dimensional nonlinear partial differential equation is decreased to a sequence of nonlinear ordinary differential equations (ODEs). Then, by employing numerical techniques such as Maple packages, the solution of system of nonlinear equations is represented using the RK4 method. The numerical findings are derived under specific unique situations. The Nusselt number and coefficient of skin-friction are also given numerically. The increase in Brinkman number [Formula: see text] raises the temperature profile for both the dusty and the fluid phases. The results also demonstrate that rise in the suction number S falls the temperature distribution within the boundary layer for the dusty phase and fluid phase. For a variety of flow quantities of attention, the variation of parameters is studied, and the outcomes are reported in the shape of graphs and tables. Several industrial processes make advantage of boundary layer flow and heat transfer over such a stretched surface in porous materials.

Unsteady Fluid Flow in a Darcy–Brinkman Porous Medium with Slip Effect and Porous Dissipation

In this paper, the significance of slip situations in the appearance of a porous medium and frictional heating on unsteady fluid flow through a porous medium has been explored. The numerical solutions of the differential equation representing fluid flow through a porous material, including slip effects, are presented. We have obtained a nonlinear ordinary differential equation using a similarity transformation. Under velocity and thermal slip conditions, the Maple packages were used to numerically solve the resulting set of nonlinear problems. Both the velocity and temperature increase when the Brinkman viscosity ratio parameter [Formula: see text] increases. The effects of the nondimensional parameters on the governing flow velocity and temperature are examined with graphical profiles. The implications of relevant parameters on dimensionless temperature, velocity, local Nusselt number and skin friction coefficient are shown and explained. For various flow quantities of interest, the fluctuation of parameters is investigated, and the results are given in the system of graphs and tables.

Rotating Casson nanofluid convection for Au, Ag, CuO and Al2O3 nanoparticles embedded by Darcy-Brinkman porous medium

The present study examines convection in a Casson nanofluid layer in a porous media under the effect of Coriolis force using Darcy-Brinkman model. For a variety of metallic and non-metallic nanoparticles, the analysis is conducted by utilizing the linear stability theory, normal mode approach, and one term Galerkin type weighted residual method. When current numerical findings are compared to those that have already been published, good agreements are found for the permitted range of parameters. Blood (Casson fluid) is numerically simulated for porous media using the Mathematica software to make the analysis valuable for practical applications. Top-heavy configuration of nanoparticles is found to lead to a stationary mode of convection. The effect of porous medium, rotation, Casson parameter and nanoparticle parameters is discussed numerically. Interestingly, it is found that though Casson fluids are more stable as compared to regular fluids but Casson parameter itself has a destabilizing effect on the system. The really important and novel result of the study comes out as the fact that Coriolis force can stabilize the gold-nanoparticle-based Casson fluid layer system which is otherwise totally unstable. As far as metallic and non-metallic nanoparticles are concerned; the stability pattern followed by metallic nanofluids is iron-blood>copper-blood>silver-blood>gold-blood and for non-metallic nanofluids is silica-blood> alumina-blood> titanium oxide-blood>copper oxide-blood.

UNSTEADY TRIPLE-DIFFUSIVE CONVECTION EMBEDDED WITH DARCY-BRINKMAN THREE-TEMPERATURE MODEL

The theory of binary nanofluid layer heated and soluted from below under the effect of local thermal non-equilibrium has been investigated by applying the technique of superposition of basic feasible modes with one-term Galerkin residual method. The so-called Darcy-Brinkman model for the top-heavy distribution of nanoparticles has been employed. A three-temperature local thermal non-equilibrium (LTNE) model, assuming one-temperature field for the solid matrix, one for the base fluid, and one for the suspended nanosized particles, is employed, incorporating the effects of Brownian and thermophoretic diffusions. Numerical computations are carried out with the software Mathematica (version 12.0). The novelty of the problem lies in the fact that destabilizing influence of nanoparticles and solute is countered with stabilization due to the presence of Darcy-Brinkman porous medium. Further, it has been observed that the two LTNE parameters namely, Nield parameter for particles and modified solute thermal capacity ratio, have destabilizing effects which are balanced by the other two parameters, viz. Nield parameter for solute and modified thermal capacity ratio for particles. The impact of nanofluid parameters is found to destabilize this top-heavy configuration of nanoparticles. Due to the consideration of Darcy-Brinkman model, Darcy number came into existence, which postpones the onset of instability. Similar is the effect of porosity and modified thermal diffusivity ratios for the particles as well as the solute.

Analysis of Magneto-Thermo-Bioconvection of Nanofluid Containing Gyrotactic Microorganisms Through Porous Media

The present work aims to study the combined effect of external magnetic field and heating from below on the bioconvection of nanofluid containing gyrotactic microorganisms. Modified Maxwell’s equations and generalized Buongiorno’s model are used to frame the flow constitutive equations of nanofluid saturated in the Darcy-Brinkman porous medium. The present investigation has been done in the framework of linear stability. The resulting eigenvalue problem along with boundary conditions has been solved using Chebyshev-Gauss-Lobato Spectral Method. Appropriate transformations are used to convert Neumann boundary conditions into Dirichlet’s one. The influence of various pertinent parameters on the critical thermal Rayleigh number has been shown through graphs and tables. It has been observed that magnetic field stablizes the system whereas fast moving microorganisms hasten the onset of convection.

Analysis of Jet Wall Flow and Heat Transfer Conveying ZnO-SAE50 Nano Lubricants Saturated in Darcy-Brinkman Porous Medium

The problem of 2D (two-dimensional) wall jet flow, along with heat transfer incorporated by nanofluid in a Darcy-Brinkman medium, while recognizing the requirement for efficient heating and cooling systems. Following the use of similarity variables, the resultant system of ODEs (ordinary differential equations) is solved using the well-known and efficient bvp4c (boundary-value problem of the 4th order) technique. The significance of physical quantities for the under-consideration parameters is illustrated and explained. The findings show that the nanoparticle volume fraction and porosity parameters decrease the velocity, but increase the temperature. In addition, the temperature uplifts in the presence of radiation effect. The suction parameter initially decreases and then increases the velocity near the surface, while the temperature declines.

Thermal convection in a rotating porous medium layer saturated by a nanofluid under a helical magnetic field

In recent years, experiments with flows of liquid metals in a helical magnetic field have been actively carried out. The study of the processes of mixing and crystallization of a liquid metal is of practical importance for metallurgy. With the development of nanotechnology, more and more new types of nanofluids (hybrid, ternary nanofluids) are being synthesized, and the thermophysical characteristics of which can compete with liquid metals. This circumstance served as a motivation for conducting this theoretical study. In this study, the criterion for the onset of convection in a Darcy–Brinkman porous medium layer saturated by an electrically conductive nanofluid under a helical magnetic field is investigated. The Brownian motion and thermophoresis effects are combined in the model for nanofluids, whereas the Darcy–Brinkman model is used for porous media. Instead of prescribing the nanoparticle volume fraction on the borders, we adopted a boundary condition in which the nanoparticle flow is considered to be zero. In the absence of a temperature gradient, a new type of instability in a helical magnetic field in a thin layer of a nanofluid is considered. The growth rate and the region of the development of this instability are numerically obtained depending on the profile of the azimuthal magnetic field (the magnetic Rossby number Rb) and the radial wave number k. In the presence of temperature, the stationary regime of nonuniformly rotating magnetoconvection is studied. The accurate analytical equation for the critical Rayleigh–Darcy number in terms of various non-dimensional parameters is determined using the linear stability theory. The results show that rotation and the axial (vertical) part of the helical magnetic field retard the onset of convection. While the azimuthal part of the helical magnetic field has a destabilizing effect at positive Rossby numbers Rb. The conditions for stabilization and destabilization of stationary convection in a helical magnetic field are determined for metal oxide, metallic, and semiconductor nanofluids.

Significance of Darcy-Brinkman porous drag forces and Cattaneo-Christov thermal transportation on the features of second-grade fluid flows conveying copper nanomaterials past an unsteady stretching permeable sheet heated convectively

The main thermo-hydro-rheological behaviors featuring the unsteady convective laminar motion of copper-methanol second-grade nanofluid over a linearly stretching permeable sheet is explored numerically in the framework of Cattaneo-Christov theory to provide a better understanding of the heat transfer mechanism within a Darcy-Brinkman porous medium. By adopting the single-phase nanofluid model along with the boundary layer approximations, the leading partial differential equations (PDEs) are derived properly and then converted mathematically into a differential structure of ordinary differential equations (ODEs) via appropriate similarity alterations. Accordingly, the resulting dimensionless boundary layer equations are tacked numerically for convective and suction boundary conditions by utilizing the generalized differential quadrature method (GDQM). To reveal the effect of such a pertinent flow parameter, extensive GDQM numerical data are outputted graphically for the velocity and temperature fields as well as tabularly for skin friction coefficient and the Nusselt number. As the main findings, it is noted that both the velocity profile and the wall temperature lessen with the suction parameter and the nanoparticle’s loading. However, an enhancement is depicted for the wall heat transfer rate with the reinforcement in those influences. In addition, it is witnessed that the effect of the surface drag forces is strengthened with the nanoparticle’s loading and weakened with a higher estimation of the suction effect.

Thermo-diffusion impacts on the flow of an elastico-viscous fluid over an inclined heated plane with magnetized wall

The focus is in this article is to scrutinize the simultaneous significances of magnetic diffusion, thermo-diffusion and angular location on the hydromagnetic flow of an elastico-viscous fluid over an inclined heated plane with magnetized wall. The flow medium is considered to be uniformly permeable (Darcy-Brinkman porous medium) and the flow of the fluid is considerably affected due to the appearance of a strong magnetic field in the direction normal to the flow surface. The significances of Hall current, induced magnetic field and Coriolis force on flow nature is also included in the study. The leading non-dimensionalized equations are explored by regular perturbation analysis. Ultimately, the expressions for velocity field, induced magnetic field, temperature and concentration are obtained. We further derived the surface skin friction, surface current density, heat and mass fluxes. The computation of results is performed with the aid of Mathematica software and results are presented in graphical and tabular forms for distinct flow impacting parameters. Numerical simulation explores that mass diffusion factor brings growth in the fluid velocity, temperature and normal induced magnetic field while it reduces the main induced magnetic field. Magnetic diffusion develops the primary flow and primary induced magnetic field and lessens the normal flow and normal induced magnetic field. Inclination angle of the heated plane upgrades primary induced magnetic field while downgrading normal induced magnetic field.

MIXED CONVECTIVE FLOW OF A CASSON FLUID OVER A VERTICAL PLATE IN DARCY-BRINKMAN POROUS MEDIUM WITH SLIPS

MIXED CONVECTIVE FLOW OF A CASSON FLUID OVER A VERTICAL PLATE IN DARCY-BRINKMAN POROUS MEDIUM WITH SLIPS

Boundary Layer Flow through Darcy–Brinkman Porous Medium in the Presence of Slip Effects and Porous Dissipation

This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs.