Darcy-Forchheimer Relation Research Articles

Magnetic dipole ramifications on squashed flow characterization of a ferrofluid roaming a Darcy–Forchheimer sensor surface

This mathematical structure is modeled to explore the magnetic dipole and thermal radiation effects on the magnetically driven squashed flow of a ferrofluid. The flow is subjected to a Darcy–Forchheimer sensor medium placed in superficially free stream. Squashed flow in sensor surface is characterized by Darcy–Forchheimer relation. The fluid viscosity and thermic conductivity are presumed to be vary with temperature variation. The originated structure of complex equations is highly intricate, so a combination of significant parameters is subjected to attain the dimensionless equations. The developed equations are then resolved numerically to find the converging solutions. The consequences of related parameters on the profiles of temperature and velocity are deliberated and presented through graphs. For the present geometry, the flow behavior analysis of ferrofluid has made through stream lines. The significant findings of current investigation are as follows: Both Nusselt number and local shear stress are seemed to increase for rise in magnetic parameter and squashing velocity; influence of squeezed flow index $$ b $$ on temperature and velocity curve is inconsistent.

RETRACTED: Entropy optimized magnetohydrodynamics Darcy–Forchheimer second order velocity slip flow of nanomaterials between two stretchable disks

Here magnetohydrodynamics Darcy–Forchheimer second order velocity slip flow of nanomaterials is discussed between two stretchable surfaces of rotating disks, where the both disks are rotating with altered angular frequencies and rates. Flow in permeable medium is designated by implementing Darcy–Forchheimer relation. The energy expression is discussed and modeled subject to various effects like dissipation, Ohmic heating (Joule heating), and heat source/sink. Two different types of nanoparticles, i.e. graphene oxide (GO) and titanium dioxide (TiO2), are utilized and H2O as a base fluid. Total entropy rate which depends on five different types of irreversibilities (i.e., heat, mass fluid friction, Ohmic heating and Darcy–Forchheimer or porosity) is calculated via thermodynamics law (second). Furthermore, binary chemical reaction is accounted for the analysis of mass with activation energy. Numerical solutions are found out with the help of shooting method. Behaviors of flow variables on the skin friction coefficients, velocity field, Nusselt numbers, temperature distribution, entropy generation, concentration, and Bejan number are plotted graphically and discussed. The results are compared with previous literature and found good agreement with them. Our obtained results illustrate that the entropy rate is more subject to rising Brinkman number.

Flow analysis by Cattaneo–Christov heat flux in the presence of Thomson and Troian slip condition

This communication considers entropy minimization in stagnation point flow of a hybrid nanofluid past a nonlinear permeable stretching sheet with Thomson and Troian boundary condition. Due to the porous medium, the Darcy–Forchheimer relation is added. The nonlinear thermal radiation, heat generation, and viscous dissipation by using Cattaneo–Christov heat flux model are explained. Further the influence of variable viscosity, activation energy, and variable mass diffusivity is taken into account. For first time, hybrid nanofluid consisting of carbon nanotubes with Thomson and Troian boundary conditions and induced MHD has been implemented and has not yet been studied. The finite difference method, i.e., bvp4c from Matlab, is utilized to solve the transformed ordinary differential equations (ODEs). This method has good certainty to solve this problem, compared to previous works. Comparison of simple nanofluid and hybrid nanofluid is graphically illustrated. It is noticed that the solid volume fraction decreases the velocity profile and enhances the temperature distribution. Further, compared to simple nanofluid, hybrid nanofluid has greater thermal conductivity and better heat transfer performance.

Darcy–Forchheimer flow over an exponentially stretching curved surface with Cattaneo–Christov double diffusion

This article deals with Darcy–Forchheimer viscous liquid flow by an exponentially stretching curved surface. Flow in permeable space is specified via Darcy–Forchheimer relation. Cattaneo–Christov mass and heat diffusion relations are considered in the mathematical formulation. Appropriate variables lead to highly non-linear ordinary differential equations. The obtained problem is solved numerically through NDSolve technique. The outcomes of different sundry variables on velocity, temperature and concentration are sketched and discussed. The physical quantities like skin friction and heat and mass transfer rates are examined graphically. Our results indicate that the heat and mass transfer rates are enhanced for larger values of thermal and concentration relaxation parameters respectively.

Darcy–Forchheimer three-dimensional flow of carbon nanotubes with nonlinear thermal radiation

The present study elaborates three-dimensional (3D) thermally radiative flow of carbon nanotubes dispersed in water with Darcy–Forchheimer porous space. A bidirectional linear stretchable sheet is used to generate the flow. Darcy–Forchheimer relation specifies porous space. Single-wall carbon nanotubes and multi-wall carbon nanotubes are accounted. Solutions development is due to optimal homotopy analysis technique. Optimal data of sundry variables are obtained. The optimal solution interpretations of velocities and temperature are interpreted via plots. Physical quantities are also elaborated. Our results reveal that thermal field against radiation and temperature ratio parameter is enhanced.

Analysis of chemically reactive species with mixed convection and Darcy–Forchheimer flow under activation energy: a novel application for geothermal reservoirs

In the present article, an analysis has been performed to discuss the impact of steady mixed convection with Darcy–Forchheimer flow towards linear surface. Investigation has been achieved in the presence of Arrhenius activation energy and radiative heat flux which are associated with the heat and mass transport analysis which has not been performed so far. Porous media features are elaborated by utilizing Darcy–Forchheimer relation. Boundary-layer idea is employed for the simplification of governing expressions. The resulting set of mathematical expression is now solved with the help of bvp4c MATLAB package which applies a three-stage Lobatto IIIa finite-difference collocation scheme. Diagrams are drawn against pertinent parameters such as buoyancy forces ratio parameter, mixed convection parameter, porosity parameter, local inertia coefficient, activation energy, chemical reaction rate constant, Schmidt number, temperature difference ratio, exponentially fitted constant, magnetic parameter, radiation parameter, first-order and second-order slip parameter, suction or injection parameter and Prandtl number. It is observed that both mixed convection and activation energy parameters have an opposite impact on species profile. Also the present results are compared with those available in the literature for some cases, and an excellent agreement is found between them.

Darcy-Forchheimer nanofluidic flow manifested with Cattaneo-Christov theory of heat and mass flux over non-linearly stretching surface.

This research article aims to disclose the features of nanofluidic flow manifested with Cattaneo-Christov model of heat and mass flux over non-linearly stretching surface. An incompressible visco-elastic nanofluid saturates the given porous medium through Darcy-Forchheimer relation. A non-uniformly induced magnetic effect is considered to accentuate the electro-magnetic and thermal conductivity of the base fluid. The model is restricted to small magnetic Reynolds. Boundary layer assumptions are incorporated for the given flow model. Governing equations are remodeled into non-linear ordinary differential equations through transformations. So formulated nonlinear system is solved through homotopy analysis method (HAM) to achieve series solutions for velocity field, concentration of nanoparticles and temperature distribution. It is noticed that the temperature distribution and corresponding thermal boundary layer pattern shows declination for Cattaneo-Christov model of heat and mass flux as compared to classical Fourier’s law of heat flux/conduction. Furthermore, the intensive resistance offered by the addition of porosity factor in the flow model results in rise of temperature profile, however, opposite behavior is noticed in concentration of nanoparticles. The wall-drag intensity, the heat flux and the mass flux are discussed on the premise of numerical information obtained upon simulation of the problem.

Magnetohydrodynamic Darcy–Forchheimer nanofluid flow over a nonlinear stretching sheet

This paper presents an analysis of the features of magnetohydrodynamic Darcy–Forchheimer nanofluid flow over a nonlinear stretching sheet. A viscous incompressible nanofluid saturates the porous medium via the Darcy–Forchheimer relation. Heat and mass transfer is analyzed through the Brownian motion factor and thermophoresis. A non-uniform magnetic field is induced to enhance the electric conductivity of the nanofluid. The model emphasizes a small magnetic Reynolds number and boundary layer formulation. The governing partial differential equations are converted into nonlinear ordinary differential equations using similarity transformations and thereafter solved utilizing the homotopy analysis method. Graphs are sketched for different values of various fluid parameters. Drag force, heat flux, and mass flux are interpreted numerically. The porosity factor results in increasing the skin friction due to the high resistance offered by the porous medium. The heat and mass flux are reduced for a stronger porosity factor, which is an important finding for industrial applications of nanofluids. The temperature profile shows increasing values of both Brownian diffusion and thermophoresis.

Study of Three dimensional Darcy–Forchheimer squeezing nanofluid flow with Cattaneo–Christov heat flux based on four different types of nanoparticles through entropy generation analysis

In this research article, the unsteady nanofluid flow between two horizontal plates is discussed. The main focus of this study is on the explanation of the relative study of water-based nanofluids with four different types of nanoparticles. The nanoparticles selected for this specific research article are copper oxide [Formula: see text], aluminum oxide [Formula: see text], copper [Formula: see text], and silver [Formula: see text]. The upper plate is moving downward with time-dependent velocity while the lower plate is stretching horizontally. Also the lower plate is made up of porous medium. The stream in permeable region is characterized by Darcy–Forchheimer relation. Cattaneo–Christov heat flux model is used for heat transfer phenomena. Viscous dissipation effect is taken in account. Skin friction and Nusselt number are numerically calculated. Total entropy generation is also discussed for squeezing system. Transformation technique is applied to transform the model from partial differential equations to ordinary differential equations. Homotopy techniques are applied to solve the problem. The influence of important parameters on velocity, temperature, and entropy profiles have been shown graphically and discussed in detail.

Darcy–Forchheimer flow of Maxwell fluid with activation energy and thermal radiation over an exponential surface

The main purpose of this article is to investigate three-dimensional steady rotating flow of rate type fluid (Maxwell fluid) over an exponential stretching surface. The Maxwell fluid saturates the porous space via Darcy–Forchheimer relation. Flow caused by the exponential stretchable surface of sheet. Chemical reaction along with Arrhenius energy is considered at the surface. Energy expression is modeled subject to heat source/sink and radiation flux. Appropriate transformations leads to ordinary ones. Homotopy method is implemented for the series solutions. Pertinent parameters are discussed graphically. Special consideration is given to the engineering quantities such as Sherwood and Nusselt numbers and discussed numerically through tabular form. Temperature distribution enhances versus higher radiation and heat source/sink parameter while decays for larger Prandtl number. Furthermore, velocity shows decreasing trend through larger porosity and Deborah number.

Modeling and analysis of Maxwell nanofluid considering mixed convection and Darcy–Forchheimer relation

This research describes mixed convective Maxwell nanoliquid stretching flow subject to Newtonian heating. Porous medium characteristics are elaborated utilizing non-Darcian relation. Modeling is based on Brownian movement, heat generation, thermophoresis and chemical reaction aspects. Boundary-layer idea is employed for simplification of governing expressions. Optimal homotopy algorithm is implemented for computations of nonlinear problems. Besides, the Sherwood and Nusselt numbers along with temperature, velocity and nanoparticle concentration are analyzed. Our outcomes reveal opposite characteristics for porosity factor and Deborah number against velocity field.

Entropy generation in Darcy–Forchheimer flow of nanofluid with five nanoarticles due to stretching cylinder

In the present paper, formulation and computations are made to investigate the flow of nanofluid past a heated stretching cylinder. Flow in porous space is specified by Darcy–Forchheimer model. Water with silver (Ag), copper (Cu), copper oxide (CuO), titanium oxide (TiO2) and aluminum oxide (Al2O3) are considered as nanofluids. Heat transport mechanism is expressed through nonlinear radiation and non-uniform heat generation/absorption. Convective condition is also utilized for heat transport phenomenon. Through implementation of second law of thermodynamics the total entropy generation is calculated. Moreover, entropy generation for fluid friction and heat transfer is discussed. This study is specially investigated for the impact of Darcy–Forchheimer relation with entropy generation subject to distinct flow parameters. Optimal homotopy algorithm computes the nonlinear strong differential systems. Plots reflecting outcomes of influential variables are examined. The obtained results indicate that entropy rate directly depends on Brinkman number, temperature difference parameter and Forchheimer number. Estimations of skin friction coefficient and heat transfer rate are also carried out. It is found that magnitude of rate of heat transfer and skin friction coefficient enhances via volume fraction of nanoparticles.

Darcy–Forchheimer flow of nanofluid due to a curved stretching surface

Purpose The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface. Design/methodology/approach The resulting nonlinear system is solved through shooting technique. Findings Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter. Originality/value To the best of author’s knowledge, no such consideration has been given in the literature yet.

Darcy Forchheimer nanofluid thin film flow of SWCNTs and heat transfer analysis over an unsteady stretching sheet

This article analyzes the Darcy Forchheimer 2D thin film fluid of nanoliquid. Flow of nanoliquid is made due to a flat unsteady stretchable sheet. In nanoliquids, nanomaterial is in form of CNTs (carbon nanotubes). Also, in present analysis, single walled carbon nanotubes (SWCNTs) are accounted as nanoparticles. The classical liquid ‘water’ is treated as based liquid. The flow in permeable region is characterized by Darcy–Forchheimer relation. Heat transport phenomena are studied from convective point of view. The transformation of partial differential set of equations into strong ordinary differential frame is formed through appropriate variables. Homotopy Analysis Method (HAM) scheme is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtl number), λ (unsteadiness factor), k (porous medium factor), F (Darcy-porous medium factor) on liquid velocity and thermal field are scrutinized and studied through sketches. Certain physical factors like f″(0) (friction factor coefficient) and −θ′(0) (rate of heat transport) are first derived and then presented through tables.

Integration of Biomass Gasification and Hot Gas Cleaning Processes

In the near future, most of the world population will live in the developing countries, and it is plausible that biomass will be one of the main renewable energy sources of the future. Fluidized bed reactors should be the best solution to transform biomasses having different physical properties in energy and chemical vectors through gasification, due to its possibility to operate continuously, at high temperatures, and to utilize catalysts into the reactor and downstream of it, in order to reduce tar, NH3 etc. in the product gas.Catalytic filter candles are an innovative solution for hot gas cleaning & conditioning. It has been demonstrated that catalytic ceramic filters inserted in the freeboard of a fluidized bed gasifier, allow the complete removal of particulate by means of their anisotropic porous filtering structure, and furthermore act as catalyst to remove tar and ammonia, thanks to the Ni based catalyst contained into the filter itself (Rapagna, Gallucci and Foscolo, 2017).To by-pass the preparation of the catalytic ceramic filters and to render the overall process more feasible in practice, ceramic filters filled with commercial steam reforming catalyst pellets have been located in the freeboard of a 0.1 m ID fluidized bed reactor, where olivine particles act as bed inventory.Experimental tests were carried out to check the values of the gas pressure drop through the plain filter and through the filter containing catalyst pellets, at different temperatures and gas filtration velocities. It has been found that at the highest temperature and filtration velocity (T 800°C and v 140 m/h) the pressure drops are around 48 mbar, while at the operating conditions (T 800°C and v 100 m/h) the total pressure drops are only 35 mbar. Furthermore it was observed that there is an almost negligible difference between the pressure drops in the case of empty and filled candle; it was thus deduced that the catalyst pellets do not cause relevant additional losses compared to the empty filter. The trends of pressure drops were fitted with the empirical Darcy-Forchheimer relation and with the Ergun equation, and it was found that the major contribution is given by the viscous term of the relation. Furthermore an additional contribution of concentrated pressure drops was identified and ascribed to the outer Al2O3 membrane of the candle characterized by very fine pores.

A theoretical analysis of SWCNT–MWCNT and H2O nanofluids considering Darcy–Forchheimer relation

The remarkable features of carbon nanotubes (CNTs) such as physicochemical compatibility, high conductivity, effective electrical conductivity, light weight and stability (chemical, mechanical) form them a superlative substance to be manipulated in electrochemical mechanisms. Having such effectiveness of CNTs in view our intention in this investigation is to elaborate the significance of non-Darcian relation in flow of CNTs based on water by rotating disk. Outcomes for both CNTs (single walled, multi walled) are presented and elaborated. Thermal radiation and Partial slip aspects are further a part of this research. The process of non-dimensionalization is performed utilizing Von Karman approach. Optimal homotopic scheme is employed for analysis. Velocity, Nusselt numbers, temperature and skin friction have been computed and addressed.

Numerical simulation for radiative flow of nanoliquid by rotating disk with carbon nanotubes and partial slip

The extraordinary characteristics of carbon nanotubes like good electrical conductivity, high thermal conductivity, chemical and mechanical stability, physicochemical compatibility and light weight make them an ideal material to be utilized in electrochemical devices. Having such importance of carbon nanotubes in mind our objective in this research is to describe the significance of Darcy–Forchheimer relation in water-based carbon nanotubes (CNTs) flow subject to a rotating disk. Analysis for single and multi walled carbon nanotubes (SWCNTs, MWCNTs) is acquired and compared. The current research further comprises slip (velocity, thermal) and heat generation aspects. Relevant ordinary differential systems after utilizing proper transformations are computed. Shooting scheme is utilized for the analysis. Temperature, skin friction, velocity and Nusselt number have been addressed. The described analysis reveals similar impacts of velocity and thermal slip variables against velocities and temperature fields. Furthermore temperature distribution and rate of heat transfer are enhanced for higher estimation of radiation parameter.

Mixed convective stagnation point flow of nanofluid with Darcy-Fochheimer relation and partial slip

Abstract Here axisymmetric mixed convective, stagnation point flow of electrically conducting nanofluid by a permeable cylinder is examined. Magnetic field in transverse direction is applied. The Darcy-Forchheimer relation is accounted to specify the flow nature in porous medium. Formulation of mathematical model is given by using Tiwari-Das nanofluid model. The velocity and thermal slip conditions.are taken. This whole communication comprises water as a base fluid with nano-sized particles (Aluminum oxide, Copper and Titanium Oxide). The nonlinear coupled ordinary differential equations are obtained after using appropriate transformations. The convergent series solution of nonlinear system is accomplished by homotopic approach. The nondimensional velocity and temperature curve are examined under the impact of physical parameters like the nanoparticle volume fraction, permeability parameter, curvature parameter, the magnetic parameter and the mixed convection parameter. Numeric values of coefficient of skin friction and Nusselt number are analyzed.

Numerical study for Darcy-Forchheimer flow of nanofluid due to an exponentially stretching curved surface

Abstract Here Darcy-Forchheimer flow of viscous nanofluid with Brownian motion and thermophoresis is addressed. An incompressible viscous liquid saturates the porous space through Darcy-Forchheimer relation. Flow is generated by an exponentially stretching curved surface. System of partial differential equations is converted into ordinary differential system. Nonlinear systems are solved numerically by NDSolve technique. Graphs are plotted for the outcomes of various pertinent variables. Skin friction coefficient and local Nusselt and Sherwood numbers have been physically interpreted. Our results indicate that the local Nusselt and Sherwood numbers are reduced for larger values of local porosity parameter and Forchheimer number.

On framing potential features of SWCNTs and MWCNTs in mixed convective flow

Abstract Our target in this research article is to elaborate the characteristics of Darcy-Forchheimer relation in carbon–water nanoliquid flow induced by impermeable stretched cylinder. Energy expression is modeled through viscous dissipation and nonlinear thermal radiation. Application of appropriate transformations yields nonlinear ODEs through nonlinear PDEs. Shooting technique is adopted for the computations of nonlinear ODEs. Importance of influential variables for velocity and thermal fields is elaborated graphically. Moreover rate of heat transfer and drag force are calculated and demonstrated through Tables. Our analysis reports that velocity is higher for ratio of rate constant and buoyancy factor when compared with porosity and volume fraction.