Solution Of Fluid Flow Research Articles

Different families of new exact solutions for planar and nonplanar second grade fluid flows

Three different families of new exact solutions for second grade fluid flows are derived in this paper. First family of two dimensional exact solutions are obtained by assuming a novel form for the stream function and these solutions contain spatially periodic as well as non-periodic solutions. The subclass of periodic solutions extends the rectangular array of Taylor vortices to more complex structures of two dimensional vortices. Second family of planar solutions are also having vortex structures similar to Taylor vortices. Third family of exact solutions are pseudo planar flows of second kind. All these exact solutions reduce to corresponding new exact solutions for Newtonian fluid flows when the normal stress moduli are absent. • Three different families of new exact solutions for second grade flows are derived. • The first family of spatially periodic solutions exhibit complex array of vortices. • Rectangular array of Taylor vortices are special cases of the derived solutions. • Second family also contains solutions which are spatially periodic. • Third family of solutions represents pseudo planar solutions of second kind.

Analysis of Hydromagnetic Double Exothermic Chemical Reactive Flow with Convective Cooling through a Porous Medium under Bimolecular Kinetics

In this study, the analytical solution of steady hydromagnetic double exothermic combustible reaction fluid flow in a porous medium with convective cooling wall is presented. The viscous heating reactive liquid is totaling exothermic without consumption of material. The combustion reaction of the fluid takes place in a Poiseuille device, and it is been propelled by pressure gradient and pre-exponential bimolecular kinetics. The device is exposed to convective cooling to keep the reactive hydromagnetic fluid from distortion. The weighted residual method (WRM) is analytically used to get the numerical values for the dimensionless nonlinear governing equations. The solution to temperature and velocity distribution is carried out and the result is graphically depicted. The Nusselt number and skin friction coefficient is also showed for some significant parameters engrained in the flow and the solution obtained is compared with numerical method. As obtained in the study, the second exothermic reaction term increases the combustion process; hence the term will assist in reducing toxic discharge from the engines that pollute the environment. The Frank-Kamenetskii parameter contributes highly to system thermo-fluid destruction; as such it must be monitored.

Numerical solution of micropolar fluid flow with heat transfer by finite difference method

In this paper, we focused on time-dependent flow of micropolar fluid between parallel permeable plates. Fluid is electrically conducting. Magnetic field is applied in the transverse direction to flow. Energy equation is modeled in the presence of viscous dissipation, thermal radiation and Joule heating. Suction is considered at lower plate while injection is considered at upper plate. Appropriate dimensionless variables are employed to reduce the governing PDE’s system into dimensionless one. Nondimensional PDE system is tackled numerically by finite difference technique. Effects of flow parameters on velocity, micro-rotation, temperature, couple and shear stresses at plates and Nusselt number are discussed. The obtained outputs show that for nonzero electric field parameter the velocity increases with Hartmann number. For zero electric field parameter the velocity decreases with Hartmann number. Temperature increases with both electric and magnetic field parameters. Micro-rotation decreases with micro-rotation material parameter and it increases with time.

Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow

This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with a newly proposed approach using a discrete time derivative of the Laplacian of the extra stress tensor. Both methods are implemented in a finite element code and demonstrated in the solution of a viscoelastic fluid flow in a two-dimensional corrugated channel for a range of Weissenberg numbers. The numerical simulations have shown that this new temporal stress diffusion not only efficiently stabilizes numerical simulations, but also vanishes when the solution reaches a steady state. It is demonstrated that in contrast to the standard tensorial diffusion, the temporal artificial stress diffusion does not affect the final solution.

Existence of dual solution for micro-polar fluid flow with convective boundary layer in the presence of thermal radiation and suction/injection effects

The goal of this research is to see if there exist dual solutions for the two-dimensional magneto-hydrodynamics (MHD) flow of a micro-polar fluid in a porous media with thermal radiation and suction/injection effects. By considering the porosity and permeability effects, the Darcy model is used to create a micro-polar fluid model over the pores. The nonlinear ordinary differential equations are obtained using an appropriate linear similarity transformation. In terms of the incomplete gamma function, the dual branches of two-dimensional fluid flow are derived in the closed form solution. The analytic closed form solution with duality for all fluid flow parameters, as well as the impacts of the micro-rotation parameter on the Nusselt number due to the dual nature closed form solutions, the impacts of physical parameters on non-dimensional velocity, temperature, skin friction coefficient, micro-rotation, and local Nusselt number are investigated and demonstrated graphically.

Smoothed Particle Hydrodynamics vs Lattice Boltzmann for the solution of steady and unsteady fluid flows

Smoothed Particle Hydrodynamics vs Lattice Boltzmann for the solution of steady and unsteady fluid flows

Similarity solution of second grade fluid flow over a moving cylinder

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter [Formula: see text] increase, which means the momentum boundary layer increases for enhancing the material parameter [Formula: see text]. The temperature gradient reduced due enhancing the values of material parameter [Formula: see text] because thermal boundary layer reduced for higher values of material parameter [Formula: see text].

Effect of stress diffusion on the Oldroyd-B fluid flow past a confined cylinder

• The stress diffusion is thermodynamically consistent. • Mesh convergence is obtained by adding the diffusion term to the Oldroyd-B model. • The diffusion term does not significantly change the velocity profile. For the Oldroyd-B fluid flow past a cylinder, it has been well known that converged solutions for the stress in the wake downstream of the cylinder cannot be obtained when the Weissenberg number exceeds 0.7. This has been an unresolved problem [M.A. Alves, P.J. Oliveira and F.T. Pinho, Annu. Rev. Fluid Mech., 53:509-41, 2021]. This problem has various origins, such as the validity of numerical methods and the constitutive equation. This study examines the relationship between the convergence with respect to mesh refinement and the thermodynamically modified Oldroyd-B fluid, which has a diffusion term. We show that stress diffusion is thermodynamically natural and contributes to the convergence of the numerical solution for the Oldroyd-B fluid flow past a cylinder. Stress diffusion has typically been neglected because of its small value, although it is inherent to real polymers. The diffusion term does not change the flow behavior significantly but facilitates the determination of a mesh converged stress solution for the Weissenberg number up to 0.8. This result cannot be obtained from the original Oldroyd-B model. It is thus revealed that the diffusion term can effectively stabilize the stress in the region of steep stress gradients.

An approach to accelerate the convergence of SIMPLER algorithm for convection-diffusion problems of fluid flow with heat transfer and phase change

A new segregated pressure-based algorithm is developed to solve two-dimensional incompressible fluid flows with convective heat transfer and liquid to solid phase change by the finite volume method. The predictive-correction scheme is based on the SIMPLER algorithm with n added iterative cycles to increase the accuracy of pressure in satisfying the discretized continuity equation. The performance of SIMPLERnP is compared with SIMPLER and IDEAL in the solution of the laminar fluid flow in a lid driven cavity, natural heat convection inside a square cavity, convective heat transfer in the annular space between two concentric cylinders and conjugate natural heat convective solidification of a binary alloy that included the transient heat conduction in the thick mold walls. The results indicate that the proposed algorithm is highly stable, even when a value of 0.99 is used for the under-relaxation of the velocity components, and allows significant improvements in the reduction of the number of iterations and time of computation. • SIMPLERnP improved sequential pressure algorithm for convection-difussion problems. • Natural heat convection of water including properties varying with temperature • Robust and stable segregated numerical solutions for heat transfer and phase change • P-v-T fast accurate finite volume heat predictions almost without under-relaxation • Improved numerical performance for complex heat transfer problems with larger grids

Analytical closed-form solution for fluid flow through microchannel heat sinks including axial conduction

An analytical study on the convective heat transfer through a rectangular microchannel heat sink including solid axial conduction, has been performed. The system has been split into two coupled boundary value problems, each addressing the heat transfer to the fluid through different routes (namely, the sidewall or fin and the base wall or substrate ). The results are derived in the form of a net wall and fluid temperature rise. The validation of the proposed analytical model has been done using existing experimental data and a three-dimensional conjugate computational model. The results show excellent agreement in terms of solid and fluid temperature distributions. The parametric studies show an increasingly non-linear behaviour in the solid and fluid temperature profiles in the microchannel, if axial conduction is dominant. The simulated results are consistent with the CFD and experimental outcome. It has also been noted that a uniform heat flux applied at the bottom of the microchannel (substrate) cannot ensure the transfer of heat uniformly to the fluid. If axial conduction is high, a significant fraction of the applied heat influx is transmitted to the fluid near the channel entry region with a corresponding reduction in the flux distribution at the channel exit.

Comsolic solution of an elliptic cylindrical compressible fluid flow

In this article, the primary focus is to investigate the heat transfer effects with viscous compressible laminar flow in the permeable elliptic cylinder. The Reynolds number is kept 100 for flow to be laminar. The physics of heat transfer is selected to be coupled with the laminar flow. The results for particular step-size time for Velocity distribution, pressure profile, temperature profile, isothermal temperature contours, and drag coefficient have been analyzed. Mesh has been generated through COMSOL, mesh entities have been elaborated statistically. The maximum and minimum velocity profile is observed at the elliptical cylinder’s walls and upper, lower boundary respectively. The maximum velocity observed is 2.22 m/s. Pressure profile around elliptic corners is found maximum, distinct patterns are observed even under the influence of applied heat. Temperature is observed maximum at walls but it gradually increases as moving from the upper boundary towards the lower boundary. The isothermal contour patterns are observed maximum near the walls, drag coefficient of gradual decrease is observed. COMSOL multi-physics is utilized for mathematical modeling of problems and the Backward-Differentiation-Formula has been exploited to handle problems numerically. The results will help greatly to understand the characterizations of viscous fluids and in industries like air furnaces and automobile cooling systems.

A high-order accurate meshless method for solution of incompressible fluid flow problems

Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or elements, issues such as grid skewness that adversely impact accuracy are eliminated. Gaussian, Multiquadrics and inverse Multiquadrics are some of the most popular RBFs used for the solutions of fluid flow and heat transfer problems. But they have additional shape parameters that have to be fine tuned for accuracy and stability. Moreover, they also face stagnation error when the point density is increased for accuracy. Recently, Polyharmonic splines (PHS) with appended polynomials have been shown to solve the above issues and give rapid convergence of discretization errors with the degree of appended polynomials. In this research, we extend the PHS-RBF method for the solution of incompressible Navier-Stokes equations. A fractional step method with explicit convection and explicit diffusion terms is combined with a pressure Poisson equation to satisfy the momentum and continuity equations. Systematic convergence tests have been performed for five model problems with two of them having analytical solutions. We demonstrate fast convergence both with refinement of number of points and degree of appended polynomials. The method is further applied to solve problems such as lid-driven cavity and vortex shedding over circular cylinder. We have also analyzed the performance of this approach for solution of Euler equations. The proposed method shows promise to solve fluid flow and heat transfer problems in complex domains with high accuracy.

Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls

In this paper, the temporal stability of multiple similarity solutions (flow patterns) for the incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is analyzed. This work extends the recent results of similarity perturbations of Sun et al. [“Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls,” Appl. Math. Modell. 77, 738–755 (2020)] by examining the temporal stability with perturbations of general form (including similarity and nonsimilarity forms). Based on the linear stability theory, two-dimensional eigenvalue problems associated with the flow equations are formulated and numerically solved by a finite difference method on the staggered grids. The linear stability analysis reveals that the stability of the solutions is same with that under the perturbations of a similarity form within the range of the wall expansion ratio α. [−5≤α≤3 as in Sun et al., “Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls,” Appl. Math. Modell. 77, 738–755 (2020)]. Further, it is found that the expansion ratio α has a great influence on the stability of type I flows: in the case of wall contraction (α<0), the stability region of the cross-flow Reynolds number (R) increases as the contraction ratio (|α|) increases; in the case of wall expansion and 0<α≤1, the stability region increases as the expansion ratio (α) increases; in the case of 1≤α≤3, type I flows are stable for all R where they exist. The flows of other types (types II and III with −5≤α≤3 and type IV with α = 3) are always unstable. As a nonlinear stability analysis or a validation of the linear stability analysis, the original nonlinear two-dimensional time-dependent problem with an initial perturbation of general form over those flow patterns is solved directly. It is found that the stability with the nonlinear analysis is consistent with the linear stability analysis.

An exact solution of a fluid‐structure interaction problem

AbstractWe construct an exact solution for a stationary fluid flow through a channel with upper wall attached to an elastic spring. The position of the upper wall is determined from the interaction between the fluid and the wall. It is displacement computed from a quartic equation that can be solved by radicals and the solution is proved to be physically reasonable.

The impact of isothermal flow assumption on accuracy of pressure transient analysis results

AbstractAdiabatic expansion and viscous dissipation of fluid flow in porous media result in considerable heating or cooling of hydrocarbon fluids when pressure gradients are very large. Traditionally, fluid flow in porous media has been assumed isothermal in hydrocarbon reservoirs. While this assumption helps with simplifying the physics of fluid flow by neglecting the thermal effects, it imposes a dominant impact on fluid properties in situations where flow undergoes fast paced and abrupt changes in flow rate and or pressure. The analytical solutions of fluid flow for pressure transient analysis rely on the isothermal flow assumption. Since the variations of fluid properties are not accounted for in temperature fluctuations, there is an inherent error in standard methods of well test analysis. In this paper, the errors in pressure transient analysis as a consequence of the assumption of isothermal fluid flow are investigated. The magnitude of error is quantified as a function of flow rate and pressure drop. Error analysis shows that at higher flow rates, the thermal impacts are elevated such that the application of isothermal flow models becomes erroneous and invalid. It can be shown that oil well tests are more influenced by thermal effects compared to gas well tests in conventional dry gas reservoirs. This study highlights an important thermal impact that is often neglected and should be considered in the design, execution, and analysis stages of well testing. Also, it suggests that isothermal analytical models should be avoided for well test analysis with large flow rates.

Finite element solutions of non-Newtonian dissipative Casson fluid flow past a vertically inclined surface surrounded by porous medium including constant heat flux, thermal diffusion, and diffusion thermo

This research investigates the simultaneous effects of thermal diffusion and diffusion thermo on incompressible, viscous, electrically conducting non-Newtonian Casson fluid flow past a vertically inclined surface through a porous medium in the presence of the uniform transverse magnetic field, chemical reaction, viscous dissipation, and constant heat flux. The action of thermal radiation and viscous dissipation is scrutinized. The fundamental governing equations determining the flow condition are transfigured as nonlinear coupled partial differential equations through self-similarity transmutations. The finite element technique is implemented to acquire the solution to the problem. Graphs are plotted to inspect the influence of sundry physical quantities on the three routine profiles of the flow field. Further, expressions are procured for friction factor and the rate of heat and mass transfers and discussed comprehensively through tabular forms. Favorable comparisons with previously published work on various exceptional cases of the problem are obtained. This research shows that the Soret number increases both the velocity and concentration fields, and the Dufour number increases the velocity and temperature fields. It is also observed that concentration and velocity fields reduce toward chemical reaction parameter. Furthermore, the Schmidt number decreases the velocity and concentration profiles. It is also noteworthy that velocity decays for the magnetic variable. An improvement in radiation declines the velocity and temperature profiles.

Example-based terrain synthesis with pit removal

Artificial terrain synthesis is challenging because natural terrain contains many types of features generated by a diverse range of natural processes over vastly different time-scales. Example-based terrain synthesis has been used to overcome the challenge by using real-world terrain as the basis for synthesis. This produces good local behaviour but can have poor global behaviour. We introduce fluid-flow solutions that can be overlaid on multi-resolution example-based terrain synthesis to improve global realism. We apply these to an existing pixel-based terrain synthesis method and to a novel terrain synthesis method, terrain optimisation, based on texture optimisation. Our fluid-flow solutions improve results for artificial terrains.

Development of a phase change solver for concentrated energy beam applications

A phase-change computational fluid dynamics (CFD) solver module was developed for the numerical solution of melting, solidification and evaporation of any substrate under a concentrated energy beam (CEB). The solver module was developed as a part of general purpose CFD solver AnuPravaha. It is a finite volume method-based CFD solver capable of numerical solution of various fluid flow and heat transfer problems over the hybrid unstructured grid. The phase change module for CEB applications was developed in 2-D planer, 2-D axis-symmetric and 3-D framework. A fixed grid enthalpy-porosity technique was used to capture the phase change phenomena. CEB was implemented as a surface heat flux boundary conditions. Various associated phenomena like Marangoni flow and natural convection was studied for laminar flow regime.The solver for turbulent flow is currently getting developed. The numerical solver was validated for melting of copper and melting and evaporation of tin under a 270 o bend pencil Electron Beam Gun (EBG) evaporator. The numerical solutions from the solver were found to be in very good agreement with experimental results with less than 5% deviation. A case study was carried out using the validated solver for maximizing the molten pool fraction in the evaporator system for laser based purification processes. It was observed that for the particular geometry of the evaporator, the e-beam power and crucible thickness variation did not assist significantly in maximizing the molten pool fraction. However, the variation in the aspect ratio improves the molten pool fraction significantly. Studies like these can be utilized for designing new evaporator cavity with optimized parameters.

A least-squares finite element method for steady flows across an unconfined square cylinder placed symmetrically in a plane channel

• LSFEM is used for simulating non-Newtonian power-law unconfined square cylinder flows. • A square cylinder at two inclination angles is placed symmetrically in a plane. • An a priori error estimate for LSFEM and the a posteriori error bound have addressed. • Results agree with the theoretical estimates and others published in the literature. • The effects of the inclination angles and physical parameters have presented. This paper develops a least-squares finite element method (LSFEM) for non-Newtonian flows of power-law fluid across an unconfined square cylinder at two inclination angles, placed symmetrically in a two-dimensional channel. We used Newton's method to linearize the equation of motion and employed the least-squares approach with systematic mesh refinements to flow past the square cylinder. The LSFEM offers a direct approximation of the extra stress tensor components, a symmetric positive definite system, and the openness of choosing finite element spaces. We proved that the least-squares approximation converges to linearized solutions of non-Newtonian fluid flows. We demonstrated that the numerical results using low-order basis functions agree with the theoretical estimates and presented the effects of different physical parameters on the physical attributes of the power-law model at a low Reynolds number, such as drag coefficients, viscosity, and velocity. These results agree with others published in the literature. Hence, the LSFEM in non-Newtonian fluid simulations can accomplish the identification of shear-thinning and shear-thickening characteristics.

Laguerre wavelet numerical solution of micropolar fluid flow in a porous channel with high mass transfer

This paper provides the Laguerre wavelet method (LWM) for the 2-dimensional flow of a rotating micropolar fluid in a permeable channel with high mass transfer. The governing coupled nonlinear partial differential equations (PDEs) are reduced to the coupled nonlinear ordinary differential equations (ODEs) using Berman’s similarity transformation before being solved numerically by a Laguerre wavelet method. We also compare this work with the Optimal Homotopy Asymptotic method (OHAM) and the Runge-Kutta method. Moreover, in the graphs of the F(η), F′(η) and G(η), we show that solutions obtained by the future method are more precise and applicable than other available methods in the literature. Numerical outcomes illuminating the properties of different physical parameters connected with the flow are discussed.