Solution Of Fluid Flow Research Articles

Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation

The two-dimensional boundary layer flow of a non-Newtonian Casson fluid and heat transfer due to an exponentially permeable shrinking sheet with viscous dissipation is investigated. Using similarity transformations, the governing momentum and energy equations are transformed to self-similar nonlinear ODEs and then those are solved numerically by very efficient shooting method. The analysis explores many important aspects of flow and heat transfer of the aforesaid non-Newtonian fluid flow dynamics. For the steady flow of non-Newtonian Casson fluid, more amount of wall mass suction through the porous sheet is required in comparison to that of Newtonian fluid flow. Dual similarity solutions are obtained for velocity and temperature. The viscous dissipation effect has major impact on the heat transfer characteristic. In fact, heat absorption at the surface occurs and it increases due to viscous dissipation. For higher Prandtl number, the temperature inside the boundary layer reduces, but with larger Eckert number (viscous dissipation) it is enhanced.

Analysis of boundary layer in MHD flow of non-Newtonian visco-elastic fluid on stretching sheet

This article aims to the study of fluid flow and heat transfer in non-Newtonian viscoelastic fluid magnetic hydrodynamics steady laminar flow is expanded on a horizontal plane. Among the many processes in chemical engineering, metallurgy, polymer extrusion process involves cooling the molten liquid is drawn into the cooling system, the production of paper and glass. In this process, the rate of cooling and shrinking influences very much on the final quality of the product. Equations for fluid flow and heat transfer analysis solutions are helping homotopy analysis. In this regard and in order to validate the results of the homotopy analysis, we are comparing the results of this study and other researchers published the results will be accepted. Also, the influence of various parameters on curves, speed and temperature have been investigated.

Identification of the noise using mathematical modelling

In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today’s computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.

Flow in Linear Composite Reservoirs

Summary This study presents a fast and accurate closed-form, fully analytical solution for modeling fluid flow in linear composite reservoirs. A linear composite system, as mentioned here, refers to a porous medium that can be represented as a linear assembly of distinct homogeneous regions. It is assumed that adjacent regions are connected along an interface of pressure and flux continuity. The solution presented here differs from known analytical models in literature because it does not contain an infinite series that often takes a toll on computational time, especially when accuracy is of prime importance. Thus, this solution finds great use in inverse problems encountered in both rate and pressure transient analyses primarily because of its accuracy and the relatively short computational time required. Depending on the values of the interface coefficients (key parameters in our solution), infinite boundaries, no-flow boundaries, constant-pressure boundaries, and transition interfaces (that is, partially sealing boundaries) can be represented in our model without much computational effort.

Benchmark solutions for two-dimensional fluid flow and heat transfer problems in irregular regions using multigrid method

In the previous researches about the benchmark solutions in the irregular regions, there are some obvious shortcomings, such as small number of computational grids, simple computational domain, small characteristic number, and lack of mixed convection benchmark solution. In order to improve this situation, this article deeply studied the benchmark solutions for two-dimensional fluid flow and heat transfer problems in the irregular regions under the body-fitted coordinate system. Taking the lid-driven flow, natural convection, and mixed convection problems as the research objects and considering the influence of boundary configurations of the computational domains, Reynolds number, Prandtl number, and Grashof number, this article designed three groups of test cases. The program code is first verified through employing the nonlinear multigrid method based on the collocated finite volume method and then the numerical solutions of three test cases with 1024 × 1024 grids and convergence criterion of 10−14 are obtained to get the benchmark solutions estimated by the Richardson extrapolation method.

Numerical analysis of mixing performance in sinusoidal microchannels based on particle motion in droplets

This numerical study was conducted to analyze and understand the parameters that affect the mixing per- formance of droplet-based flow in sinusoidal microfluidic channels. Finite element analysis was used for modeling fluid flow and droplet formation inside the microchannels via tracking interface between the two heterogeneous flu - ids along with multiple particle trajectories inside a droplet. The solutions of multiphase fluid flow and particle trajec - tories were coupled with each other so that drag on every single particle changed in every time step. To solve fluid motion in multiphase flow, level set method was used. Para - metric study was repeated for different channel dimensions and different sinusoidal channel profiles. These results were compared with mixing in droplets inside a straight microchannel. Additionally, tracking of multiple particles inside a droplet was performed to simulate the circulating flow profile inside the droplets. Based on the calculation of the dispersion length, particle trajectories, and velocities inside droplets, it is concluded that having smaller chan- nel geometries increases the mixing performance inside the droplet. This also shows that droplet-based fluid flow in microchannels is very suitable for performing chemical reactions inside droplets as it will occur faster. Moreover, narrower and sinusoidal microchannels showed better dis- persion length difference compared to straight and wider microchannels.

High performance computations of steady-state bifurcations in 3D incompressible fluid flows by Asymptotic Numerical Method

This paper presents a powerful numerical model that implements the Asymptotic Numerical Method to compute 3D steady-state incompressible fluid flow solutions. This continuation algorithm enables to explore branches of steady-state solutions, stable or unstable, to accurately determine any simple steady-state bifurcation points and their emanating bifurcated branches. The powerfulness of the model stands on an optimal step length continuation thanks to the combination of power series analysis in the framework of ANM along with an efficient parallel implementation of the resulting algorithm on high performance computers. The outcome of this approach is demonstrated throughout 3D incompressible fluid flows inside a sudden expansion channel (expansion ratio E=3, cross-section aspect ratio 10≤B≤20). We have computed for the first time up to four steady symmetry breaking (pitchfork) bifurcations together with their associated bifurcated branches. The main characteristic of this 3D symmetric expansion configuration is that for a given cross-section aspect ratio the first bifurcation mode induces a top–bottom asymmetry, as in the 2D case, whereas the subsequent ones modulate the former in the span-wise direction with increasing wave numbers.

Existence of steady solutions for micropolar electrorheological fluid flows

In this paper we study the existence of weak solutions to a steady system describing the motion of micropolar electrorheological fluids. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of the problem leads naturally to weighted Sobolev spaces. The emphasis of the paper is devoted to the study of the degenerate problem. Using the Lipschitz truncation and the L∞-truncation we derive various lower bounds, depending also on the electric field, ensuring the existence of solutions.

Numerical Solutions By Method of Lines Approach for Fluid Flow in a Modified Rotating Disk Electrode Apparatus

Studying the reaction kinetics of the electrochemical redox reactions on a rotating disk electrode (RDE) is a well-known technique to access kinetic information under various competing levels of kinetic and diffusion dominated conditions. Reactions of flow batteries are typically carried out on graphite felt electrode surfaces at both cell and stack level. But the kinetics of the both positive (VO2 +/VO2+) and negative (V3+/V2+) redox couple reactions are not well understood, as there is no clear agreement of redox kinetics information available in literature1-2for these electrolytes. Porous rotating disk electrode (PRDE) is a commonly used technique to study the kinetics of graphite felt electrodes. A semi-infinite condition is typically used to arrive at well-known Levich profiles for velocity and limiting current analysis for rotating disk electrodes3. However, this type of analysis didn’t account for the data observed for felt electrodes in a RDE set up. To obtain a numerical solution for fluid flow around a rotating disk electrode in a modified RDE setup is proposed in this work as shown in Figure 1. In this setup, the boundary conditions at the stationary walls, rotating walls and axial symmetry are well-defined. This method can be used for obtaining primary and secondary distributions effectively in electrochemical systems efficiently and also for simulating flow problems4. Numerical solutions with well-defined boundary conditions will help in enhancing the reliability of the simulated results. In this 2D fluid flow model, an axially symmetric cylindrical geometry is used and fluid flow was assumed to vary in radial (r) and axial (z) directions, whereas azimuthal (θ) dependence of fluid flow is ignored. Three components of Navier-Stokes equations (r, θ and z) and a continuity equation represent the fluid flow outside the rotating disk electrode. The velocities (ur, u θ and uz ), pressure and radial and axial distances were non-dimensionalized through a method, using fluid properties and angular velocity, as reported in literature5. The 2D model equations were simulated using a new technique in which numerical method is applied in the z-direction and the resulting equations are integrated using efficient Boundary value problem (BVP) solvers in r. Efficiency and accuracy of the proposed method compared with different finite difference and discretization schemes in r will be presented. Acknowledgement: This work was supported by a contract from The American Chemical Society- Petroleum Research Fund (ACS-PRF) Grant PRF# 52588-ND10.

Symmetric singular boundary method for potential problems with mixed boundary conditions

The paper presents a symmetric formulation of the singular boundary method (SBM) for potential problems, whose resultant interpolation matrix is symmetric irrespective of boundary conditions. The SBM is a recent strong-form boundary discretization numerical technique, which is meshless, integration-free, and easy-to-implement. In stark contrast to the method of fundamental solution that requires the fictitious boundary outside physical domain to avoid the singularity of fundamental solution, the SBM can place source points, which coincide with collocation points, on the real physical boundary via the concept of origin intensity factor. The proposed symmetric formulation preserves all the merits of the SBM. The novel idea behind this study is that the unknown solution is represented by both the single and double layer potentials compared with the single layer potential in the original SBM. Numerical solution of three-dimensional potential and two-dimensional fluid flow and heat transfer problems demonstrates the utility and validity of the present SBM symmetric formulation.

Solution of micropolar fluid flow through porous channels - a differential transform approach

The steady laminar two-dimensional flow of a micropolar fluid through a porous channel with variable permeability is studied. Various cases of injection at one wall and suction at the other wall with different velocities and injection at both walls or suction at both walls are considered. A semi-analytical Differential Transform Method is used to solve the problem. Comparison of the results with the corresponding Newtonian case is carried out and the efficiency of the DTM is analysed.

Analytic Solution for Fluid Flow over an Exponentially Stretching Porous Sheet with Surface Heat Flux in Porous Medium by Means of Homotopy Analysis Method

In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these highly non-linear ordinary differential equations are found analytically by means of Homotopy Analysis Method (HAM). The result obtained by HAM is compared with numerical results presented in the literature. The accuracy of the HAM is indicated by close agreement of the two sets of results. By this method, an expression is obtained which is admissible for all values of effective parameters. This method has the ability to control the convergence of the solution.

Study of cellular flow structure and pitchfork bifurcation in a laterally-heated cube

This paper is the continuation of our study of flow development from a motionless conductive state in a thermally driven cavity. A series of complex nonlinear bifurcations was addressed in a three-dimensional partially heated rectangular cavity. Prior to chaos, the dynamic phenomena in the investigated nonlinear system include pitchfork bifurcation, Hopf bifurcation, periodic ultraharmonics, and quasi-periodic bifurcation. In this study the formation of different cellular flow structures and the scenario of pitchfork bifurcation are addressed. The solutions for the incompressible fluid flow investigated at different Rayleigh numbers are computed from the divergence-free compensated solution algorithm and the wavenumber-optimized upwinding scheme for accurately approximating the convection terms. The three-dimensional cellular flow details and the physically meaningful vortical flow insight are extracted to improve our understanding of the change of three-dimensional vortical and cellular flow features with respect to the Rayleigh number in the thermal driven cavity.

A Compressible Thermal Lattice Boltzmann Model with Factorization Symmetry

A fully compressible multispeed lattice Boltzmann model is introduced and numerically demonstrated to simulate compressible thermal flow. The equilibrium distribution functions are derived by a nonperturbative algebraic theory in coordinate symmetry product form to avoid complex polynomial expansion of the Maxwellian function and Gauss-Hermite quadrature. An important characteristic of the proposed model is that it can be easily extendied to a multidimentional model with factorization symmetry. For compressible flows, Sod shock tube, Couette flow, and high-Mach double-reflection compressible flow are carried out to validate the present model for compressible flow and heat transfer. Numerical results are in excellent agreement with the theoretical solutions of fluid flows.

An Innovative Treadmill-Magnus Wind Propulsion System for Naval Ships

The Magnus force was successfully employed by Flettner in his ship Buckau operating with two large propelling cylinders. The spinning cylinders produced propulsive force from the wind on seas as a clean and free source of energy. The rise of fossil fuel costs, extinction of fossil fuel resources, and environmental issues such as global warming and pollutions produced by fossil fuels have caused a renew interest in Flettner type propulsion in naval ships. This is becoming a hot topic in Europe and the rest of world. Many other applications of producing high lift values from spinning symmetrical cylinders have failed due to high values of drag force and also rapid increase of frictional torques. In this patent, the new application of Treadmill-Magnus, wind driven propulsion system is introduced which can be effectively used for any size ships. To show validity of the concept, the NACA0020 aerofoil section with treadmill skin is computationally investigated at the low Reynolds number of 8.2x104. The viscous fluid flow solutions were obtained at variety of treadmill speeds of the aerofoil skin and different incident angles. The results show that high lift to drag ratios may be obtained using treadmill motion.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid

Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

An Orthorhombic Lattice Boltzmann Model for Pore-Scale Simulation of Fluid Flow in Porous Media

One application of the lattice Boltzmann equation (LBE) models is in combination with tomography to simulate pore-scale flow and transport processes in porous media. Most LBE models in the literature are based on cubic lattice, and if the voxels in a tomography image are not cubic or cannot be divided into cubes due to computational limitations, these models will lose most of their advantages. How to deal with such images is, hence, an interest in use of the LBE model to simulate pore-scale processes. In this paper, we present an orthorhombic LBE model based on the single-relaxation time approach with the relaxation parameter varying with lattice directions. The equilibrium distribution functions in the standard LBE model were modified to correct the anisotropy induced by the non-cubic lattice, and the calculations of the fluid density and momentum were also redefined in order to maintain the conservation of mass and momentum during the collision. We tested the model against analytical solution for fluid flow in a tube, and against the standard cubic-based LBE model for fluid flow in a duct with an island inside. The model was then applied to simulate fluid flow in a 3D image in attempts to analyse the errors if the voxels in the image are not cubic but are assumed to be cubic.

The Convergence Rate of Iterative Procedures for Elliptic Problems in Heterogeneous Media

We investigate the convergence rate of two iterative procedures that approximate the solutionof fluid flow problems in heterogeneous porous media. Porous media flows at large scales arecomplex problems, which require fine grid solutions to provide accurate results. Pressures and velocitiesassociated to these problems are governed by second order elliptic equations. We discretizesuch equations by a mixed and hybrid finite element method, combined with domain-decompositioniterative procedures. In order to minimize the computational effort involved in the numerical approximation,we have presented an iterative procedure to accelerate the convergence rate in the approximation.In this paper, we perform numerical experiments to compare iterative procedures in order tocheck which one provides the best convergence rate. We believe that steady-state diffusion problemscan be solved efficient and accurately by the most robust procedure.

Computational fluid dynamics investigation of human aspiration in low velocity air: orientation effects on nose-breathing simulations.

An understanding of how particles are inhaled into the human nose is important for developing samplers that measure biologically relevant estimates of exposure in the workplace. While previous computational mouth-breathing investigations of particle aspiration have been conducted in slow moving air, nose breathing still required exploration. Computational fluid dynamics was used to estimate nasal aspiration efficiency for an inhaling humanoid form in low velocity wind speeds (0.1-0.4 m s(-1)). Breathing was simplified as continuous inhalation through the nose. Fluid flow and particle trajectories were simulated over seven discrete orientations relative to the oncoming wind (0, 15, 30, 60, 90, 135, 180°). Sensitivities of the model simplification and methods were assessed, particularly the placement of the recessed nostril surface and the size of the nose. Simulations identified higher aspiration (13% on average) when compared to published experimental wind tunnel data. Significant differences in aspiration were identified between nose geometry, with the smaller nose aspirating an average of 8.6% more than the larger nose. Differences in fluid flow solution methods accounted for 2% average differences, on the order of methodological uncertainty. Similar trends to mouth-breathing simulations were observed including increasing aspiration efficiency with decreasing freestream velocity and decreasing aspiration with increasing rotation away from the oncoming wind. These models indicate nasal aspiration in slow moving air occurs only for particles <100 µm.