Flow Field Equations Research Articles

Analysis of Carreau fluid in the presence of thermal stratification and magnetic field effect

Abstract In current article theoretical analysis is executed to examine flow features of Carreau fluid by conferring scintillating aspects of thermal stratification. Flow field equations are attained by incorporating infinite shear rate viscosity and magnetic field effects. Afterwards, the partial differential obtained from the fundamental laws of continuity, momentum and energy containing stratification aspects are attained. These consequent partial differential expressions are so intricate that it seems difficult to solve analytically. Therefore Prandtl layer approximation is capitalized to retain efficient parts of flow narrating differential equations. Then next step is to eradicate the in active parts of partial equations by implementing transformations. The solution structured of reduced system is acquired by self-coded shooting algorithm. The variation in physical profiles with respect to involved parameters is exhibited with the aid of graphs and tables. It is inferred that Carreau fluid behaves in opposite pattern for n > 1 (shear thickening) and n

Numerical analysis on solar air collector provided with artificial square shaped roughness for indirect type solar dryer

Abstract Drying agricultural food products in an indirect type solar dryer (ITSD) is a topic of frequent research. Heat transfer rate to the fluid flow in the solar collector can be enhanced by providing artificial roughness on the surface of the absorber plate. The present work concentrates on air flow and heat transfer characteristics in a solar air collector provided with roughness of square shaped rib over the absorber of ITSD. 2D numerical simulations are performed for flow through the solar air collector for relevant Reynolds number (Re) which ranges from 3800 to 18,000. The Re, relative roughness pitch (P/e), relative roughness height (e/D) and thermo-hydraulic performance parameter (THPP) are chosen as design variables. The governing equations for turbulent flow field are solved using RNG k–ɛ turbulence model. The simulation results are compared with smooth duct which shows that the duct with roughened surface enhances the heat transfer and friction factor (fr) by 2.13 and 3.54 times, respectively. The solar air collector with roughness of square shaped rib with P/e = 7.14 gives better THPP of 1.45 at Re of 15000. It is found that the additional drying chamber temperature of 4 K and heat gain of 106% when the dryer is upgraded to roughened surface from smooth surface. The present simulation model is validated with experimental outcomes of existing literature and good agreement is noticed.

Second Law Analysis of MHD Squeezing Flow of Casson Fluid Between Two Parallel Disks

AbstractThe present article deals the entropy generation due to heat and mass transfer of an unsteady MHD flow of a Casson fluid squeezed between two parallel disks. The upper disk is taken to be impermeable and the lower one is porous. The flow field equations are reduced to non-linear ordinary differential equations by using similarity transformations and the resulting ODE problem is solved by shooting technique with Runge-Kutta 4thorder method. The effects of various non dimensional fluid and geometric parameters on the velocity components, temperature, concentration, entropy generation number, Bejan number, skin friction and Nusselt number are illustrated through graphs and tables. It is noticed that the temperature of the fluid is enhanced with Eckert number, whereas the concentration of the fluid decreased with Casson fluid parameter. The present study is applicable to nuclear engineering cooling systems, wire and blade coating, extrusion of polymer fluids, optical fibers, magnetohydrodynamics and optimization of chemical engineering processes.

Parametric Study on Electric Field-Induced Micro-/Nanopatterns in Thin Polymer Films.

Electric field-induced micro-/nanopatterns in thin polymer films, sometimes referred as electrohydrodynamic patterning, is a promising technique to fabricate micro-/nanostructures. Extensive attention has been attracted because of its advantages in microcontact (easy demolding) and low cost. Although considerable work has been done on this technique, including both experimental and theoretical ones, there still appears a requirement for understanding the mechanism of electrohydrodynamic patterning. Thus, we systematically studied the effect of different parameters on electrohydrodynamic patterning with a numerical phase field model. Previous researchers usually employed lubrication approximation (i.e., long-wave approximation) to simplify the numerical model. However, this approximation would lose its validity if the structure height is on the same scale or larger than the wavelength, which occurs in most cases. Thus, we abandoned the lubrication approximation and solved the full governing equations for fluid flow and electric field. In this model, the deformation of polymer film is described by the phase field model. As to the electric field, the leaky dielectric model is adopted in which both electrical permittivity and conductivity are considered. The fluid flow together with electric field is coupled together in the framework of phase field. By this model, the effect of physical parameters, such as external voltage, template structure height, and polymer conductivity, is studied in detail. After that, the governing equations are nondimesionalized to analyze the relationship between different parameters. A dimensionless parameter, electrical Reynolds number ER, is defined, for which, a large value would simplify the electric field to perfect dielectric model and a small value leads it to steady leaky model. These findings and results may enhance our understanding of electrohydrodynamic patterning and may be a meaningful guide for experiments.

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part II: verification and numerical example

A fully implicit, fully coupled, and fully consistent finite element framework has been formulated in part I of this work for modeling reservoir compaction through linearizing coupled solid and flow field equations and constructing a local material integrator. In part II of this work, we focus on verification and performance analysis of our numerical formulation and computer implementation using several numerical examples. First, we design a cube problem in triaxial compression to verify our numerical formulation and computer code implementation especially for rock formation in compaction using cap plasticity models. The finite element prediction on stresses is compared with the analytical solution. The second problem we select is a strip footing problem popular in the geotechnical area where the evolution of soil consolidation degrees following the diffusion of pore pressure is the main interest. In this example, we demonstrate a good performance of the proposed numerical formulation on solving different shear and compaction-dominated deformation behaviors by varying the footing length. Importantly, an extremely sharp cap model based on real experimental data for Leda clays, a challenging cap model, is successfully applied in this footing problem. Our focus in this work is to model field reservoirs undergoing serious compaction. A reservoir with complex payzone geometries, multiple horizontal wells, and cap plasticity models with sharp cap surfaces has been successfully solved using our fully implicit formulation. The last example is to model a horizontal wellbore damage problem. Finally, the sensitivity of predicted subsidence to nonlinear flow model, cap hardening parameters, and Lode angles have been systemically investigated and documented in detail, which can provide a constructive guidance on how to successfully model field reservoir compaction problems with cap plasticity models.

Simulation of dendritic growth of magnesium alloys with fluid flow

Fluid flow has a significant impact on the microstructure evolution of alloys during solidification. Based on the previous work relating simulation of the dendritic growth of magnesium alloys with hcp (hexagonal close-packed) structure, an extension was made to the formerly established CA (cellular automaton) model with the purpose of studying the effect of fluid flow on the dendritic growth of magnesium alloys. The modified projection method was used to solve the transport equations of flow field. By coupling the flow field with the solute field, simulation results of equiaxed and columnar dendritic growth of magnesium alloys with fluid flow were achieved. The simulated results were quantitatively compared with those without fluid flow. Moreover, a comparison was also made between the present work and previous works conducted by others. It can be concluded that a deep understanding of the dendritic growth of magnesium alloys with fluid flow can be obtained by applying the present numerical model.

Axisymmetric flow and heat transfer of the Carreau fluid due to a radially stretching sheet: Numerical study

The prime objective of this article is to study the axisymmetric flow and heat transfer of the Carreau fluid over a radially stretching sheet. The Carreau constitutive model is used to discuss the characteristics of both shear-thinning and shear-thickening fluids. The momentum equations for the two-dimensional flow field are first modeled for the Carreau fluid with the aid of the boundary layer approximations. The essential equations of the problem are reduced to a set of nonlinear ordinary differential equations by using local similarity transformations. Numerical solutions of the governing differential equations are obtained for the velocity and temperature fields by using the fifth-order Runge–Kutta method along with the shooting technique. These solutions are obtained for various values of physical parameters. The results indicate substantial reduction of the flow velocity as well as the thermal boundary layer thickness for the shear-thinning fluid with an increase in the Weissenberg number, and the opposite behavior is noted for the shear-thickening fluid. Numerical results are validated by comparisons with already published results.

Influence of electromagnetic stirrer position on fluid flow and solidification in continuous casting mold

• Numerical investigation of solidification behavior with EMS position is proposed. • Breaking of solidified layer was observed by shifting the EMS position downward. • With EMS application, liquid fraction values were decreased in mold core region. • Tangential velocity values were found to be maximum near solidified shell. A computational study of the effect of stirrer position on fluid flow and solidification in a continuous casting billet mold with in-mold electromagnetic stirring has been carried out. The numerical investigation uses a full coupling method in which alternating magnetic field equations are solved simultaneously with the governing equations of fluid flow and heat transfer. An enthalpy-porosity technique is used for the solidification analysis while the magnetohydrodynamics technique is used for studying the fluid flow behavior under the electromagnetic field. The streamline, liquid fraction, and solid shell thickness at the mold wall have been predicted with and without EMS application at different positions along the length of the mold. Recirculation loops are seen to be formed above and below the stirrer position when fluid flow and electromagnetic field equations were solved, without incorporating the solidification model. Application of the solidification model interestingly resulted in the reduction of the size of the recirculation loops formed. The tangential component of velocity of the fluid near the solidification front, stirring intensity and the effective length of stirring below the stirrer decrease as the stirrer position is moved downwards. Significant changes in characteristics of solid shell formation like delay in initiation of solidification at the mold wall and formation of a gap in the re-solidified shell have been observed with change in stirrer position.

Influence of thermophoresis and induced magnetic field on chemically reacting mixed convective flow of Jeffrey fluid between porous parallel plates

In the present article, the effect of thermophoresis on an unsteady two-dimensional laminar incompressible mixed convective chemically reacting flow and heat transfer of Jeffrey fluid between two parallel porous plates under the influence of the induced magnetic field is considered. The flow is generated due to periodic injection or suction at the plates. It is assumed that the non-uniform temperature and concentrations are varying periodically with time at the plates. The flow field equations are reduced into nonlinear ordinary differential equations by using suitable similarity transformations and solved by shooting method. The results are analysed for non-dimensional velocity components, temperature distribution, concentration, induced magnetic field, skin friction, heat and mass transfer rates with respect various fluid and geometric parameters in details through graphs and tables. It is observed the temperature of the fluid is enhanced with inverse Darcy parameter, whereas the concentration of the fluid decreases with increasing of Deborah number. Also the induced magnetic field increases with thermophoresis whereas it decreases with increasing of magnetic parameter. The present results have the better agreement with published work for the Newtonian case.

Numerical solution procedure for Hall electric field of the hypersonic magnetohydrodynamic heat shield system

Magnetohydrodynamic (MHD) heat shield system is a novel-concept thermal protection technique for hypersonic vehicles, which has been proved by lots of researchers with both numerical and experimental methods. Most of researchers neglect the Hall effect in their researches. However, in the hypersonic reentry process, the Hall effect is sometimes so significant that the electric current distribution in the shock layer can be changed by the induced electric field. Consequently, the Lorentz force as well as the Joule heat is varied, and thus the efficiency of the MHD heat shield system is affected.In order to analyze the influence of Hall effect, the induced electric field must be taken into consideration. According to the weakly-ionized characteristics of hypersonic flow post bow shock, the magneto-Reynolds number is assumed to be small. Therefore, the Maxwell equations are simplified with the generalized Ohm's law, and the induced electric field is governed by the potential Possion equation. Numerical methods are hence established to solve the Hall electric field equations in the thermochemical nonequilibrium flow field. The electric potential Poisson equation is of significant rigidity and difficult to solve for two reasons. One is that the coefficient matrix may not be diagonally dominant when the Hall parameter is large in the shock layer, and the other is that this matrix including the electric conductivity is discontinuous across the shock. In this paper, a virtual stepping factor is included to strengthen the diagonal dominance and improve the computational stability. Moreover, approximate factor and alternating direction implicit method are employed for further improving the stability. With these methods, a FORTRAN code is written and validated by comparing the numerical results with the analytical ones as well as results available from previous references. After that, relation between the convergence property and the virtual stepping factor is revealed by theoretical analysis and numerical simulations. Based on these work, a local variable stepping factor method is proposed to accelerate the iterating process. Results show that the convergence property is closely related to the mesh density and Hall parameter, and there exists a best stepping factor for a particular mesh as well as a particular Hall parameter. Since the best stepping factor varies a lot for different meshes and different Hall parameter, its appropriate value is hard to choose. The best value of stepping factor coefficient still exists in the local step factor method, but its value range is relatively smaller. More importantly, the local stepping factor method yields better convergence property than the regular constant one when employing a locally refined mesh.

Numerical Exploration of Non-Newtonian Polymeric Boundary Layer Flow over an Isothermal Sphere

This paper examines the nonlinear steady state boundary layer flow and heat transfer of an incompressible Jeffery non-Newtonian fluid from an isothermal sphere. The governing partial differential equations of the flow field are converted to a system of non-linear coupled non-similarity ordinary differential equations. Finite difference technique followed by Keller Box method, the system is solved numerically. The numerical code is validated with previous studies. The effects of the various physical parameters countered in the flow field on the velocity, temperature as well as the skin friction coefficient and the rate of heat transfer near the wall are computed and illustrated graphically. It is found that increasing suction decelerates the flow and also cools the boundary layer i.e. reduces temperatures. With increasing tangential coordinate the flow is also decelerated whereas the temperatures are enhanced. The simulation is relevant to polymer coating thermal processing. Polymeric enrobing flows are important in industrial manufacturing technology and process systems. Such flows are non-Newtonian. Motivated by such applications, we did the present problem.

Unsteady MHD Free Convective Flow Past an Inclined Parabolic Accelerated Plate with Hall Current, Radiation Effects and Variable Temperature in a Porous Medium

We analyze the effects of hall current and radiation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an inclined parabolic accelerated plate in a porous medium by applying a transverse magnetic field which makes an angle α to the inclined plate.The fluid is assumed to be viscous, incompressible and electrically conducting with a strong magnetic field. Using the modified Ohm’s law and the Bossinesq approximation the governing equations of the problem are reduced to local non-similarity boundary layer equations using suitable transformation.The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference method for different values of governing flow parameters. The velocity and temperature profiles are shown through graphs.

Numerical investigation of the interaction, transport and deposition of multicomponent droplets in a simple mouth-throat model

A basic analysis of inhaled multicomponent droplet-vapor interaction and subsequent aerosol deposition is very important for the understanding of natural phenomena as well as for health-care related applications. Employing a highly idealized mouth-throat (MT) model as a test bed, the transport and deposition mechanisms of a water-droplet are simulated, considering ethanol, sodium chloride and fluorescein as components. The flow-field equations are solved with a validated transition SST model which can predict the effects of flow rate, relative humidity (RH), and wet vs. dry airway walls on aerosol deposition efficiency (DE). The simulation results indicate that the hygroscopic growth of sodium chloride particles is sensitive to the saturation pressure of water vapor. A high flow rate decreases the RH in the airways as well as the average growth ratios of deposited and escaped droplets; but, still increases the DE. When compared to a dry boundary condition, the wet airway-wall increases the DE up to 4.6% when RH=30% and the flow rate is 60L/min. It also increases the average growth ratio of deposited droplets notably, i.e., larger than 0.5 for most conditions, while its effect on the average growth ratio of deposited droplets is not apparent. A high inlet RH can significantly enhance the hygroscopic growth of the droplets and DE, especially when it is larger than the RH threshold for the hygroscopic component. Besides, it can elevate the growth ratios of deposited and escaped droplets at the same time, which could be utilized to reduce the deposition of submicron hygroscopic aerosol in the upper airway.

Flow-field differences and electromagnetic-field properties of air and N2 inductively coupled plasmas

A numerical model for simulating air and nitrogen inductively coupled plasmas (ICPs) was developed considering thermochemical nonequilibrium and the third-order electron transport properties. A modified far-field electromagnetic model was introduced and tightly coupled with the flow field equations to describe the Joule heating and inductive discharge phenomena. In total, 11 species and 49 chemical reactions of air, which include 5 species and 8 chemical reactions of nitrogen, were employed to model the chemical reaction process. The internal energy transfers among translational, vibrational, rotational, and electronic energy modes of chemical species were taken into account to study thermal nonequilibrium effects. The low-Reynolds number Abe-Kondoh-Nagano k-ε turbulence model was employed to consider the turbulent heat transfer. In this study, the fundamental characteristics of an ICP flow, such as the weak ionization, high temperature but low velocity in the torch, and wide area of the plasma plume, were reproduced by the developed numerical model. The flow field differences between the air and nitrogen ICP flows inside the 10-kW ICP wind tunnel were made clear. The interactions between the electromagnetic and flow fields were also revealed for an inductive discharge.

Influence of Inclined Magnetic Field on a Mixed Convective UCM Fluid Flow Through a Porous Medium with Thermophoresis and Brownian Motion

In this paper, an incompressible electrically conducting mixed convective upper convected Maxwell fluid flow in a porous medium between parallel plates under the influence of inclined magnetic field, thermophoresis and Brownian motion is considered. Assume that there is periodic injection and suction at the lower and upper plates respectively. The temperature and concentration at the lower and upper plates are varying periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations by using similarity transformations and a numerical solution has been obtained by using shooting technique with fourth order Runge–Kutta method. The velocity components, temperature distribution and concentration with respect to different fluid and geometric parameters are discussed in detail and presented in the form of graphs. It is observed that the temperature of the fluid is enhanced with Brownian parameter whereas the concentration decreases with increasing thermophoresis parameter. The present results are compared with the existing literature and are found to be good agreement.

Influence of Cross-Diffusion on Slip Flow and Heat Transfer of Chemically Reacting UCM Fluid between Porous Parallel Plates with Hall and Ion Slip Currents

The present paper deals with the Hall and ion slip currents on an incompressible unsteady free convection flow and heat transfer of an upper convected Maxwell fluid between porous parallel plates with Soret and Dufour effects by considering the velocity slip and convective boundary conditions. Assume that there are periodic injection and suction at the lower and upper plates, respectively. The temperature and concentration at the lower and upper plates change periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations by using similarity transformations and a semi-analytical-numerical solution has been obtained by the differential transform method. The velocity components, temperature distribution, and concentration with respect to different fluid and geometric parameters are discussed in detail and presented in the form of graphs. It is observed that the Biot number increases the temperature and concentration of the fluid. Further, the concentration of the fluid is enhanced whereas the temperature decreases with increasing slip. The present results are compared with the existing literature and are found to be in good agreement.

The Effects of Soret and Dufour on a Steady MHDFree Convection Flow over an Inclined Porous Plate with Viscous Dissipation

This paper deals with the effects of Soretand Dufouron a steady MHD free convection flow over an inclined porous plate with viscous dissipation. The models were non-dimensionalisedand the following parameters arise in the flow: Soret number Sr, Dufour number Du, Prandtl number Pr, magnetic parameter M, Schmidtl number Sc, radiation parameter R, permeability of porous medium K, thermal Grashof number Gr, solutalGrashof number Gm, Eckert number Ec and inclination angle . The influences of these parameters which control the flow were analysedand given a place in this work. The dimensionless governing equations of flow field are solved numerically by collocation weighted residual method. The effects of various parameters on the velocity, temperature and concentration profiles are discussed and displayed graphically

Hyperbolicity Criteria for System of Field Equations of One-Dimensional Two-Phase Flow with Compressible Components

As part of an effort to improve the stability of the RELAP5-3D computer code, a characteristic analysis of the governing differential equations for a compressible, one-dimensional, two-fluid, nonhomogeneous nonequilibrium model is presented. The study is limited to the case when small timescale relaxation terms can be neglected, and therefore, a two-pressure model can be reduced to an equivalent volume-average, one-pressure model. The primary focus of the work is to consider flow with compressible components and to compare hyperbolicity criteria with the results of commonly used limitations of flow with incompressible phases. Based on a review of current achievements in this area, a generic form of momentum conservation equations that are invariant from the definition of differential interfacial terms is suggested. New analytical criteria of strict hyperbolicity of the governing system for the compressible two-phase-flow model are developed and supported by numerical calculations and comparisons. Furthermore, overrestriction of results of eigenvalue analysis based on an incompressible components model is demonstrated.The derived criteria are applied to RELAP5-3D in the form of modifications to momentum equations. Upon implementing the developed criteria, the simulation results show marked improvement in stability without otherwise affecting the calculations. Theimportance of well-posedness of the initial value problem for numerical solution stability is demonstrated.

Influence of the air inlet configuration on the performances of a paraglider open airfoil

A finite volume flow solver was used to solve the Reynolds averaged Navier-Stokes equations for the 2D flow field on a paraglider open airfoil. The canopy was assumed to be smooth, rigid and impermeable. The parametric study performed concerns the position and the width of the air inlet at the leading edge. The range of values used covers the air inlet geometries from classical ram-air parafoil to sport paraglider airfoil, including transition towards the full closed baseline airfoil. Results are focused both on lift and drag coefficients for performance analysis and on the internal pressure coefficient, which can be critical for a real flexible wing regarding the risk of collapse. Depending on the appearance of a separation bubble over the upper edge, two well separated behaviours can be observed. The first behaviour is more typical of ram-air parachutes and the second one corresponds to the design of performance paragliders. For paraglider configurations, it is shown that the aerodynamic coefficients of the open airfoil can be easily deduced from the pressure coefficients of the baseline airfoil without solving the internal flow.

Influence of the air inlet configuration on the performances of a paraglider open airfoil

A finite volume flow solver was used to solve the Reynolds averaged Navier-Stokes equations for the 2D flow field on a paraglider open airfoil. The canopy was assumed to be smooth, rigid and impermeable. The parametric study performed concerns the position and the width of the air inlet at the leading edge. The range of values used covers the air inlet geometries from classical ram-air parafoil to sport paraglider airfoil, including transition toward the full closed baseline airfoil. Results are focused both on lift and drag coefficients for performance analysis and on the internal pressure coefficient which can be critical for a real flexible wing regarding the risk of collapse. Depending on the appearance of a separation bubble over the upper edge, two well separated behaviours can be observed. The first behaviour is more typical of ram-air parachutes and the second one corresponds to the design of performance paragliders. For paraglider configurations, it is shown that the aerodynamic coefficients of the open airfoil can be easily deduced from the pressure coefficients of the baseline airfoil without solving the internal flow.