Steady Fluid Flow Research Articles

A flow of Newtonian fluid through annular region between curved pipes: Analytical study

A steady Newtonian fluid flow through annular region in curved pipes is studied in this paper. The flow takes place due to an axial pressure gradient and it is three-dimensional in nature. The equations governing the flow are highly coupled and nonlinear. The solutions are obtained, analytically, using a regular perturbation method. The effects of curvature ratio [Formula: see text], Reynolds number (Re) and the radius ratio [Formula: see text] on the axial velocity and stream function are presented graphically. It is observed that, along with curvature ratio and Reynolds number, radius ratio highly affects the fluid flow in annular curved pipes.

Numerical study of heat and mass transfer for micropolar fluid flow due to two symmetrical stretchable disks

In this study, heat transfer is analyzed for an incompressible steady laminar micropolar fluid flow among two symmetrical stretchable disks. The associated partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) through appropriate similarity transformations and then solved numerically by applying the quasi-linearization method along with the finite difference method (FDM). This impact from certain inclusive parameters in the heat transfer and fluid flow is presented schematically. The results are tabulated and depict that the shear stress rises for the upper disk and the opposite trend for the lower disk. It is also noted that a couple stress and heat transfer rates were reduced across the disks. The slip factor enhances the tangential stress on the top disc and it reduces on the bottom disc. Twisting stress decreases where increases due to the effect of the slip factors.

Thermal examination of chemical interaction and thermophoretic diffusion of Williamson fluid flow across Riga Plate surface with nonlinearity radiation flux

The purpose of this research is to investigate the thermophoretic diffusion and chemical reaction on steady magnetized Williamson fluid flow, heat, and mass transfer along a Riga surface in the presence of variable thermal properties. By imposing the appropriate similarity technique, the system of higher-order formulas has been transformed from partial order into ordinary order. An efficient numerical technique named the classical Keller box scheme has been incorporated to solve these dimensionless coupled non-linear ordinary differential equations. The obtained results are visualized graphically with physical justification. In addition to that, we validated the obtained outcomes by comparing them to earlier literature, and we identified an excellent match, supporting the reliability of the present method. We discovered from our analysis that acceleration in the values of Williamson fluid and viscosity leads to enhancement in both velocity plots. Also, the material and stretching parameters have a major role in the fluid flow control process.

On Exact Solutions to Problems of Steady Flow of Incompressible Viscous Fluid in a Channel and in a Circular Pipe

Turning to the well-known Couette flow, we again, but now in a new formulation, consider the steady motion of an incompressible viscous fluid in a channel with two parallel flat walls, one of which is stationary while the other moves at a constant speed in its plane. In the classical formulation of this problem on a layered (laminar) fluid flow in a channel, the wall velocity and the constant pressure drop along the channel are independent quantities and are considered predetermined. However, when a solid body moves along the fluid surface, the fluid particles are set in motion. This occurs due to the arising pressure generated in the fluid caused by the movement of the solid body. Therefore, here the pressure or pressure drop is not predetermined but is determined as a result of solving the corresponding two-dimensional boundary value problem of a steady flow of a viscous fluid in a channel. For this, the corresponding boundary value problem of a fluid flow in the channel is formulated based on the linearized Navier-Stokes equations obtained from the general nonlinear Navier-Stokes equations for a steady flow of a viscous fluid neglecting the convective terms, which is true for small Reynolds numbers. Using the Fourier integral transform method, an exact (closed) solution to this boundary value problem is constructed; the velocity and pressure components are determined. Then it is shown that the resulting solution, different from the known Couette flow solution, also satisfies the original nonlinear Navier-Stokes equations, the continuity equation, and boundary conditions. A comparative analysis of the new solution with the Couette flow solution is carried out. The well-known Hagen-Poiseuille problem is also discussed from the point of view of establishing the conditions for the laminar axisymmetric and steady flow of an incompressible viscous fluid in a straight circular pipe According to the study's results, to implement laminar flow under the indicated conditions, the pressure drop along the pipe must be constant. The study demonstrates that this condition is simultaneously sufficient, and therefore, the necessary and sufficient condition is established for a laminar flow in a straight circular pipe.

Analytical approach for micropolar fluid flow in a channel with porous walls

This article aims to analyze and reach new physical achievements in a well-known nonlinear problem of two-dimensional, steady, and steady micropolar fluid flow between two parallel permeable porous walls. Micropolar fluids are considered a class of non-Newtonian fluids. The nonlinear governing equations of this problem were analyzed using two analytical methods. The achievements and novelty of this article, apart from showing the application of two mathematical methods in solving non-linear equations, are more about achieving new results that are obtained from solving the governing equations of this article. From the results, it is obvious that with the raise of the coupling parameter, other dimensionless parameters increase, except for the dimensionless microrotation. Also, when the spin gradient viscosity parameter increases, all the average values of the mentioned dimensionless parameters increase. From the problem's solution, it is clear that when the micro-inertia density ratio increases across the channel, all the average values of the dimensionless parameters decrease except for the dimensionless flow function characteristics. Also, when the Peclet number for the heat diffusion parameter is changed, it only affects the dimensionless temperature profile. When the Peclet number for the mass diffusion parameter is changed, it only affects the dimensionless concentration profile.

Evolution of Entropy Generation on Mixing Process Using a Novel Chaotic Micromixer

This study aims to compare numerically the laminar steady flow of shear-thinning non Newtonian fluids in novel chaotic micromixer. The process is verified for non-Newtonian flow in a complex geometry that is heated with a constant flux. The selected geometry produce secondary flow structures that greatly improve fluid dynamic performance. To measure this performance, the Poincaré map method is used for various cases of fluid power-law index in different geometries. In addition, thermal mixing behavior is studied for shear-thinning fluids in the chosen geometry with two different inlet temperatures.In different cases of fluid power-law indexes, the novel geometry resulted in an 82% increase in thermal mixing degree relative to the thermal mixing degree observed in the C-shaped and serpentine channels. The second law of thermodynamics is examined in terms of entropy generation caused by thermal and hydrodynamic processes, as a function of low rates of generalized Reynolds number and power-law index, while taking into consideration the effects of chaotic advection. As a result, the new configuration showed a significant improvement in the degree of mixing compared to other geometries considered, while also minimizing friction and thermal irreversibilities.

MHD VISCOELASTIC STAGNATION-POINT FLOW AROUND A STRETCHING SHEET WITH INDUCED MAGNETIC FIELD AND VISCOUS DISSIPATION

The present study deals with a steady MHD stagnation-point flow of incompressible viscoelastic fluid in a porous medium around a stretching/shrinking sheet. The influence of induced magnetic field, heat source parameter and viscous dissipation are considered. The resulting nonlinear partial differential equations are solved under suitable boundary conditions using the bvp4c method. The effect of various physical parameters affecting on the flow has been studied. It is observed that the viscoelastic parameter enhances the induced magnetic field profile and temperature profile, whereas fluid velocity reduces. Moreover, the stretch parameter has a significant influence on the fluid velocity. The temperature profile can be improved by increasing the viscoelastic parameter, magnetic parameter, heat source parameter and radiation parameter, while the opposite effect is observed for Eckert number, reciprocal of the magnetic Prandtl number and Prandtl number.

Parametric sensitivity analysis to select the relevant natural fractures in reservoir rock cells based on the equivalent permeability response

Over the last few years, several works have been conducted to improve the productivity of unconventional highly fractured reservoirs, in which the fracture network strongly affects the hydraulic behavior of the porous medium. However, fracture networks can present a complex geometry making difficult its spatial discretization. This work proposes to use a statistical method to select a group of natural fractures that reproduces the equivalent permeability response. An adapted Box-Behnken experimental design together with steady state fluid flow analyses is carried out in order to determine the relevance of each fracture, which is instrumental to select the dominant fractures based on the statistical significance. The results of the model with only few dominant fractures were validated and verified against the ones from the original model, which contains all natural fractures. The time evolution of pressure and the accumulated fluid curve obtained by means of transient analyses showed that a model with the selected fractures is able to properly represent the hydraulic behavior and main trends associated with the original cell.

Magnetohydrodynamics free convection couette flow and heat transfer through a vertical porous plate with heat generation and absorption effect

This research examines the impact of suction/injection and permeability of porous materials on a steady natural convection Couette flow of a viscous incompressible fluid passing through a vertical porous plate. The dimensionless governing momentum and energy equations were solved exactly. Graphs were plotted to check the impact of the governing flow parameters and a table was plotted for comparison of the results. It was found from the investigation that, the fluid injection (λ>0) increases the fluid velocity and temperature distributions while the magnetic field (M) retards the fluid velocity. It is also noteworthy to mention that the suction (λ>0) reduces the fluid velocity and temperature distributions in the channel. The velocity profile is observed to increase with increase in the permeability (K) of the materials.

Non-uniqueness in plane fluid flows

Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point produces an infinite number of solutions with the same initial data. Dafermos appeals to a maximal entropy rate criterion to recover uniqueness. These results are here interpreted as non-unique Lagrange trajectories on a particular spatial region. The corresponding special velocity is proved consistent with plane steady compressible fluid flows that for specified pressure and mass density satisfy not only the Euler equations but also the Navier-Stokes equations for specially chosen volume and (positive) shear viscosities. The maximal entropy rate criterion recovers uniqueness.

A steady flow of MHD Maxwell viscoelastic fluid on a flat porous plate with the outcome of radiation and heat generation

Maxwell fluids display viscous flow on a long timescale but exhibit additional elastic resistance during rapid deformations. Among various types of rate-type fluids, the Maxwell fluid has achieved prominence in numerous study fields. This viscoelastic fluid has viscous and elastic properties. Due to their reduced complexity, this Maxwell fluid is utilized used in the polymeric industries. We have established a mathematical model based on the applications. This article examines the mathematical and graphical analysis for steady-state magnetohydrodynamic flow in a horizontal flat plate of Maxwell viscoelastic fluid for a permeable medium with heat and thermal radiation. The non-dimensional and similarity transformation used to frame the partial differential equations with restored ordinary differential equations. The shooting technique is originated to find solutions to nonlinear boundary value problems with the help of MATLAB software via the Runge-Kutta Fehlberg method. The primary idea behind this strategy is to change the boundary conditions of boundary value problems into initial value problems. Several plots illustrate the leading parameters such as Prandtl number (Pr), Deborah number (De), Eckert number (Ec), heat generation (Q), radiation (Rd), Lewis number (Le), magnetic parameter (M), and thermal slip condition (β) on the velocity profile and energy transfer behaviour. We validated our results with published work. The most significant impact of this study is that the Nusselt number drops as the Eckert number rises and climbs when heat radiation increases. The skin friction coefficient increases as Deborah number increases.

Artificial neural network modelling for predicting classical air pressure profile curves in building drainage systems

Water trap seal loss can lead to the ingress of foul odours from the sewer network carrying harmful pathogens which can affect the health of building occupants. This loss is due to excessive negative or positive pressures within the system as a consequence of rapidly changing flow due to the unsteady nature of air and water flow discharges from appliances. This pressure regime within the system is often represented by a pressure profile along the height of the main vertical stack in the Building Drainage System (BDS). Experimental data from peer-reviewed literature and data from a unique 34-storey drainage test rig have been used as pressure profile data (Test data) for an Artificial Neural Network (ANN) model. Discharge input height (storey number) and discharge flow rate are considered to be the two independent input parameters and the pressure along the vertical stack is considered to be the output. In this work, both a Feed Forward and Back Propagation (FFBP) ANN model and a Radial Basis Function (RBF) ANN model have been used to train the algorithm. The work has confirmed the applicability of the FFBP-ANN model for steady two-phase fluid flow phenomena in BDS and allows for the prediction of pressures in a system for which no pressure data exists, by the prediction of modelled weights, based only on its physical and flow characteristics. Practical Application: Of great concern to designers of building drainage systems (BDS) is the control of pressure fluctuations within the system to prevent water trap seal loss. Prediction of a pressure profile based on the characteristics of the building – e.g. height, location of water discharge, discharge flow rate and ventilation type, would therefore increase confidence in designs, particularly in tall buildings. The work presented here addresses, for the first time, the applications of two ANN models for predicting the pressure profile in the BDS vertical stack of multi-storey buildings.

A Bingham Plastic Fluid Solver for Turbulent Flow of Dense Muddy Sediment Mixtures

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1×10−4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results.

Darcy–Brinkman porous medium for dusty fluid flow with steady boundary layer flow in the presence of slip effect

This study looks at the Darcy–Brinkman flow across a stretched sheet of porous dissipation and frictional heating. The geometry of a steady flow of dust particles fluid through a porous material in the existence of slip effect and porous dissipation is the subject of this study. The equations that govern the system are shown and summarized as boundary layer assumptions, and then modified into framework of first-order DEs using the similarity approach. By using similarity transformation, a two-dimensional nonlinear partial differential equation is decreased to a sequence of nonlinear ordinary differential equations (ODEs). Then, by employing numerical techniques such as Maple packages, the solution of system of nonlinear equations is represented using the RK4 method. The numerical findings are derived under specific unique situations. The Nusselt number and coefficient of skin-friction are also given numerically. The increase in Brinkman number [Formula: see text] raises the temperature profile for both the dusty and the fluid phases. The results also demonstrate that rise in the suction number S falls the temperature distribution within the boundary layer for the dusty phase and fluid phase. For a variety of flow quantities of attention, the variation of parameters is studied, and the outcomes are reported in the shape of graphs and tables. Several industrial processes make advantage of boundary layer flow and heat transfer over such a stretched surface in porous materials.

Ohmic dissipation impact on flow of Casson-Williamson fluid over a slippery surface through a porous medium

Through the investigation, in this work, we focused at the steady flow of a Casson-Williamson fluid due to an stretchable, impenetrable sheet with Ohmic dissipation. It is assumed that the impermeable stretched sheet is incorporated into a porous media and has a rough surface. The porous media through which the non-Newtonian fluid is flowing are supposed to obey Darcy’s law. Magnetic and electric fields’ impacts are considered. We investigate how the process of heat transfer is affected by viscous dissipation and varying thermal conductivity. On the basis of a little magnetic Reynolds number, the controlling basic equations are represented by a system of nonlinear ordinary differential equations. The shooting technique is used to get a numerical solution for this system, which controls both the temperature and velocity fields. Graphical representations of the impact of various parameters on the velocity and temperature profiles are shown. Regarding the significant results, we note that the local electric parameter tends to improve both the velocity and temperature fields, while the porous parameter, Casson parameter and slip velocity parameter decrease the velocity profiles.

An Evaluation of Accuracy and Efficiency of a 3D Adaptive Mesh Refinement Method with Analytical Velocity Fields

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

Mathematical analysis of heat and mass transport under thermal radiations and dissipation for electrically conducting second-grade fluid

This research deals with heat and mass transport in 2D, steady laminar unidirectional flow of second-grade fluid inside converging/diverging stretchable channel with no slip effects. The similarity equations were engaged for the model development and acquired a model in the form of a joint system of ODEs comprising the innovative effects of thermal radiations, magnetic field and dissipation function. Then, mathematical treatment of the model was done via HAM Package and the results were furnished under the inspiration of physical constraints. It is pointed out that the fluid moves quite slowly in diverging cases than that of converging ones under multiple Re values, whereas magnetic field effects are almost negligible for the velocity profile. The temperature of the fluid can be enlarged by increasing Ec and Pr and Rd is not proven good in this study. Further, as far as the mass transport is concerned, the dominant contribution of Sc is observed for both stretching/shrinking walls.

Perspective: How to overcome dynamical density functional theory

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.

On the steady flow of non-newtonian fluid through multi-stenosed elliptical artery: A theoretical model

The study of blood flow through stenotic arteries is more important as the existence and progression of stenosis may lead to severe damage. The current study aims to analyze and understand the non-Newtonian nature of blood flow through the multi-stenosed artery of an elliptical cross-section. The Carreau fluid model accounts for the non-Newtonian nature of blood. The mathematical equations are transformed to dimensionless form, and assumptions of mild stenosis are employed to reduce the non-linearity of the mathematical model. The perturbation method via polynomial technique is utilized to solve the resulting equations by considering We2 as the perturbation parameter. The results of the velocity and wall shear stress are examined graphically. It is found that stenosis severity substantially impacts flow velocity in the narrower portion of the artery. The stenosis growth strongly affects the flow velocity and wall shear stress in the stenotic region. The non-Newtonian effects are found to dominate along the minor axis. This fact assures that the conduit’s narrower cross-section strengthens the fluid’s non-Newtonian behavior. It is observed that the non-Newtonian fluid has a smaller velocity than the Newtonian fluid. Moreover, non-Newtonian fluid has a different nature along the minor and major axes, but Newtonian fluid has the same behavior.

Investigation of the Performance of a Centrifugal Pump Impeller Design with the Addition of a Junction Disc Plate

This research analyzes the impeller design performance that has been modified based on previous impeller designs. The previous impeller design used high engine power consumption due to the total head, so the modification of the impeller design is expected to reduce the engine power consumption. The existing design and the modified impeller design with the addition of the junction disc plate are used by this research. This research used experiment methods and theoretical methods to compare both of impeller design performances. The experiment method measures total head, fluid capacity, engine speed, and engine power consumption. The theoretical method analyzes actual fluid velocity, specific velocity, total suction head, NPSH, and pump efficiency. The results showed that the fluid flow rate was able to increase the efficiency of the centrifugal pump by 2.8%. The conclusion explains that the addition of a junction disc plate produces energy from a steady fluid flow rate to reduce the engine power consumption and escalation of pump efficiency.