Governing Flow Equations Research Articles

Analysis of two non‐miscible electrically conducting micropolar fluid flow through an inclined porous channel: Influence of magnetic field

AbstractThis work aims to analyse the flow of immiscible micropolar fluid through an inclined porous channel in presence of uniform magnetic field. The flow model have divided in two different porous regions and permeability of each porous region is taken different. The two immiscible electrically conducting micropolar fluids which have different densities and viscosities, take place through these two porous regions. The flow in an inclined porous channel is caused by a constant pressure gradient which acts on entrance section of flow domain. The flow of the micropolar fluids in the respective regions is governed by Brinkman's equation. The governing flow equations of the proposed model are solved analytically by reliable techniques and exact solution of flow field, flow rate and wall shear stress is evaluated by using well‐known boundary conditions. In this work, authors examined the influence of existing parameters such as permeability parameters, Hartmann number, gravitational parameter, viscosity ratio and so forth, which describes the physical significance of the presented model, on velocity profile, flow rate and wall shear stresses and these effect presented by graphs. The results are validated with the findings of past published article.

Significance of multiple solutions on the dynamics of ethylene glycol conveying gold and copper nanoparticles on a shrinking surface

All previously published data on the dynamics of ethylene glycol conveying copper and gold nanoparticles over a convective surface, nothing is known about the importance of dual branch solutions. Hybrid nanofluids improve the thermal conductivity of the fluid. The nanoparticles copper and gold having ethylene glycol as a base fluid are used here. The flow problem is described over a stretching/shrinking surface with the influence of Ohmic heating, non-linear radiation, and a convectively heated surface. Furthermore, the magnetic field strength is applied perpendicular to the direction of the flow. To control the fluid, flow-governing equations are numerically solved by using bvp4c, a built-in approach in MATLAB. For hybrid nanomaterials, the consequence of different physical parameters is discussed graphically and with tabular data. A comparison with previous findings reveals that the present findings are in good agreement. The results revealed that the coefficient of skin friction for the physically stable branch declines over a certain range of shrinking parameters; nonetheless, for the unstable branch, the reverse pattern is discovered. The magnetic force diminishes the flow field and energy dispersion in the upper branch but improves it in the lower branch.

Numerical Simulation of Scalar Mixing and Transport through a Fishing Net Panel

With the rapid development of commercial aquaculture in recent decades, large numbers of submerged cages or pens are clustered in fish farms that are commonly located within inland lakes, reservoirs, and coastal embayments around the world. The submerged structures have significant influence on both the flow fields and mass transport processes in surrounding water bodies. While existing studies have concentrated mainly on the flow blockage effects produced by fish cages, the associated effect on near-field mass transport processes, important for pollution transport and dispersal, remains largely unclear. To address this knowledge gap, a CFD (computational fluid dynamics) model was established using OpenFOAM to investigate the wake characteristics and scalar transport processes through a fishing net panel, as representative of a key component of the fish cage or pen. In this model, the net panel was represented as porous media, and the finite volume method was applied to solve the governing flow equations with the standard k-ε model used for turbulence closure. Experimental data from previous studies were used to calibrate and validate the numerical model, which was applied to different scenarios over a range of net solidities and incoming flow velocities. Overall, the numerical model results demonstrated that porous media schematization could adequately reproduce the blocking effect from the net panel on the mean flow field, as well as the induced changes to scalar transport, with satisfactory accuracy. The flow velocity reduction across the net panel was found to strengthen with increasing net solidity and decreasing incoming velocity, while the scalar concentration decay tended to become enhanced when the incoming velocity was decreased. The lateral profile of the scalar concentration exhibited a self-similar Gaussian distribution with the spreading width of the plume reduced by increasing the incoming velocity. This lateral concentration distribution was minimally affected by the upstream scalar source location relative to the net panel, when adopting the current RANS and porous media modelling approach. The model results provide useful references for the assessment of the environmental impacts and carrying capacity of cage-based fish farming.

Dynamics of slip phenomenon in micropolar nanofluid flowing over a stretchable disk with Arrhenius activation energy

An incompressible, laminar, and electrically conducting micropolar nanofluid flowing above a stretchable disk is examined. The surface is located in the plane [Formula: see text] and the axi-symmetric flow occupies its space in the region [Formula: see text]. The activation energy is considered in concentration equation of the flow model. The uniform temperature and nanofluid volume fraction are assumed at the surface. The approach of similarity transformations is utilized to normalize the governing flow equations. The resulting system is then solved using Runge-Kutta-Fehlberg (RKF-45) solver to obtain the graphical and numerical results of various dimensionless physical variables. It is scrutinized that the porosity parameter is important in the reduction of radial velocity. The microrotation curves are enhanced magnitude wise due to enhancement in the vortex viscosity parameter. It is also perceived that the concentration field is enhanced against the increasing activation energy parameter. Temperature is augmented by increasing the thermophoresis and Brownian movement parameters while the heat transport rate is reduced by the larger thermophoresis and Brownian movement parameters. Concentration field is reduced by the larger Brownian movement parameter while enhanced against the higher thermophoresis parameter.

Extraction Of Temperature Fields From PIV Data Of Turbulent Rayleigh-Bénard Convection Using DNS

To gain insights into the dynamical processes that govern the problem of turbulent Rayleigh-Bénard convection, information about the temperature field---next to the velocity field---is required. In the present study, we exploit the governing flow equations to extract the temperature field from a velocity field measured via tomographic particle image velocimetry. The methods used within this study are derived from algorithms originally used in the framework of direct numerical simulations. First, we enforce the divergence-free condition on the measured velocity field using a fractional-step method based on a Poisson equation. Second, we extract the temperature field from the velocity field via the momentum equation. Third, we extract the temperature field from the velocity field via the solution of the stationary convection-diffusion equation. The extracted velocity field---together with the corresponding divergence-free velocity field---can serve as an initial condition for a direct numerical simulation of the problem. Validating the extraction method based on the stationary convection-diffusion equation with data from direct numerical simulations shows a good correlation coefficient between the extracted and the simulated temperature field (0.86). Although the third method incorporates the ambitious assumption of stationarity, temperature fields are successfully extracted from the measured velocity fields. However, with a correlation coefficient of 0.57, the agreement between the average extracted temperature field and the average temperature field measured in a subvolume of the flow domain is somewhat less than the one found in the simulated data. The latter is presumably attributed not only to the extraction method, but also to the underlying measurement data. Thus, an increase in measurement accuracy in future applications is likely to improve the accuracy of the extraction methods as well.

Suction effect on the dynamics of EMHD casson nanofluid over an induced stagnation point flow of stretchable electromagnetic plate with radiation and chemical reaction

This research examines the radiative characteristics of electromagnetohydrodynamic (EMHD) boundary layer flow with combined thermal transport properties on a reactive stretching surface using Casson nanofluid. The momentum, temperature, and diffusion equations' governing flow equations are reduced to dimensionless forms through variable transformations. The remedies to the resulting equations are numerically generated using the MATLAB bvp4c. Validation against prior research is carried out. The impact of emerging factors on velocity, temperature, concentration patterns, drag force coefficient, Sherwood number, and Nusselt number are graphically represented and in tables. It indicates that when Prandtl number, lower variables of Suction, and Casson parameters increases with a decline in velocity distribution, the contrasting trend enhancement is perceived for modified Hartmann number. In addition, an increment in the modified Hartmann number increases the rate of energy, mass flux, and friction. Conclusively, As Lewis number, Brownian motion, and chemical reaction rise, the thickness of the concentration boundary layer decreases on the stretching Riga surface.

Nonsimilar convective thermal transport analysis of EMHD stagnation Casson nanofluid flow subjected to particle shape factor and thermal radiations

Nanofluids are quite popular among researchers due to their high heat transfer rates, which have significant industrial applications. The primary objective of this article is to give a novel analysis of the two-dimensional electromagnetohydrodynamic (EMHD) stagnation point flow of Casson nanofluid with heat source/sink and thermal radiations. Nanoparticles such as Iron Oxide (Fe2O3) and Gold (Au)) are used with blood as base fluid. Nanomaterials are classified into several categories based on their shapes, properties, and sizes. The effects of shape factors namely sphere, tetrahedron, hexahedron, column, and lamina with various parameters are also included in this analysis. This study presents the implementation of single-phase (Tiwari-Das) model for Casson nanofluid by considering blood as base fluid. Instead of the Buongiorno model, which largely depends on Brownian and thermophoresis diffusion effects for heat transfer analysis. The single-phase model incorporates the volume fraction of nanoparticles for the evaluation of heat transfer. Relying on the Tiwari–Das model for nanofluids, a mathematical framework is constructed. To simplify the governing flow equations, proper nonsimilar conversions are used to appropriately transform the given partial differential system to dimensionless form. The rehabilitated mathematical model is simulated by employing local non-similarity technique via bvp4c. The consequences of sundry parameters against velocity and temperature profiles of Casson nanofluid are presented pictorially. The velocity profile is observed to decrease with increasing Casson fluid parameter values while enhancement is noticed with rising electric field parameter values. The temperature profile improves with increasing magnetic number, nanoparticle concentration, Eckert number, Biot number, and heat generation parameter, whereas it degrades with increasing electric field parameter. Temperature profile is maximum for lamina shaped particle while it has minimum values for sphere shape nanoparticles. The Nusselt number and skin-friction coefficients are also introduced as tools for determining the physical characteristics of Casson nanofluid flow. The obtained results of this model meticulously match those existents in the literature for various limiting constraints. The authors discussed the local non-similarity technique for simulating the dimensionless non-similar structure. To the best of authors observations, no such study for the considered flow model is yet published in literature.

Recent progress in melting heat phenomenon for bioconvection transport of nanofluid through a lubricated surface with swimming microorganisms

The cooling of numerous microelectronic devices has become a need in today's world. Nanofluids, a novel type of heat transport fluid containing nano-sized particles embedded in a host liquid, were developed a few years ago. Impact of ultra-fine nanoparticles with oil, water, or ethylene glycol produces these fluids. Nano-liquids have a variety of applications, including engine cooling, electronic devices, biomedicine, and the manufacture of thermal exchangers. The main objective of current research article is to scrutinizes theoretically, the effects of axisymmetric magnetohydrodynamic flow of bio-convective nanoliquid through a moving surface in the occurrence of swimming microorganisms. The idea of the envisaged model is improved by considering the consequence of thermal radiation, activation energy with generalized slip effects under convective boundaries. The present analysis is developed in the form of mathematical formulation and then solved numerically. The governing flow equations are transmuted into dimensionless nonlinear ODEs system by compatible similarity transformations and then integrated this so-formulated highly nonlinear problem numerically via bvp4c built-in scheme in MATLAB. The significance of influential parameters versus velocity field, temperature profile, concentration field and motile density of microorganism’s profile are examined with the aid of graphs and tabular data. The physical interpretation of outcomes highlight that the velocity receives increment for amplified mixed convection parameter. The thermal profile is found to be reducing with a greater Prandtl number. The concentration profile of nanoparticle boosts up for greater activation energy parameter. The microorganism’s profile is reduced via bioconvection Lewis number. This investigation contains the significance of bioconvection phenomenon, thermal radiation, slip effects and activation energy under convective boundary conditions. These impacts are used in axisymmetric, stagnation point flow of bioconvective magnetized nanofluid containing swimming gyrotactic motile microorganisms over a lubricated surface. The present analysis is not yet published.

Performance analysis of two different sizes of wind turbine rotors based on Nigerian low wind regime

Nigeria can reduce its level of dependency on fossil fuel by making use of wind energy which is an indigenous renewable energy source for electricity generation. For large energy generation, large wind turbine is more preferable over a wind farm of smaller wind turbine units that will generate the equivalent amount of energy because, there will be loss of energy due to transmission and generation system of every turbine unit of the wind farm while the larger turbine has only one transmission and generation units. However, smaller wind turbines are generally more efficient than the bigger ones in terms of wind energy conversion and they are therefore good for small power generation. In this research work the performance of two different sizes of small wind turbine rotors, a 4-metre rotor (D4-Rotor) and a 4/5-metre one (D4/5-Rotor) were studied at 6m/s wind speed using numerical method. The POINTWISE software is used for modelling the rotor blade and meshing the flow domain. The software used for the simulation is ANSYS 20 which uses finite volume method (FVM) of analysis for solving governing flow equations. From the result of performances, the D4/5-Rotor has higher power coefficient (0.2995) than that of D4-Rotor (0.237), and this indicate about 26 per cent performance improvement of the smaller rotor. Conclusively, smaller wind turbines are more efficient than the bigger ones in terms of wind energy conversion and they are therefore good for small power generation especially in low wind regime.

Effects of Joule heating, thermal radiation on MHD pulsating flow of a couple stress hybrid nanofluid in a permeable channel

The current work deals with the pulsatile hydromagnetic flow of blood-based couple stress hybrid nanofluid in a porous channel. For hybrid nanofluid, the fusion of gold (Au) and copper oxide (CuO) nanoparticles are suspended to the blood (base fluid). In this model, the employment of viscous dissipation, radiative heat, and Ohmic heating is incorporated. The governing flow equations (set of partial differential equations) are modernized to set of ordinary differential equations by using the perturbation technique. The nondimensional governing equations are solved by adopting the shooting procedure with the help of the Runge–Kutta fourth-order approach. Temperature distributions of hybrid nanofluid and conventional mono nanofluids are portrayed via pictorial results to claim that the hybrid nanofluid has better temperature distribution than mono nanofluids. Temperature is raising for the magnifying viscous dissipation, whereas the reverse behavior can be found with a rise in couple stress parameter. The heat transfer rate is getting high for the higher values of the Eckert number, and the same behavior is noticed with the uplifting magnetic field.

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

This study examines viscoelastic fractional nanofluid flow through Darcy medium. Memory characteristics due to elasticity are explored with noninteger time derivatives. The unsteady motion of MHD flow is modeled by nonlinear differential equations. Buoyancy forces are incorporated via convection parameters in the flow domain. Fractional relaxation time is considered to control the propagation speed of temperature. A finite difference, along with finite element, a numerical algorithm has been developed for the computation of governing flow equations. Friction coefficient, Sherwood numbers, and Nusselt numbers are computed for the noninteger derivative model. Simulations revealed that noninteger numbers have congruous behavior for concentration, temperature, and velocity fields. It is also noted that heat flux, δ 1 , and mass flux, δ 2 , numbers have contradictory effects on the friction coefficient. Various flows, particularly in polymer industries and electrospinning for the production of nanofibers, can be tackled in a comparable pattern.

Crank Nicholson scheme to examine the fractional-order unsteady nanofluid flow of free convection of viscous fluids.

Fractional fluid models are usually difficult to solve analytically due to complicated mathematical calculations. This difficulty in considering fractional model further increases when one considers nth order chemical reaction. Therefore, in this work an incompressible nanofluid flow as well as the benefits of free convection across an isothermal vertical sheet is examined numerically. An nth order chemical reaction is considered in the chemical species model. The specified velocity (wall's) is time-based, and its motion is translational into mathematical form. The fractional differential equations are used to express the governing flow equations (FDEs). The non-dimensional controlling system is given appropriate transformations. A Crank Nicholson method is used to find solutions for temperature, solute concentration, and velocity. Variation in concentration, velocity, and temperature profiles is produced as a result of changes in discussed parameters for both Ag-based and Cu-based nanofluid values. Water is taken as base fluid. The fractional-order time evaluation has opened the new gateways to study the problem into a new direction and it also increased the choices due to the extended version. It records the hidden figures of the problem between the defined domain of the time evaluation. The suggested technique has good accuracy, dependability, effectiveness and it also cover the better physics of the problem specially with concepts of fractional calculus.

Hydraulic conductivity requirement of granular and geotextile filter for internally stable soils

A filter media satisfying the hydraulic conductivity requirements allows unimpeded seepage without generation of surplus pressure head and decrease of flow rate. This paper proposes design criteria for the hydraulic conductivity requirements of a filter based on governing flow equations. The results have shown that the hydraulic conductivity requirements of pressure head and flow rate are satisfied with a single condition of hydraulic conductivity of filter greater than or equal to the hydraulic conductivity of soil times the hydraulic gradient in soil. The proposed model is developed for saturated conditions and is also applicable for partially saturated conditions. The developed model is validated based on the experimental evaluations of sandy soil with three granular filters and two needle punched non-woven geotextile filters. The developed design criterion applies to internally stable soils with granular and geotextiles filters and offers an improvement in the standards and current design guidelines for protective filters.

Melt Conveying in Single-Screw Extruders: Modeling and Simulation.

Numerous analyses have modeled the flow of polymer melts in the melt-conveying zones of single-screw extruders. While initial studies mainly provided exact analytical results for combined drag and pressure flows of Newtonian fluids, more recently developed, numerical methods seek to deepen the understanding of more realistic flow situations that include shear-thinning and non-isothermal effects. With the advent of more powerful computers, considerable progress has been made in the modeling and simulation of polymer melt flows in single-screw extruders. This work reviews the historical developments from a methodological point of view, including (1) exact analytical, (2) numerical, and (3) approximate methods. Special attention is paid to the mathematical models used in each case, including both governing flow equations and boundary conditions. In addition, the literature on leakage flow and curved-channel systems is revisited.

Coupled Impression of Radiative Thermal Flux and Lorentz Force on the Water Carrying Composite Nanoliquid Streaming Past an Elastic Sheet

Abstract A mathematical model for hybrid nanofluid is proposed to study the influence of oblique magnetic field and thermal radiation on an exponentially elongated sheet. A comparison of the thermal characteristics of the hybrid nanofluid and the mono nanofluids (Al2O3 /water and TiO2/water) is made. The governing flow equations are transformed into a system of ODEs with the assistance of similarity variables and are then computationally addressed using bvp4c.The graphs are displayed for velocity, heat measure, and reduced frictional coefficients for selected flow parameters. Hybrid nanofluid has 1–4% growth in the rate of heat transfer when compared to mono nanofluid while it is 1–4.5% in comparison to viscous fluid for increasing radiation parameter. The outcomes of this work revealed that the heat transfer as a consequence of the dispersion of dual nanomaterials is more promising than the mono nanofluid. To accomplish very effective cooling/heating in industrial and engineering applications, hybrid nanofluids can substitute mono nanofluids.

Fully developed free convective flow of a Bingham fluid in a circular pipe with permeable wall

The present work focuses on the convection flow of a Bingham liquid in a circular pipe with permeable wall using nonlinear density temperature variation (NDT) relationship. The novelty of this communication is to study the impression of yield stress, NDT parameter on convective flow of Bingham liquid in a circular pipe with heat source. The governing flow equations are nonlinearly coupled and therefore complex to solve. Hence, perturbation method is applied to transform into linear ordinary differential equation to obtain the velocity and temperature fields. The expressions for velocity, plug flow velocity, temperature, plug flow temperature and heat transfer rate are derived. The outcomes of heat source parameter, permeable parameter, slip parameter and yield stress parameter on the fluid momentum and dimensionless temperature are obtained. The velocity field decreases with increase in yield stress and for negative values of NDT parameter. The increase in the NDT parameter increases the rate of heat transfer. When the yield stress and permeability parameter , our results concur with [Bhargava, R., and R. S. Agarwal. 1979. “Fully Developed Free Convection Flow in a Circular Pipe.” Indian Journal of Pure and Applied Mathematics 10 (3): 357–365]. The results obtained for the flow characteristics reveal many interesting behaviours that warrant further investigation on the non-Newtonian fluid phenomena and NDT variation.

Unsteady Magnetohydrodynamic Convective Flow of a Nanoliquid via a Radially Stretched Riga Area via Optimal Homotopy Analysis Method

This article presents the investigation of the mechanism of mass and heat transport of an unsteady incompressible electrically conducting viscous convective nanoliquid through a radially stretching Riga plate with viscous dissipation, velocity slip, Brownian motion, Thermophoresis parameter, and first-order chemical reaction. The optimal homotopy analysis technique has been utilized to compute the solutions for the differential equations system after using the similarity variables to the governing flow equations. For physical clarification, the acquired outcomes are illustrated graphically and also in the form of tables. These graphs and tables are used to exhibit physical quantities, namely, Sherwood number, skin friction coefficient, concentration, Nusselt number, temperature and velocity. One of the significant outcomes of the current scrutiny is velocity profile improves for rising values of Hartman number, and this investigation finds several applications in various fields of automobile industries and engineering.

Energy and mass transfer analysis of 3-D boundary-layer flow over a rotating disk with Brownian motion and thermo-phoretic effects

The advancement of nanofluid technology has become an essential tool for investigating thermal conductivity enhancement, which is highly valuable for industrial and engineering applications in many fields including mathematics, physics, engineering, and materials science. This analysis focuses on 3-D boundary-layer flow on nanofluid over a rotating disk by incorporating chemical reaction and thermal radiations effects. One aim of this article is to analyze the energy and mass transport rates for nanofluids. In this study, the Brownian motion and thermophoretic impacts are considered. The governing flow equations are converted to ODE via suitable similarity transformations. The resulting equations were solved via well know technique Keller box method. This analysis revealed that the azimuthal and axial velocities show an inverse pattern against the various values of index factor, n, although the radial velocity has the highest value and decreases significantly. The behavior of the von Karman flow is also recovered for setting the index factor (n = 1). Moreover, it is found that the temperature of nano liquid increases by increasing the Brownian motion and thermophoretic factors.

The use of computational fluid dynamics applications to various flow problems

To deal with any such applications, it is a must to understand the basic form and nature of the governing equations of fluid dynamics. It is imperious to fully understand the basic of numerical discretization that can be applied in equations. This paper aims to present some CFD tools that are the starting point in solving problems related to the field of fluid dynamics. During this work, we will note that anyone CFD technique will not be appropriate for all problems and the diverse mathematical nature of partial differential equations will ensure that some algorithms will best work for hyperbolic equations and others will do best for elliptic equations. In addition, this paper examines precisely how CFD techniques can be used to solve various flow problems. In other words, CFD applications requires the simultaneous knowledge of some major aspects, such as the governing flow equations and their mathematical behavior, aspects of numerical discretization of partial differential equations, also known as finite differences or of integral equations, known as finite volumes. Computational fluid dynamics has a major impact on airplane design and soon to be a critical technology for aerodynamic design with the purpose to enhance the design process for any machine that deals with fluid flow.

A Unified Framework for Governing Equations of Hydrologic Flows

AbstractLaws of conservation of mass, momentum, and energy lead, respectively, to the equations of continuity, momentum, and energy, which are used to mathematically represent hydrologic flow syste...