Thermally Enhanced Darcy-Forchheimer Casson-Water/Glycerine Rotating Nanofluid Flow with Uniform Magnetic Field

This numerical study aims to interpret the impact of non-linear thermal radiation on magnetohydrodynamic (MHD) Darcy-Forchheimer Casson-Water/Glycerine nanofluid flow due to a rotating disk. Both the single walled, as well as multi walled, Carbon nanotubes (CNT) are invoked. The nanomaterial, thus formulated, is assumed to be more conductive as compared to the simple fluid. The properties of effective carbon nanotubes are specified to tackle the onward governing equations. The boundary layer formulations are considered. The base fluid is assumed to be non-Newtonian. The numerical analysis is carried out by invoking the numerical Runge Kutta 45 (RK45) method based on the shooting technique. The outcomes have been plotted graphically for the three major profiles, namely, the radial velocity profile, the tangential velocity profile, and temperature profile. For skin friction and Nusselt number, the numerical data are plotted graphically. Major outcomes indicate that the enhanced Forchheimer number results in a decline in radial velocity. Higher the porosity parameter, the stronger the resistance offered by the medium to the fluid flow and consequent result is seen as a decline in velocity. The Forchheimer number, permeability parameter, and porosity parameter decrease the tangential velocity field. The convective boundary results in enhancement of temperature facing the disk surface as compared to the ambient part. Skin-friction for larger values of Forchheimer number is found to be increasing. Sufficient literature is provided in the introduction part of the manuscript to justify the novelty of the present work. The research greatly impacts in industrial applications of the nanofluids, especially in geophysical and geothermal systems, storage devices, aerospace engineering, and many others.

Numerical Scrutinization of Darcy-Forchheimer Relation in Convective Magnetohydrodynamic Nanofluid Flow Bounded by Nonlinear Stretching Surface in the Perspective of Heat and Mass Transfer

The aim of this research is mainly concerned with the numerical examination of Darcy-Forchheimer relation in convective magnetohydrodynamic nanofluid flow bounded by non-linear stretching sheet. A visco-elastic and strictly incompressible liquid saturates the designated porous medium under the direct influence of the Darcy-Forchheimer model and convective boundary. The magnetic effect is taken uniformly normal to the flow direction. However, the model is bounded to a tiny magnetic Reynolds number for practical applications. Boundary layer formulations are taken into consideration. The so-formulated leading problems are converted into highly nonlinear ordinary problems using effectively modified transformations. The numerical scheme is applied to solve the governing problems. The outcomes stipulate that thermal layer receives significant modification in the incremental direction for augmented values of thermal radiation parameter Rd. Elevation in thermal Biot number γ1 apparently results a significant rise in thermal layer and associated boundary layer thickness. The solute Biot number is found to be an enhancing factor the concentration profile. Besides the three main profiles, the contour and density graphs are sketched for both the linear and non-linear cases. Furthermore, skin friction jumps for larger porosity and larger Forchheimer number. Both the heat and mass flux numbers receive a reduction for augmented values of the Forchheimer number. Heat flux enhances, while mass flux reduces, the strong effect of thermal Biot number. The considered problem could be helpful in any several industrial and engineering procedures, such as rolling, polymeric extrusion, continuously stretching done in plastic thin films, crystal growth, fiber production, and metallic extrusion, etc.

Oxytactic Microorganisms and Thermo-Bioconvection Nanofluid Flow Over a Porous Riga Plate with Darcy–Brinkman–Forchheimer Medium

The aim of this paper is to analyze the behavior of oxytactic microorganisms and thermo-bioconvection nanofluid flow through a Riga plate with a Darcy–Brinkman–Forchheimer porous medium. The Riga plate is composed of electrodes and magnets that are placed on a plane. The fluid is electrically conducting, and the Lorentz force evolves exponentially along the vertical direction. The governing equations are formulated with the help of dimensionless variables. With the aid of a shooting scheme, the numerical results are presented in graphs and tables. It is noted that the modified Hartmann number boosts the velocity profile when it is positive, but lowers these values when it is negative. The density-based Rayleigh number and the nanoparticle concentration enhance the fluid velocity. The thermal Rayleigh number and the Darcy–Forchheimer number decrease the velocity. An increase in Lewis number causes a remarkable decline in the oxytactic microorganism profile. Several useful results for these flows with oxytactic microorganisms through Darcy–Brinkman–Forchheimer porous media are presented in this paper.

Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow

This article is concerned with the nanofluid flow in a rotating frame under the simultaneous effects of thermal slip and convective boundary conditions. Arrhenius activation energy is another important aspect of the present study. Flow phenomena solely rely on the Darcy–Forchheimer-type porous medium in three-dimensional space to tackle the symmetric behavior of viscous terms. The stretching sheet is assumed to drive the fluid. Buongiorno’s model is adopted to see the features of Brownian diffusion and thermophoresis on the basis of symmetry fundamentals. Governing equations are modeled and transformed into ordinary differential equations by suitable transformations. Solutions are obtained through the numerical RK45-scheme, reporting the important findings graphically. The outputs indicate that larger values of stretching reduce the fluid velocity. Both the axial and transverse velocity fields undergo much decline due to strong retardation produced by the Forchheimer number. The thermal radiation parameter greatly raises the thermal state of the field. The temperature field rises for a stronger reaction within the fluid flow, however reducing for an intensive quantity of activation energy. A declination in the concentration profile is noticed for stronger thermophoresis. The Forchheimer number and porosity factors result in the enhancement of the skin friction, while both slip parameters result in a decline of skin friction. The thermal slip factor results in decreasing both the heat and mass flux rates. The study is important in various industrial applications of nanofluids including the electro-chemical industry, the polymer industry, geophysical setups, geothermal setups, catalytic reactors, and many others.

Radiative MHD Nanofluid Flow over a Moving Thin Needle with Entropy Generation in a Porous Medium with Dust Particles and Hall Current

This paper investigated the behavior of the two-dimensional magnetohydrodynamics (MHD) nanofluid flow of water-based suspended carbon nanotubes (CNTs) with entropy generation and nonlinear thermal radiation in a Darcy–Forchheimer porous medium over a moving horizontal thin needle. The study also incorporated the effects of Hall current, magnetohydrodynamics, and viscous dissipation on dust particles. The said flow model was described using high order partial differential equations. An appropriate set of transformations was used to reduce the order of these equations. The reduced system was then solved by using a MATLAB tool bvp4c. The results obtained were compared with the existing literature, and excellent harmony was achieved in this regard. The results were presented using graphs and tables with coherent discussion. It was comprehended that Hall current parameter intensified the velocity profiles for both CNTs. Furthermore, it was perceived that the Bejan number boosted for higher values of Darcy–Forchheimer number.

Numerical Study for Darcy–Forchheimer Flow of Nanofluid due to a Rotating Disk with Binary Chemical Reaction and Arrhenius Activation Energy

The present article investigates Darcy–Forchheimer 3D nanoliquid flow because of a rotating disk with Arrhenius activation energy. Flow is created by rotating disk. Impacts of thermophoresis and Brownian dispersion are accounted for. Convective states of thermal and mass transport at surface of a rotating disk are imposed. The nonlinear systems have been deduced by transformation technique. Shooting method is employed to construct the numerical arrangement of subsequent problem. Plots are organized just to investigate how velocities, concentration, and temperature are influenced by distinct emerging flow variables. Surface drag coefficients and local Sherwood and Nusselt numbers are also plotted and discussed. Our results indicate that the temperature and concentration are enhanced for larger values of porosity parameter and Forchheimer number.

Numerical simulation for Darcy-Forchheimer flow of carbon nanotubes due to convectively heated nonlinear curved stretching surface

Purpose This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs. Design/methodology/approach Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development. Findings Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter. Originality/value Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

A paired quasilinearization method for solving the MHD mixed convection flow of a micropolar fluid through a truncated cone in a non-Darcy porous medium

The aim of this paper is to investigate the flow, heat and mass transfer through a truncated cone in a non-Darcy porous medium in the presence of a transverse magnetic field by considering chemical reaction and radiation effects where the fluid is micropolar. The nonlinear equations governing the flow are solved using the paired quasilinearization method (PQLM). The study reveals that increasing radiation parameter, mixed convection parameter and Forchheimer number decreases microrotation. It is also noted that an increase in the radiation parameter leads to a corresponding increase in both the velocity and temperature of the fluid.

Numerical treatment for Darcy–Forchheimer flow of nanofluid due to a rotating disk with convective heat and mass conditions

Purpose The purpose of this study is to examine the Darcy–Forchheimer flow of viscous nanoliquid because of a rotating disk. Thermophoretic diffusion and random motion aspects are retained. Heat and mass transfer features are analyzed through convective conditions. Design/methodology/approach The governing systems are solved numerically by the shooting technique. Findings Higher porosity parameter and Forchheimer number Fr depict similar trend for both velocity profiles f' and g. Both temperature and concentration profiles show increasing behavior for higher Forchheimer number Fr. An increase in Prandtl number Pr corresponds to lower temperature profile, while opposite trend is noticed for thermal Biot number. Larger concentration Biot number exhibits increasing behavior for both concentration and its associated layer thickness. Originality/value To the best of the author’s knowledge, no such consideration has been given in the literature yet.