Solution Of Fluid Flow Research Articles

Analytical Solution for Fluid Flow and Heat Transfer in a Three-Dimensional Inclined Horizontal Channel and Under The Influence of Thermal Radiation

Analytical Solution for Fluid Flow and Heat Transfer in a Three-Dimensional Inclined Horizontal Channel and Under The Influence of Thermal Radiation

Calculating the entropy generation of a Bingham plastic fluid flow due to a heated rotating disk

We present the numerical study of the flow on a heated rotating disk for Bingham plastic fluid. Thermo-physical properties and viscous dissipation are assumed with the influence of entropy generation. This kind of study has a significant attentiveness in the fields of applied engineering for their increased mathematical advantages. We analyzed the solutions of fluid flow and entropy phenomenon for the Bingham fluid. The similarity solution was firstly presented by von Kármán for Newtonian fluid, it is found to be beneficial for the Bingham plastic fluid by transforming the boundary layer partial differential equations into ordinary differential equations. Shooting method is used to crack the dimensionless ordinary differential equations. The Bingham model is momentous for unlimited high shear rates for this we suggest these numerical data provide accurate description of the Bingham fluid and entropy minimization near a rotating disk. The outcomes exhibits that the azimuthal velocity profiles upsurges for upward values of Bingham fluid, and the similar behavior for tangential radial velocity is perceived. The temperature curve is noted to be enhanced for higher magnitudes of Eckert number and thermal conduction parameter. The soret number and diffusivity coefficient creates increment in concentration curve. The entropy function in the flow system enhances for up surging the inputs of Bingham fluid coefficient and thermophoresis diffusion. The results are locally similar for various parameters. We have also included the comparison analysis with published works.

MHD flow and conductive heat transfer on a permeable stretching cylinder: Benchmark solutions

Research is conducted on parametric heat transfer and fluid flow solutions under the influencing factors of the porous stretching cylinder, magnetic field, curvature, permeable media, radiation, Joule heating, viscous dissipation, and heat generation/absorption. High non-linear coupled PDEs are solved and result in high non-linear coupled ODEs. The confluent hypergeometric function solves the energy equation with the PHF (prescribed heat flux) boundary condition. An analysis of physical parameters' effects is presented as tables and figures. According to the results, the variation of radiation parameters and Eckert numbers for the local Nusselt number in the injection area is negligible, while the variation of the heat source/sink parameters is considerable. The suction/injection and curvature parameters directly affect the local skin friction coefficient and Nusselt number. The porous stretching cylinder has a higher skin friction coefficient and heat transfer rate when compared to the porous stretching sheet.

Closed‐form solution of fluid flow in and around a crack disk embedded in a 3D porous medium

AbstractThis paper considers the fluid flow through a porous medium containing intersecting fractures and presents three main analytical findings, namely: (1) mass exchange between fractures and surrounding matrix at the fracture intersection; (2) fluid potential solution (pressure field) within the whole domain under the form of a single singular integral equation; and (3) closed‐form solutions of fluid flow in and around a crack disc under a far field pressure gradient. The crack is represented mathematically by a 2D smooth surface (i.e., zero thickness) within a 3D porous medium, while physically by a constant aperture. The fluid flow within the crack obeys Poisseuille's law, while Darcy's law is used to represent the fluid flow in the surrounding matrix. The general solution of pressure field for the general case of multiple intersecting cracks is firstly derived under a singular integral equation form. The mass exchange between the porous matrix and the crack, as well as the mass conservation at the intersection between cracks are the keys to obtaining this general solution. Then, the general solution is written for the case of a single crack. Rigorous derivation of the latter equation allows obtaining a closed‐form solution of flow through a single crack. Introducing this solution of flow into the general equation gives the pressure field around the crack. The solution derived in this paper for a crack disk with Poisseuille's flow is slightly different from the well‐known Eshelby's solution for the case of flattened inclusion in which the flow obeys Darcy's law.

Lattice Boltzmann model in general curvilinear coordinates applied to exactly solvable 2D flow problems

Numerical simulation results of basic exactly solvable fluid flows using the previously proposed by H. Chen Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a fundamental one-to-one exact advection feature in producing minimal numerical diffusion, as the Cartesian lattice Boltzmann model. As we numerically show, the new model converges to exact solutions of basic fluid flows with the increase of grid resolution in the presence of both natural curvilinear geometry and/or grid non-uniform contraction, both for near equilibrium and non-equilibrium LBM parameter choices.

Computational analysis in underexpanded jets simulations

Flammable gases leaks at high pressures are hazardous, especially the free underexpanded jets. Therefore, understanding their behavior is fundamental to guarantee a safe environment. Due to the difficulty to obtain experimental data from free under expanded jets, related to the great speeds and gradients, computational fluid dynamics (CFD) has become an essential tool. Simulations for free underexpanded jets to identify algorithms that better represent this problem were performed in this work. The analysis involved different algorithms for fluid flow solution and a local time stepping approach using both OpenFOAM and ANSYS Fluent CFD packages. Our study concluded that all algorithms and software studied had a satisfactory result compared to experimental data. However, we observed that Fluent had a considerable advantage because the simulation was faster compared with other solvers in OpenFOAM, for instance.

A computationally efficient model for fracture propagation and fluid flow in naturally fractured reservoirs

There is a need to develop computationally efficient models for oil and gas production from naturally fractured reservoirs. In this paper, we present an efficient, integrated fracturing-production simulator by combining a boundary element method (for fracture propagation) and a general Green's function solution (for fluid flow) that eliminates the need to discretize the matrix domain. First, the model is validated against analytical solutions and then compared with a fully numerical model. A comparison of results and computation time shows that our simulator significantly reduces the computation cost without any significant loss in accuracy. The simulator is then applied to investigate the effect of cluster spacing and pumping schedule on production from a hydraulically fractured horizontal well in a naturally fractured reservoir. The results show an optimal cluster spacing that can maximize the contact area between fractures and reservoirs while maintaining the highest production rate. Based on the chosen optimal cluster spacing, we observe that changes in the pumping schedule can have an impact on the production rate due to changes in the created fracture network.

New classes of periodic and non-periodic exact solutions for Newtonian and non-Newtonian fluid flows

Two different families of planar exact solutions for second grade fluid flows are derived in this paper. Exact solutions for Newtonian fluid flows are derived as particular case when normal stress moduli vanish. The novelty of the solutions is that they are obtained by assuming the stream functions as a finite sum of functions with different arguments. An important property of the derived solutions is that solutions in a given family are all superposable flows. The first family of solutions can be considered as a generalization of rectangular array of Taylor vortices as these classical solutions are special cases of the derived exact solutions. A subfamily of spatially periodic exact solutions for both Newtonian and non-Newtonian fluid flows are also derived. The complex structures of the two dimensional vortices are illustrated in several cases. • Two new families of exact solutions for second grade fluid flows are derived. • These solutions are classified as generalized Taylor vortices. • The solutions in a given family are superposable flows. • Subfamily of spatially periodic solutions are constructed. • Exact solutions for Newtonian flows are also derived.

Mixed electroosmotic/pressure-driven flow for a generalized Phan–Thien–Tanner fluid in a microchannel with nonlinear Navier slip at the wall

This work derives an approximate solution of the laminar viscoelastic fluid flow through a parallel flat plate microchannel, driven by electroosmotic and external pressure forces. In contrast to other works published in the past, in the present analysis, the fluid’s rheology obeys the generalized Phan–Thien–Tanner model that has been proposed recently, which uses the Mittag-Leffler function instead of linear or exponential functions of the trace for the stress tensor. The hydrodynamic analysis considers a non-linear Navier slip law at the wall that follows a power-law behavior on the shear stress. For the electric potential in the electric double layer, the Debye–Hückel approximation was used, and it is assumed that the wall’s zeta potentials are symmetric. The solution obtained in this work depends on several dimensionless parameters that allow controlling the flow: ɛWi2 characterizes the fluid’s viscoelasticity, the electrokinetic parameter κ̄, the dimensionless slip coefficient L̄, the slip-power exponent m, and the ratio between pressure and electroosmotic forces, G. Besides, the influence of two parameters of the Mittag-Leffler function, α and β, notably affects the flow’s characteristics. Our results evidence the important consequences of considering the generalized Phan–Thien–Tanner model and the slippage effect on the flow field compared to that described by the Phan–Thien–Tanner model.

Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems

Viscous flows through compliant conduits apply forces at the solid-liquid interface, leading to deformation of the cross-section, which affects the flow rate--pressure drop relation. Conventionally, calculating this relation requires solving the coupled elastohydrodynamic problem of flow and deformation. Instead, we employ reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate--pressure drop relation in deformable channels, using a domain perturbation expansion that only requires the fluid flow solution and the elastic deformation due to the fluid stress distribution in an undeformed channel.

Automated regional citrate anticoagulation based on online monitoring of ionized calcium concentration: Proof of concept.

Regional citrate anticoagulation (RCA), a complex and effective technique, is recommended as the anticoagulation of choice for continuous renal replacement therapy. One of its key objectives is to keep the ionized calcium in the targeted range. In this study, we aimed to develop an automated RCA based on online monitoring of the ionized calcium concentration and closed-loop feedback. We constructed calcium-selective electrodes with liquid inner contact, which measured a potentiometric signal as the output. We tested the responses, stability, and selectivity of the electrodes in flowing fluid containing calcium chloride. We compared the measurement accuracy between the electrodes and an i-STAT system in vivo. Moreover, we established closed-loop feedback using a proportional-integral-derivative controller model. We performed simulated automated RCA both in vivo and in vitro. The electrode gave a Nernstian response to the variation of ionized calcium concentration. It showed high stability and a relatively short response time. Changes in the fluid flow rate, solution PH, and addition of metal ions including Mg2+ and K+ did not interfere with the measurements of ionized calcium. These measurements in whole blood by the electrode were very close to those assessed by the i-STAT system. The feedback control system responded quickly to an abnormal ionized calcium concentration and regulated the infusion rates of calcium or citrate to maintain the concentration of ionized calcium within the targeted range. We successfully trialed automated RCA, which may help simplify the complexities of RCA in the future.

Steady-State Solution of MHD Heat and Mass Transfer Fluid Flow over a Semi-Infinite Vertical Plate in a Rotating System Dipped in a Porous Medium with Hall Current, Thermal Radiation, Heat Generation/Absorption and Joule Heating

The steady-state solution of unsteady MHD radiating fluid flow concerning heat and mass transfer in a rotating system dipped in a medium of porosity with Hall current along a semi-infinite vertical plate have been inquired numerically. By using appropriate usual conversions, the governing equations for the present study are converted into the form of dimensionless non-linear partial differential equations (PDEs). The explicit finite difference method (FDM) is imposed to solve the acquired coupled non-linear PDEs. MATLAB R2020a has been employed as a numerical simulation tool. For assuring accuracy and for obtaining convergence solutions the stability and convergence criteria of the present model have been fabricated. The stability analysis imposes circumscriptions on several elements as 0.50≤M≤10, 0.01≤βh≤5, K≤326.50, 0.185≤Pr≤7.56, 0.00≤R*≤80, Sc≥0.18 and Q0≤326.50. The mesh sensitivity experiment for finer mesh space and time validation experiment for steady-state solutions are comprised of acquired solutions. The consequences of the present findings are compared with several previously published research works for claiming validation. The present study accentuates the effects of those parameters, which are relevant to the dimensionless model equations. Finally, the obtained results are placed in graphs and sorted into tables.

Impacts of slip and mass transpiration on Newtonian liquid flow over a porous stretching sheet

AbstractThis article focuses on analytic solutions for Newtonian fluid flow with slip and mass transpiration on a porous stretching sheet using the differential transform method and Pade approximants of an exceptionally nonlinear differential equation. The impacts of different parameters including mass transpiration (suction/injection), Navier's slip, and Darcy number parameters on the velocity of the liquid and tangential stress are discussed. A comprehensive comparison of our results with the previous one in the literature is made, and the results showed good agreement. An investigation is conducted of a combination of magnetic liquids that are conceivably pertinent for wound medicines, skin repair, and astute coatings for natural gadgets. It is found that there is a decrease in the velocity profiles and the boundary layer thickness for the case of suction.

Unsteady electromagnetohydrodynamic flow of couple stress fluid through a microchannel: A theoretical analysis

In this work, we investigate the transient electromagnetohydrodynamic (EMHD) flow of non-Newtonian fluid in a narrow/micro-fluidic channel. We consider the couple stress fluid (CSF) model to characterize non-Newtonian behaviour. We present an analytical solution for electric potential and temporal EMHD flow velocity by applying the standard Laplace transform method using physically relevant boundary conditions. We demonstrate the excellent agreement between the present analytical solution for fluid flow with the CSF model and previously reported results for a Newtonian fluid. We analyse the transient flow velocity and volume flow rate for a wide range of flow governing parameters. We notice that the steady-state flow velocity magnitude is higher for magnetic parameter/ Hartmann number values than for the couple stress parameter values, which characterizes the flow’s viscous resistance. We demonstrate that the contribution of couple stresses in the fluid medium is prominent in the combined pressure, magnetic and electroosmotic force to increase the volume flow rate, which contrasts with the EMHD flow of Newtonian fluid. We observe that the critical Hartmann number attains a fixed value (about 1.3) for higher values of the couple stress parameter due to the transverse electric field effect. The present work hold the key towards explaining non-Newtonian behaviour impersonating bio-fluid transport in the narrow/micro-fluidic channel under the combined effect of electromagnetic force and pressure gradient. The results anticipated from the present attempt are useful to develop efficient electro-magneto-mechanical and micro-bio-fluidic devices.

A Bayesian Multi-Region Radial Composite Reservoir Model for Deconvolution in Well Test Analysis

Abstract In petroleum well test analysis, deconvolution is used to obtain information about reservoir systems, for example the presence of heterogeneities and boundaries. This information is contained in the response function, which can be estimated by solving an inverse problem in the pressure and flow rate measurements. Our Bayesian approach to this problem is based upon a parametric physical model of reservoir behaviour, derived from the solution for fluid flow in a general class of reservoirs. This permits joint parametric Bayesian inference for both the reservoir parameters and the true pressure and rate values, which is essential due to the typical observational error levels. Using sets of flexible priors for the reservoir parameters to restrict the solution space to physical behaviours, samples from the posterior are generated using Markov Chain Monte Carlo. Summaries and visualisations of the posterior, response, and true pressure and rate values can be produced, interpreted, and model selection can be performed. The method is validated through a synthetic application, and applied to a field data set. The results are comparable to the state of the art solution, but through our method we gain access to system parameters, we can incorporate prior knowledge, and we can quantify parameter uncertainty.

One-dimensional optimal system of Lie sub-algebra and analytic solutions for a liquid film fluid flow

Lie symmetry procedure enables reduction of the dependent and/or independent variables of the differential equations through similarity transformations, if they admit a Lie point symmetry algebra. A 7-dimensional Lie point symmetry algebra for the fluid flow and heat transfer in a thin liquid film due to an unsteady stretching sheet has been obtained earlier. Here we construct the 1-dimensional optimal system of Lie sub-algebras, corresponding invariants and similarity transformations. We use these transformations in reduction of the independent variables of the considered flow model. We achieve double reductions of the model that convert the governing partial differential equations into ordinary differential equations. We present all classes of ordinary differential equations that are obtainable through the invariants associated with each member of the deduced optimal system. In some cases, we construct analytic solutions for these reduced systems of differential equations using Homotopy analysis method. The selection of these cases is based on the form of stretching sheet velocity, temperature and film thickness, i.e., both the former remain functions of space and time variables while the latter is a function of time only.

On the solutions of fluid flow problems with a Chebyshev collocation method using Mathematica

AbstractFluid flow problems are important in engineering applications like heat exchangers, renewable energy sources, and electromagnetic processing of materials, among other applications. Some examples related to a computational fluid dynamics (CFD) course are explored in this study. A CFD course provides tools for the numerical solution of fluid flows where an analytical cannot be found. Flows can be described by numerically solving the mass, momentum, and energy conservation equations for incompressible fluids. A Chebyshev collocation spectral method has been used to solve the governing equations. A high‐level functional programming language strategy was implemented in Mathematica including readability and adaptability. The programs are built by applying and composing functions, mappings, iterators, and pattern matching. It was noted that students can achieve a better comprehension of the algorithms using this programming approach.

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.

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.