Solution Of Fluid Flow Research Articles

Analytical solutions for unsteady electrohydrodynamics flows of Maxwell fluids in microchannels with circular cross section

Unsteady electrohydrodynamic flow of Maxwell fluids through a microchannel with a circular cross section under the influence of a time-dependent external electric field is studied in the Debye–Hückel approximation. Analytical solutions for electric potential of charge distribution, fluid velocity, and the components of a shear stress tensor are determined by using a suitable integral transform regarding the azimuthal variable, the Laplace transform with respect to the time variable, and the finite Hankel transform regarding the radial coordinate. Flows caused by an oscillating electric field have been studied as a particular case of the general model. The analytical solutions corresponding to the flow of Newtonian fluids have also been obtained as particular cases of analytical solutions of the Maxwell fluid flow. Numerical values of the analytical solutions are obtained using the MathCAD15 software. The profiles of electric potential and fluid velocity are presented in two/three-dimensional graphical illustrations.

Numerical Solution of Free Convective Stratified Fluid Flow over an Infinite Vertical Porous Plate with Hall Effect

Numerical Solution of Free Convective Stratified Fluid Flow over an Infinite Vertical Porous Plate with Hall Effect

Numerical Solution of Fluid Flow in Horizontal Tube under Effects of Radiation Field

In this work, we studied the matter of heat transfer by the natural convection for a dissipatable fluid which flows in a tube, its walls composed from porous material, and a mathematical model was constructed, represented by a system of two-dimension non-linear partial differential equations, describing the flow behavior of the fluid through a horizontal tube and the distribution of temperatures inside the tube and under the influence of a vertical magnetic field at the tube level. The resulting differential equations were treated by numerical methods using the alternating directions implicit method (ADI), which is one of the finite differences methods, and in both cases: unsteady state and steady state. And we completed the study of the effect for each of: Prandtl number, Schmidt number, Gratshof number, and Radiation parameter.

Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape

In this work, we set up a new, general, and computationally efficient way to tackle parametrized fluid flows modeled through unsteady Navier-Stokes equations defined on domains with variable shape, when relying on the reduced basis method. We easily describe a domain by flexible boundary parametrizations, and generate domain (and mesh) deformations by means of a solid extension, obtained by solving a harmonic extension or a linear elasticity problem. The proposed procedure is built over a two-stage reduction: (i) first, we construct a reduced basis approximation for the mesh motion problem, irrespective of the fluid flow problem we focus on; (ii) then, we generate a reduced basis approximation of the unsteady Navier-Stokes problem, relying on finite element snapshots evaluated over a set of reduced deformed configuration, and approximating both velocity and pressure fields simultaneously. To deal with unavoidable nonaffine parametric dependencies arising in both the mesh motion and the state problem, we apply a matrix version of the discrete empirical interpolation method, allowing treating a wide range of geometrical deformations in an efficient and purely algebraic way. The same strategy is used to perform hyper-reduction of nonlinear terms. To assess the numerical performances of the proposed technique, we address the solution of parametrized fluid flows where the parameters describe both the shape of the domain and relevant physical features. Complex flow patterns such as the ones appearing in a patient-specific carotid bifurcation are accurately approximated, as well as derived quantities of potential clinical interest.

Numerical solution of non-Newtonian fluid flow and heat transfer problems in ducts with sharp corners by the modified method of fundamental solutions and radial basis function collocation

In this paper, non-Newtonian fluid flow and heat transfer in an internally finned duct is considered. The problems are governed by nonlinear equations with linear boundary conditions. In this paper, the solution is obtained with two Picard iteration processes, separately for the fluid flow and heat transfer problems. Furthermore, in both problems the solutions consist of the general and particular solutions. The method of fundamental solutions is employed in order to obtain the general solution while radial basis function approximations are used for obtaining the general solution by two possible methods. The results obtained using both approaches give similar results.

Finite Integral Transform Based Solution of Second Grade Fluid Flow between Two Parallel Plates

The importance of the slip flow over the no-slip condition is widely accepted in microscopic scaled domains with the direct impact on microfluidic and nanofluidic systems. The popular Navier Stoke’s (N-S) flow model is largely utilized with the slip flow phenomenon. In the present study, the finite integral transform scheme along with the shift of variables is implemented to solve the equation of motion of second grade fluid having third-order mixed partial derivative term. The velocity over the flow regime is studied with both the slip and no-slip boundary conditions for Newtonian and non-Newtonian characteristics by considering the generalized Couette flow. The impact of the pressure gradient and flow time on the velocity is investigated analytically. The output of the present research reveals that due to the slip flow velocity randomly varies at the vicinity of wall surface and such nature hasn’t been found for the no-slip condition. The validation of the present work was done by comparison with the published work and the numerical values, and it shows well verified.

Effects of heat generation/absorption in the Jeffrey fluid past a permeable stretching/shrinking disc

This theoretical study expounds dual solutions of the Jeffrey model fluid flow and heat transfer around the stagnation-point regime along a radially stretching/shrinking disc. The present work also attempts to examine the effect of heat generation/absorption towards the rate of heat transfer in a Jeffrey fluid. The similarity transformation helps to reduce the complicated partial differential equations into a system of ordinary differential equations so that the system can be solved numerically via the bvp4c function in MATLAB. The dual solutions are observable within a certain range of the shrinking parameter. The heat generation or absorption in the fluid flow regime does not delay flow separations. Further, a stability analysis is performed to determine the stability of the dual solutions. The first solution is claimed to be a stable solution, and the second solution is confirmed as an unstable solution.

Pseudoplastic fluid flows for different Prandtl numbers: Steady and time-dependent solutions

In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated from sidewalls problem for Newtonian and power-law fluids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Rayleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the flow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian fluid flows for different Pr and power-law indexes n. The range of solutions were found in the range 0.6<n<1 and 0.01<Pr<1,000, and the critical Rayleigh number (Rac) where Hopf bifurcations appear were identified for all cases. Obtained results have good agreement with those previously reported in the specific literature, and new data related to the heat transfer capabilities of pseudoplastic fluids and its oscillatory behavior was identified. This non-Newtonian influence of the fluid is later checked in a 3D model of a simplified heat exchanger, where the capability of pseudoplastic fluids for energy transport proved to be enhanced when compared to the Newtonian case.

Model development for infiltration of unfrozen water in saturated frozen soil using lattice Boltzmann method

A lattice Boltzmann model for unfrozen water infiltration in saturated soil undergoing progressive freezing is proposed: (1) a stochastic growth method for particle generation is used to generate the structure of the soil particles, (2) a geometric method is used to calculate the temperature distribution at phase change, (3) the multiple relaxation time lattice Boltzmann method is selected for the solution of fluid flow through the frozen soil. The contents of unfrozen water and the hydraulic conductivities for two types of soil, sand and silt loam, obtained by the model were compared with experimental results. The correlation coefficients between the estimated and the experimental values were 0.97 and 0.96, respectively, for the contents of these two types of frozen soil in unfrozen water, and were 0.96 and 0.95, respectively, for their hydraulic conductivities.

An exact analytical model for fluid flow through finite rock matrix block with special saturation function

An exact analytical solution for one-dimensional fluid flow through rock matrix block is presented. The nonlinearity induced from flow functions makes the governing equations describing this mechanism difficult to be analytically solved. In this paper, an analytical solution to the infiltration problems considering non-linear relative permeability functions is presented for finite depth, despite its profound and fundamental importance. Elimination of the nonlinear terms in the equation, as a complex and tedious task, is done by applying several successive mathematical manipulations including: Hopf-Cole transformation to obtain a diffusive type PDE; an exponential type transformation to get a convective-diffusive type PDE with suitable boundary conditions; Laplace transformation; Integral transformation to homogenize the boundary condition in the Laplace domain; and finally Laplace inversion method to find the time domain solution. The obtained solution is used for developing a new matrix-fracture transfer function. The developed analytical equations are used for prediction of drying front in the case of evaporation from deep water table. The model results are in close agreement with the experimental data and numerical simulation of the process. Results of sensitivity analysis of different parameters on recovery rate and ultimate production based on design of experiment method are also discussed.

Numerical Solution of Non-Newtonian Fluid Flow Due to Rotatory Rigid Disk

In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced above the rotating disk. The magnetized flow field is framed with Navier’s slip assumption. The Von Karman scheme is adopted to transform flow narrating equations in terms of reduced system. For better depiction a self-coded computational algorithm is executed rather than to move-on with build-in array. Numerical observations via magnetic, Lewis numbers, Casson, slip, Brownian motion, and thermophoresis parameters subject to radial, tangential velocities, temperature, and nanoparticles concentration are reported. The validation of numerical method being used is given through comparison with existing work. Comparative values of local Nusselt number and local Sherwood number are provided for involved flow controlling parameters.

Unsteady Boundary Layer Flow of a Casson Fluid past a Permeable Stretching/Shrinking Sheet: Paired Solutions and Stability Analysis

This paper discusses the numerical solutions of the unsteady Casson fluid flow over a permeable stretching/shrinking sheet. The suitable similarity transformations are implemented to transform the governing partial differential equations into ordinary differential equations, and those are then solved numerically by the MATLAB solver bvp4c function. The effects of the governing parameters on the velocity distributions and the reduced skin friction coefficients are given in the form of graph and examined thoroughly. The existence of paired solutions is identified, and the stability analysis revealed that the upper branch solution is stable while the lower branch solution is unstable.

Spreadsheet Solutions for Rheological Properties and Viscoplastic Fluid Flow in Circular Pipes and in Parallel-plates

Spreadsheet Solutions for Rheological Properties and Viscoplastic Fluid Flow in Circular Pipes and in Parallel-plates

Local non-similar solutions of convective flow of Carreau fluid in the presence of MHD and radiative heat transfer

In this research article we studied a realistic methodology to inspect the non-similar solutions for the two-dimensional steady Carreau fluid flow in the presence of applied magnetic field and mixed convection within the sight of infinite shear rate viscosity. With the help of local non-similar method, we presented the nonlinear PDEs for the flow and heat transfer analysis. The leading PDEs are converted into an system of nonlinear ODEs by using the local non-similarity method. The final resulting non-dimensional set of coupled nonlinear PDEs is then solved with the help of bvp4c function in MATLAB. This investigation discover numerous physical aspects of flow and heat transfer. Major outcomes in the form of velocity enhancement and temperature reduction for the higher values of buoyancy parameter $$\left( \xi \right)$$ are observed. On the other hand, for increasing values of $$N_{\mathrm{R}}$$ the temperature of the fluid increases, while for larger values of suction/injection parameter the temperature of the fluid reduces. Parallel variation of buoyancy parameter and Weissenberg number shows a slight difference regarding local similar and local non-similar solution while computing the local skin friction number. The enhancement in buoyancy parameter causes enhancement in local skin friction as well as local Nusselt number. Additionally this investigation is validated through a comparison with previous results and found a good correlation with the previous results.

Vector Penalty-Projection Methods for Open Boundary Conditions with Optimal Second-Order Accuracy

Recently, a new family of splitting methods, the so-called vector penalty-projection methods (VPP) were introduced by Angot et al. [2, 3] to compute the solution of unsteady incompressible fluid flows and to overcome most of the drawbacks of the usual incremental projection methods. Two different parameters are related to the VPP methods: the augmentation parameter r ≥ 0 and the penalty parameter 0 < e ≤ 1. In this paper, we deal with the time-dependent incompressible Navier-Stokes equations with outflow boundary conditions using the VPP methods. The spatial dis-cretization is based on the finite volume scheme on a Marker and Cells (MAC) staggered grid. Furthermore, two different second-order time discretization schemes are investigated: the second-order Backward Difference Formula (BDF2) known also as Gear's scheme and the Crank-Nicolson scheme. We show that the VPP methods provide a second-order convergence rate for both velocity and pressure in space and time even in the presence of open boundary conditions with small values of the augmentation parameter r typically 0 ≤ r ≤ 1 and a penalty parameter e small enough typically e = 10 −10. The resulting constraint on the discrete divergence of velocity is not exactly equal to zero but is satisfied approximately as O(e δt) where e is the penalty parameter (taken as small as desired) and δt is the time step. The choice r = 0 requires a special attention to avoid the accumulation of round-off errors for very small values of e. Indeed, it is important in this case to directly correct the pressure gradient by taking account of the velocity correction issued from the vector penalty-projection step. Finally, the efficiency and the second-order accuracy of the method are illustrated by several numerical test cases including homogeneous or non-homogeneous given traction on the boundary.

A micropolar fluid model for hydrodynamics in the renal tubule

The creeping flow of an incompressible micropolar fluid in a small-diameter permeable tube is studied. The fluid absorption at the tube walls is taken as a function of wall permeability and the pressure gradient across the tube wall. Closed-form solutions of the governing equations for the pressure, velocity and micro-rotation fields are obtained. Expressions describing variations in the axial volume flow rate, mean pressure, wall leakage flux, wall shear stress and the fractional re-absorption are derived. Effects of the wall permeability coefficient K , the micropolar parameter m and the coupling number N on flow variables are graphically presented and implications of results are discussed briefly. The obtained solutions are applied to the flow problem in the proximal renal tubule and probable values of the wall permeability parameter and the mean pressure drop in the tubule are obtained. It is found that the mean pressure drop in the proximal tubule is higher for the micropolar fluid than for the Newtonian fluid. It is also found that the volume flow rate of the micropolar fluid decreases exponentially as a function of the axial distance. This is a biologically significant result which is well accepted and is reported in the literature by earlier researchers too. The derived solutions coincide well with the existing solutions for the Newtonian fluid flow in a permeable tube as a special case.

The effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows by Lattice-Boltzmann method

The aim of this study is to investigate the effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows in the context of single relaxation time Lattice Boltzmann method (SRT-LBM). The fluid flows are simulated using regularized, no-slip, Zou-He and bounce back boundary conditions for straight surfaces in a lid driven cavity and the two-dimensional flow in a channel. The solutions for all types of the boundary conditions show good agreement with numerical references and exact solutions. The cavity pressure contours at low relaxation time show drastic perturbations for Zou-He boundary condition, whereas, the perturbation is ignorable for regularized boundary condition. At High Reynolds number, severe velocity gradients are major reason for numerical instabilities. Therefore, regularized boundary condition, which considers the velocity gradient in its calculation, has better numerical stability comparing the Zou-He boundary condition. Overall, the selection of appropriate boundary condition depends on the flow regime and Geometry. The proper boundary conditions at low Reynolds numbers are Zou-He and bounce back boundary conditions, and at high Reynolds numbers, regularized and no-slip boundary conditions are recommended.

Open-source toolbox for electromigrative separations

We present a novel simulation toolbox for electromigrative problems. The formulation presented includes all the fields, interaction and effects that configure both electrokinetic and electroosmotic phenomena for studying capillary and chip electromigrative separation methods. This simulation toolbox was developed by using the Finite Volume Method (FVM) in the platform OpenFOAM®. This implementation defines a new scenario for numerical simulations of electromigrative separations in terms of four main novel and outstanding characteristics offered by OpenFOAM®: (i) native 3D support, (ii) electroosmotic fluid flow solution by using Navier–Stokes equation, (iii) automatic parallel and supercomputing support, and (iv) GNU-GPL license. In this way, we put into consideration of the electromigrative separation community, for the first time, a simulation tool for a wide range of experimental methods such as capillary zone electrophoresis, isotachophoresis, and isoelectric focusing, among others.After presenting the main characteristics of the implementation, different validation and application examples are provided in order to illustrate the capabilities and potentialities of the library, but also trying to motivate a discussion about its future. Program summaryProgram title: electroMicroTransportProgram Files doi:http://dx.doi.org/10.17632/9wpvypzj9y.1Licensing provisions: GNU General Public License v3External routines: OpenFOAM®v17.12, v18.06Nature of problem: 3D multiphysics problems involving fluid dynamic and electromigrative phenomena in capillaries and microfluidic chips.Solution method: Navier–Stokes, charge conservation and transport equations solved via the Finite Volume Method running in shared and distributed memory parallel platforms.

Free-surface, purely azimuthal equatorial flows in spherical coordinates with stratification

In this paper we derive an exact solution to the governing equations for geophysical fluid dynamics in spherical coordinates which incorporates fluid stratification. This solution represents a steady, purely–azimuthal equatorial flow with an associated free-surface. Following the derivation of the solution we demonstrate that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface's shape. Finally, the solution for stratified fluid flow is subjected to a short-wavelength stability analysis.

Finite Volume Solution of Non-Newtonian Casson Fluid Flow in A Square Cavity

A two dimensional unsteady flow of non-Newtonian fluid in a square cavity is investigated numerically by using finite volume method based on staggered grids. The discretized equations are integrated by using second order Adams-Bashforth time advancement scheme togather with pressure correction approach. Error history for velocities and pressure are recorded for high Reynolds number when grid resolution is \(128\times128\). The results are also compared with already published work for special case. An excellent agreement is observed. The behavior of velocity components are studied for different values of non-Newtonian parameter $\beta$, the Casson fluid parameter.