Flow Of Newtonian Fluid Research Articles

MINOR HEAD LOSS ANALYSIS OF LAMINAR FLUID FLOW IN COMPLEX GEOMETRIES

Minor head loss occurs in most hydraulic equipment because the flow is affected by a shape change. Head loss analysis is essential in designing and fabricating hydraulic equipment and systems. In the general case, the evaluation of head losses is challenging and usually done by experimental methods. Recently, the calculation has been more convenient using the computational fluid dynamics (CFD) method. This article employs the finite element method (FEM) to evaluate the local hydraulic losses in complex geometries discretized by unstructured mesh. The method is applied to the laminar flow of Newtonian fluid. First, the code is validated by comparing the numerical solution with experimental data and previous numerical results. The code is then employed to simulate different problems, including a complex geometry that mimics the control valve in hydraulic systems. Simultaneously, the minor loss coefficient is calculated for different Re numbers. From the results, the minor loss coefficient is large for low Re, and can be up to 700 for Re = 10 of complicated geometry. For a high Re, the minor loss coefficient is rapidly decreased and close to the value of a turbulent model.

Finite element method for the heated Newtonian fluid inside a connected optical cavities

The engineers are fascinated in fluid flows and heat transfer in engineering optics and devices. For such purposes, fluid flows are computed in different geometries. The engineers normally look for reduced heat transfer, enhanced cooling rate and reduced friction drag. Thus, the focus of the present article is to undertake the flow of viscous or Newtonian fluid through joined cavities which is very important in many engineering fields. The Navier-Stokes equations are operated for studying behavior of flow, while Fourier's law of heat conduction is employed for the analysis of heat flow in connected cavities. The consequences show that high pressure, lowest velocity and high temperature are observed at the thin connection of cavities.

Simulation of High-Viscosity Generalized Newtonian Fluid Flows in the Mixing Section of a Screw Extruder Using the Lattice Boltzmann Model.

The mixing quality of polymer melts in the mixing section of a single-screw extruder and an injection molding machine has considerable effects on the properties of the molded products. Therefore, the study of the flow field of polymer melts in the mixing section is of great importance. The lattice Boltzmann method (LBM) exhibits unique advantages in simulating non-Newtonian fluids. Many researchers have used LBM to study the flow of medium- and low-viscosity fluids. In their studies, the Reynolds number of fluid flows is generally moderate. However, polymer melts are typical high-viscosity fluids, and their flow Reynolds number is generally very small. The single-relaxation-time lattice Boltzmann method (SRT-LBM) has been used previously to study the flow field of power law fluids in the mixing section. Herein, the flow field of high-viscosity generalized Newtonian fluids in the mixing section of a single-screw extruder is studied using SRT-LBM, the two-relaxation-time lattice Boltzmann method (TRT-LBM), and the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). Through comparison, TRT-LBM has been found to exhibit obvious advantages regarding stability, calculation accuracy, calculation efficiency, and selection of simulation parameters. The TRT-LBM is more suitable for studying high-viscosity generalized Newtonian fluids than SRT-LBM and MRT-LBM. SRT-LBM has low computational efficiency when simulating high-viscosity generalized Newtonian fluids, and instability is easily caused when the fluid has a yield stress. For MRT-LBM, only by studying the relaxation parameters can its advantages be fully utilized. However, optimizing the accuracy and stability of the MRT-LBM via parameter research and linear stability analysis is difficult. For non-Newtonian fluids, it is difficult to optimize the relaxation parameters to make the MRT-LBM more stable and accurate than the TRT-LBM. It is difficult for the MRT-LBM to realize its potential when simulating high-viscosity generalized Newtonian fluids. In addition, we studied the flow pattern in the cross section of the screw channel and compared it to the results reported in previous studies.

Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings

A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving p-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper also provides a relatively complete picture of our main results in two regards: problems with nonlinearity is regular with respect to the gradient variable; and asymptotically regular problems, whose nonlinearity satisfies a particular structure near infinity. For such Stokes-type systems, we derive regularity estimates for both velocity gradient and its associated pressure in two special classes of function spaces: the generalized Lorentz and ψ-generalized Morrey spaces.

Asymptotic analysis of Jeffreys–Newtonian fluids flowing through a composite vertical porous layered channel: Brinkman–Forchheimer model

This study examines the flow of a Newtonian fluid enclosed between two non-Newtonian Jeffreys fluids with viscosity that varies with temperature within a composite vertical channel. Including a corotational Jeffreys liquid allows for considering stress dependence on the present deformation rate and its history. The proposed study's framework comprises three distinct regions, wherein the intermediate region governs Newtonian fluid flow under temperature-dependent viscosity. However, the outer layers oversee the flow of Jeffreys fluids within the porous medium, demonstrating temperature-dependent viscosity. The Brinkman–Forchheimer equation is employed to establish the governing equations applicable to both low and high permeabilities of the porous medium. This equation is nonlinear, making it challenging to find an analytical solution. Therefore, the regular and singular perturbation methods with matched asymptotic expansions are applied to derive asymptotic expressions for velocity profiles in various regions. The hydrodynamic quantities, such as flow rate, flow resistance, and wall shear stresses, are determined by deriving their expressions using velocities from three distinct regions. The graphical analysis explores the relationships between these hydrodynamic quantities and various parameters, including the Grashof number, Forchheimer number, viscosity parameter, Jeffreys parameter, conductivity ratio, effective viscosity ratio, absorption ratio, and the presence of varying thicknesses of different layers. An interesting finding is that a more pronounced velocity profile is noticed when the permeability is high and the viscosity parameter of the Newtonian region, denoted as α2, is lower than that of the surrounding area. This heightened effect can be linked to a relatively more significant decrease in the viscosity of the Jeffreys fluid, represented by μ1, as compared to the viscosity of the Newtonian fluid, μ2, as the temperature increases. The outcomes of this research hold special significance in situations like the extraction of oil from petroleum reserves, where the oil moves through porous layers with varying viscosities, including sand, rock, shale, and limestone.

Flow and heat transfer analysis of laminar flow in hypersonic aircraft with variable specific heat capacity at small attack angles

Purpose As to different angles of attack and nonlinear problems caused by high temperatures in coexisting hypersonic aircraft, people mainly rely on fluid software for research but lack analysis of flow mechanisms. Owing to computational difficulties, few people use numerical algorithms to combine them for discussion. Hence, this study aims to make a deep inquiry into the laminar flow and heat transfer of compressible Newtonian fluid in hypersonic aircraft with small attack angles. Design/methodology/approach In this paper, on the basis of mass, momentum and energy conservation laws, the governing equations of the hypersonic boundary layer are established. Viscosity, specific heat capacity and thermal conductivity are considered nonlinear functions concerning temperature. In virtue of the MacCormack finite difference method, the stationary numerical solutions are solved directly, and the validity of the algorithm is verified. Findings The results demonstrate that at Mach number 5, compared to the 0° attack angle, the maximum temperature near-wall at the 3° attack angle increases by about 25%. An enjoyable phenomenon is discovered, where the position corresponding to the maximum wall shear force shifts back as the attack angle and Mach number increase. The relationship between the near-wall maximum temperature versus attack angle and Mach number is fitted through numerical calculation results. Originality/value Empirical formulas can be used to estimate heat transfer characteristics at small attack angles, which will guide the design of aircraft thermal protection systems.

Lid driven cavity flow with two porous square obstacles

The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow.

Polar-plane flow in porous annular ducts with accelerated rotating walls. A region of stagnation inside the fluid

Abstract The steady laminar flow of an incompressible Newtonian fluid in a porous annular duct with accelerated rotating walls is investigated. The flow is located in the polar plane and is driven by suction and injection at the walls. As required by conservation of mass with zero axial velocity, the fluid is injected into one of the cylinders, which becomes the upstream cylinder, and suctioned into the other, which represents the downstream cylinder. Only the case of the downstream cylinder at rest is examined. The duct gap ratio, the velocity ratio comparing the radial and azimuthal velocities, the Reynolds number, and the velocity coefficient that compares the fluid velocity at the upstream and downstream cylinders are the four parameters of the problem. The purpose of this research is to identify the prerequisites for the flow’s existence and determine how the aforementioned variables affect the flow velocity and pressure gradients at a fixed Reynolds number. The Navier–Stokes equations are replaced by the polar-plane vorticity equation, which is solved using the similarity-solutions method. The shooting technique, including the fourth-order Runge–Kutta algorithm, is used to produce numerical solutions. From the findings, physical understandings of the flow are derived. More specifically, we discover an unexpected interior zone where the fluid is perpetually at rest even while flow is present. The only solution found corresponds to the case of the inner cylinder upstream and rotating provided that the velocity ratio does not exceed the threshold of 0.1 with a velocity coefficient greater than 1.

Numerical and regression analysis of horizontal magnetic field in slippery nanofluid flow with Arrhenius activation energy

The significance of magnetic field in the fluid flow models is important in order to stabilize the flow stream. The present work explores the horizontal magnetic field influences in steady-state laminar swirl Newtonian nanomaterial fluid flow triggered by disk rotation. To categorize the thermal performance, a well-established theory of nanofluid (Buongiorno model) is implemented in flow phenomenon. Thermal radiative term is demonstrated in the energy transportation equation. The impact of chemical species is investigated by the expression of AAE (Arrhenius activation energy). The flow model is normalized in accordance with von Kármán similarity transformations. The resulting normalized system of equations is converted to a system consisting of first order differential equations and then is solved by Runge-Kutta-Fehlberg (RKF-45) built-in method. The physical results are discussed graphically on velocity, temperature, and concentration streams. Shear stresses, local Nusselt and Sherwood numbers are calculated at the surface of the rotating disk. In addition, the regression process is utilized to address the parameters impacts on the variables. The stabilizing impact of magnetic field along radial direction is noticed by means of direction angle close to 00 and 900. Velocity profiles in radial direction are enhanced by the velocity slip parameter. Concentration filed is increased through activation energy. The inclination angle has a weak impact on heat transfer rate. Finally, a comparison is established with the published literature in limiting scenario.

Numerical study of Newtonian laminar Flow around circular and square cylinders

In this study, we present a novel algorithm designed to address the computational challenges posed by the governing equations of incompressible Newtonian fluid flow, particularly of bluff bodies of circular and square in a channel. This a significant innovation algorithm is developed based on the Taylor–Galerkin/Pressure-Correction finite element method. Notably, a pivotal element of this approach involves the implementation of the two-step Lax–Wendroff scheme to resolve the momentum equation. To assess the efficacy of our novel algorithm, we conducted a comprehensive analysis using a standard benchmark scenario; the initiation of Poiseuille flow through an axisymmetric rectangular channel encompassing bluff bodies. In this context, our investigation centered on the influence of the Reynolds number (Re) on various pertinent variables. The results obtained from our study underscore the remarkable congruence between the outcomes generated by the new algorithm and established physical principles, as well as findings from prior research, as evidenced through thorough comparisons with the existing body of literature. This research represents a significant stride toward advancing our understanding of fluid dynamics and computational methodologies in this domain.

Numerical study of Newtonian fluid flow characteristics in triangle enclosure considering various obstacle geometries

This article investigates the effect of cylindrical obstacles with different dimensions inside the triangular cavity on natural convection heat transfer. This study considers three cavities, each of which has one, two, and three-cylinder barriers embedded inside it. The use of one or two cylindrical barriers has been investigated in many research, but in this research, in addition to the number of cylindrical barriers, their dimensions and sizes have been changed, and an alternating temperature function has been used at the base of the cavity. The considered nanofluid is Al2O3H2O, which contains aluminum oxide nanoparticles with a concentration of 5 %. In all three cavities, the velocity of the nanofluid in the walls is zero. The temperature in the lateral sides of the cavity has low-temperature faces. Instead of being constant or adiabatic, the temperature at its base is an alternating function (sinusoidal function with a frequency of 1.0 Hz.). In contrast, it is considered that the surfaces of the obstacles of the cylinders have zero velocity and are adiabatic. In this study, the governing equations of nanofluid flow behavior have been solved using the Galerkin finite element method and analyzed in the Rayleigh number range of 103 to 105. Because triangular cavities with different ratios are used to optimize multiple objectives and increase thermal performance in microchannels, the results show that the multiplicity of cylindrical obstacles in the triangular cavity causes the expansion of the nanofluid velocity range in the whole area, which itself causes the increase of the heat transfer surface, and with the increase of the Rayleigh number and the buoyancy force, the magnitude of the velocity inside the triangular cavity increases. In the triangular cavity containing three cylindrical barriers, the nanofluid's velocity range is low, but according to the velocity contours, its extent is greater than the other two cavities. Also, the average Nusselt number in this cavity is higher than other cavities.

Cortex-driven cytoplasmic flows in elongated cells: fluid mechanics and application to nuclear transport in Drosophila embryos.

The Drosophila melanogaster embryo, an elongated multi-nucleated cell, is a classical model system for eukaryotic development and morphogenesis. Recent work has shown that bulk cytoplasmic flows, driven by cortical contractions along the walls of the embryo, enable the uniform spreading of nuclei along the anterior-posterior axis necessary for proper embryonic development. Here, we propose two mathematical models to characterize cytoplasmic flows driven by tangential cortical contractions in elongated cells. Assuming Newtonian fluid flow at low Reynolds number in a spheroidal cell, we first compute the flow field exactly, thereby bypassing the need for numerical computations. We then apply our results to recent experiments on nuclear transport in cell cycles 4-6 of Drosophila embryo development. By fitting the cortical contractions in our model to measurements, we reveal that experimental cortical flows enable near-optimal axial spreading of nuclei. A second mathematical approach, applicable to general elongated cell geometries, exploits a long-wavelength approximation to produce an even simpler solution, with errors below [Formula: see text] compared with the full model. An application of this long-wavelength result to transport leads to fully analytical solutions for the nuclear concentration that capture the essential physics of the system, including optimal axial spreading of nuclei.

Numerical Analysis of Inertia Effects on Pressure and Flow Patterns in Unidirectional and Reversed Newtonian Fluid Flows within a Channel

Numerical Analysis of Inertia Effects on Pressure and Flow Patterns in Unidirectional and Reversed Newtonian Fluid Flows within a Channel

A parametric study on the analysis of thermosolutal convection for magneto-hydrodynamics dependent viscous fluid

This article explores the influence of Joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The impact of thermal radiation is also considered. The effects of mass and heat transfer on the squeezing flow of Newtonian fluids are observed and modelled using the four fundamental governing equations of fluid flow: the mass equation, momentum equation, concentration equation, and energy equation. Using the appropriate similarity transformations, the resultant non-linear partial differential equations are then transformed into ordinary differential equations. The analytical strategy is developed using the homotopy analysis method to obtain the series solution. The influence of several physical parameters, including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter, and the Schmidt number, on the velocity profile, energy, and concentration are also discussed through graphs. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also found that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y- and z-axis, whereas the velocity field along the x-axis exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution. Further, graphs and tables are presented to illustrate an error analysis.

Direct numerical simulation of fluid/solid particles flow inside a channel

The modeling of moving solid particles in fluid flow has been the focus of many studies and has succeeded to attract significant attention from researchers. However, commonly used modeling approaches such as discrete element modeling (DEM) and direct numerical simulations (DNS) lack simplicity and have been computationally intensive. The aim of this paper is to develop a new approach to simulate solid transport in an incompressible Newtonian fluid flow. This method is based on the Finite element method with penalization of the deformation tensor. The fluid behavior is governed by the Navier-Stokes equations within the investigation domain. To take into account collisions, we present an algorithm which allows us to handle contacts between rigid particles. In this paper, 2D fluid/particles flow simulations are performed; the results are validated by comparison with results from other methods. We attempt to simulate the conveying of solid particles behavior of circular particles in a fluid flow inside a pipe. The numerical tests show that the present method provides a very efficient approach to directly simulate the solid transport inside the channels.

Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner. The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results.

A new computational approach for velocity components analysis of a solid particle in an incompressible fluid flow

In this work, the dynamic motion of a particle in an incompressible Newtonian fluid flow is investigated analytically. The shear and rotation effects on the lift and drag forces of the particle are considered for this problem. Also, the equations governing the motion of a particle are solved using the Temimi–Ansari technique. Analytical solutions for the horizontal and vertical velocities of this particle are obtained and analyzed in terms of time. The corresponding analytical findings are verified in comparison with numerical solutions. The obtained results showed very good accuracy of the solutions and the efficiency of this method in the whole time domain by employing the Padé approximation.

Hydromagnetic flow of Casson nano-fluid across a stretched sheet in the presence of thermoelectric and radiation

This work revealed the investigation of the Casson nanofluid flow's MHD (magneto-hydrodynamic) unstable boundary layer characteristics in the simultaneous transmission of thermoelectric and radiation on a stretched sheet. On MHD Newtonian and non-Newtonian (Casson) nanofluid flows, the cumulative impact of radiation and thermoelectricity has been addressed. Thermal radiation, Casson nanofluids, and MHD are pivotal in engineering and industry, transforming applications like heat exchangers, nuclear power plants, thermal energy storage, and advanced drug delivery systems. The problem-related partial differential equations have been formulated with boundary layer approximation. The boundary layer equations have been changed into dimensionless form with the help of appropriate dimensionless variables and parameters. Finite difference techniques have been employed to get the numerical solution via the FORTRAN 6.6a programming algorithm, and the numerical solutions have been illustrated graphically with the support of Tecplot-360 software. The consequences of the numerous parameters have been investigated using a variety of figures, with the amounts of the various parameters being revised. The simultaneous effects of thermoelectric and radiation on primary velocity, secondary velocity, and temperature profiles have been presented and discussed with critical physical properties such as skin friction in addition to Nusselt number. The combined effects of thermoelectric and radiation on streamlines and isotherms have been illustrated with line and contour flood views. The most significant finding is that the collective influence of thermoelectric and thermal radiation impacts promotes the physical phenomena of non-Newtonian (Casson) fluid flow comparatively more than Newtonian fluid flow. For the purpose of creating effective procedures, forecasting flow patterns, and guaranteeing product performance in a variety of industries, it is crucial to explain the Casson fluids. This model can also aid in blood flow simulation and risk assessment for thrombosis and other cardiovascular diseases.

Soret-Dufour Effects on Heat and Mass Transfer of Newtonian Fluid Flow over the Inclined Sheet and Magnetic Field

Newtonian fluid is ideal for lubrication purposes because the viscosity of this fluid remains as a function of the shear. Besides, the heat and mass transfer are an important study area in fluid dynamics due to its vast applications in industrial processes. The heat-mass transfer can be defined as the Soret and Dufour effect, which implemented in many industrial applications such as in chemical engineering and geosciences field. In addition, the fluid flow over an extending/compressing sheet has significant industrial applications such as the cooling of continuous strips, glass fibre production, the extrusion of plastic sheets from a die, etc. As a response, this study aims to investigate the impacts of Soret and Dufour parameters on the Newtonian fluid flow over an inclined stretching/shrinking sheet. The methodology of this mathematical model are stated as follow: 1) the transformation of partial differential equations (PDEs) to the ordinary differential equations (ODEs), and 2) The ODEs are solved using bvp4c solver in MATLAB software. The bvp4c solver is a MATLAB program directory that solves general form and multi-point boundary layer problems. The main sections of bvp4c are: 1) The solution of the ODEs, 2) The related boundary conditions that can produce the expected results, and 3) An initial guess to run the bvp4c solver. As a result, the numerical and graphical results show that the Soret effect increases the concentration profile whereas decreases the temperature profile. The vice versa occurrence is true for Dufour effect. The convective mass transfer caused by a temperature gradient is known as thermal-diffusion (Soret) effect. The convective heat transfer produced by concentration differences is known as diffusion-thermo (Dufour) effect. However, since the process of heat and mass transfers are related to each other, the Soret and Dufour effects are able to influence both of this process simultaneously. In conclusion, the convective heat transfer is enhanced by increasing Soret and Dufour number while the convective mass transfer is declined by increasing the two numbers.

Dispersion of a Chemically Reacting Solute in a Three - Dimensional Newtonian Fluid Flow Through a Darcy - Brinkman Porous Medium

Dispersion of a Chemically Reacting Solute in a Three - Dimensional Newtonian Fluid Flow Through a Darcy - Brinkman Porous Medium