Unsteady Fluid Flow Research Articles

Unsteady Compressed Williamson Fluid Flow Behavior under the Influence of a Fixed Magnetic Field (Numerical Study)

A numerical investigation is conducted into a two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with fixed thermal conductivity and external squeezing accompanied by viscous dissipation effect. Based on the flow geometry under consideration, the current flow model was created. The momentum equation takes into consideration the magnetic field when describing the impact of Lorentz forces on flow behavior. The energy equation takes varying thermal conductivity into account while calculating heat transmission. The extremely complex nonlinear, unstable governing flow equations for the now under investigation are coupled in nature. Due to the inability of analytical or direct methods, the Runge-Kutta scheme (RK-4) via similarity transformations approach is used to tackle the physical problem under consideration. The physical behavior of various control factors on the flow phenomena is described using graphs and tables. For increasing values of the Weissenberg parameter and the permeable velocity parameter, the temperature boundary layer thickens. As the permeable velocity parameter and squeezed flow index increased, the velocity profile shrank. The velocity profile grows as the magnetic number rises. Squeezed flow magnifying increases the Nusselt number's magnitude. Furthermore, the extremely complex nonlinear complex equations that arise in fluid flow issues are quickly solved by RK-4. The current findings in this article closely align with the findings that have been reported in the literature.

Soret and Dufour Effects on MHD Fluid Flow Through a Collapssible Tube Using Spectral Based Collocation Method

This paper examine numerical study for soret and dufour effects on unsteady Newtonian MHD fluid flow with mass and heat transfer in a collapsible elastic tube using Spectral Collocation technique. The objective of the study is to determine the velocity, temperature and concentration profiles together with heat and mass transfer rates. The governing equations are continuity, momentum, energy and concentration equation. The system of nonlinear partial differential equations governing the flow solved numerically by applying collocation method and implemented in MATLAB. The numerical solution of the profiles displayed both by graphically and numerically for different values of the physical parameters. The effects of varying various parameters such as Reynolds number, Hartmann number, Soret number, Dufour number and Prandtl number on velocity, temperature and concentration profiles also the rates of heat and mass transfer are discussed. The findings of this study are important due to its wide range of application including but not limited to medical fields, biological sciences and other physical sciences where collapsible tubes are applied.

A finite element-inspired hypergraph neural network: Application to fluid dynamics simulations

An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two nodes. Inspired by the data connectivity in the finite element method, we present a method to construct a hypergraph by connecting the nodes by elements rather than edges. A hypergraph message-passing network is defined on such a node-element hypergraph that mimics the calculation process of local stiffness matrices. We term this method a finite element-inspired hypergraph neural network, in short FEIH(ϕ)-GNN. We further equip the proposed network with rotation equivariance, and explore its capability for modeling unsteady fluid flow systems. The effectiveness of the network is demonstrated on two common benchmark problems, namely the fluid flow around a circular cylinder and airfoil configurations. Stabilized and accurate temporal roll-out predictions can be obtained using the ϕ-GNN framework within the interpolation Reynolds number range. The network is also able to extrapolate moderately towards higher Reynolds number domain out of the training range.

The Effect of Variable Heat Flux on Unsteady Laminar MHD Boundary Layer Flow and Heat Transfer Due to a Stretching Sheet

The purpose of this research is to look into the solution technique for obtaining MHD velocity and temperature profiles. In the presence of a changing heat flux, the unsteady laminar boundary layer flow and heat transfer of a viscous incompressible fluid across a stretching sheet are numerically investigated. The unsteadiness is thought to be generated by a sudden increase in the surface temperature and a time-dependent stretching velocity. The flow and heat transfer partial differential equations were numerically solved using an implicit finite difference scheme and a quasi-linearization technique. Both velocity and temperature rise with time and magnetic field, according to the findings. The computed results are compared to previous work that has been published. Variable heat flux (VHF) conditions have also been taken into account.

Unsteady non-Newtonian fluid flow past an oscillating vertical plate with temperature-dependent viscosity: A numerical study

The analysis of non-Newtonian fluid flow over an oscillating surface often involves numerical simulations and experimental investigations. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the Crank–Nicolson numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. The temperature-dependent viscosity is assumed for the flow analysis. The impact of chemical reaction and heat generation coefficient is used to examine the mass and heat transferal rates. The investigation of non-Newtonian fluid flow over an oscillating surface is crucial for a wide range of industrial, biomedical, and scientific applications. The governing model of equations occurs in the form of nondimensional PDEs and then we use the dimensionless variables in order to achieve the dimensional PDEs. These equations are numerically solved by using the Crank–Nicolson technique. The Crank–Nicolson scheme is used because it has the ability to provide accurate and stable solutions and make it a valuable numerical technique in various scientific and engineering disciplines. The findings indicate the significance of numerous parameters on the mass, velocity and energy regions. The numerical outcomes of skin friction are observed due to fluid parameter, viscosity parameter, Grashof numbers of heat and solutal rates.

Analysis of unsteady MHD fluid flow across two parallel discs with uniform fluctuation subject to modified Hall and activation energy

This study intends to examine the consequences of the externally applied magnetic field and modified Hall effect on nanofluid flow across two symmetrically spinning and extending discs, where continuously the upper disc moves upward and downward. The lower disc is vertically fixed. The discs rotate and move vertically, generating a 3D flow. The mass density, heat transfer and flow motion have been evaluated and modeled in the form of the system of partial differential equations (PDEs) with an additional influence of activation energy, heat source and chemical reaction. The system of PDEs is modified to an ordinary set of differential equations by employing the resemblance substitution method. The obtained system of ODEs is further solved through the numerical approach (bvp4c). The results are compared to the bvp4c package and published work for validity purposes. In the case of downward displacement of the upper disc, magnetic and Hall characteristics have a significant impact on the velocity curve. The energy curve elevates with the upward movement of the disc, while it reduces with the downward fluctuation. Furthermore, the mass transmission rate enhances with the influence of hall current, while diminishing with the impact of chemical reaction rate.

Examining laminar, non-stationary viscoelastic fluid flow between two parallel planes

The generalized Maxwell model is used to handle problems involving the unsteady flow of a viscoelastic fluid in a flat channel under the effect of a constant pressure gradient. Formulas for fluid flow, velocity distribution, and other hydrodynamic characteristics were found. Transient processes during unsteady flow of a viscoelastic fluid in a flat channel are investigated based on the discovered formulas. The analysis’s conclusions demonstrated that, at small Debord number values, the procedures of changing a viscoelastic fluid’s properties from an unstable to a stationary state essentially don’t differ from those of a Newtonian fluid. Exceeding the Debord number relatively unity, it has been established that the process of transition of a viscoelastic fluid from an unsteady state to a stationary state is of a wave nature, in contrast to the transition process of a Newtonian fluid, and the transition time is several times longer than that of a Newtonian fluid. It was also discovered that perturbed processes can arise during the transition. These disturbances occurring in unsteady flows of a viscoelastic fluid can be stabilized by mixing the Newtonian fluid within it. The implementation of this property is important in preventing technical failures or malfunctions.

Unsteady MHD Free Convection Flow of Fluid in Micro Channel in the Presence of Viscous Dissipation Between Vertical Parallel Two Walls

Convection is a process by which heat is transferred by movement of a heated water. The phenomenon where heat transfer process is driven by natural fluid motion due to temperature and density gradients is called free convection. The effect of slip velocity on thermal behaviours of MHD free convection flow over a vertical parallel two walls is the focus of this research. The mathematical equations which described the phenomenom includes momentum, magnetic field and energy equations. Condition for the existence and uniqueness of solution of the model equations were established using the approach of Lipschitz continuity. The model equations in dimensionless form were solved using Olayiwola’s generalized polynomial approximation method (OGPAM). The results obtained which contains the dimensionless parameters were presented graphically and discussed. It was observed that increase in Reynolds number and Knudsen number both enhanced the velocity distribution at the two walls. Also, magnetic field and temperature field were enhanced by magnetic prandtl number and Eckert number respectively.

Impact of chemical reaction, viscous dissipation and thermal radiation on MHD flow past an oscillating plate

This study analyzes the consequences of first-order chemical reactions, radiation, and viscous dissipation on the unsteady magnetohydrodynamic natural convective flow of a viscous incompressible fluid over a vertically positioned semi-boundless oscillating plate with uniform mass diffusion and temperature. An implicit finite-difference technique is employed to solve a set of dimensionless, coupled, nonlinear partial differential equations. The numerical results for fluid velocity, concentration, and temperature at the plate under different dimensionless parameters are graphically displayed. Due to first-order homogeneous chemical reactions, it has been discovered that the velocity rises at the time of a generative reaction and drops during a destructive reaction. A decline in velocity is observed with an increase in the phase angle, radiation parameter, and chemical reaction parameter. Further, it has been revealed that plate oscillation, radiation, chemical reactions, and the magnetic field significantly influence the flow behavior.

Unsteady Two-Dimensional Natural Convection Fluid Flow in a Valley Shaped Cavity

Unsteady Two-Dimensional Natural Convection Fluid Flow in a Valley Shaped Cavity

Heat and Mass Transfer Analysis of an unsteady Non-Newtonian Magnetohydrodynamic Fluid Flow (Semi-Analytical Solution)

In the presence of a time-dependent chemical reaction, this work investigates unsteady squeezing Casson nanofluid flow and heat transfer between two parallel plates under the influence of a uniform magnetic field. Considering the effects of viscosity dissipation, heat generation from friction resulting from flow shear, Brownian motion, Joule heating, and thermodiffusion. The problem's nonlinear differential equations are solved using the Runge–Kutta (RK-4) technique and the Homotopy Perturbation technique. The excellent accuracy of the results is evident since they have been compared with other results from earlier research. In the form of graphs and tables, flow behavior under the many physical factors that are modified is also covered and well described. This work has shown that, by normalizing flow behavior, magnetic fields may be utilized to manage a variety of flows. Additionally, it is demonstrated that in every situation, the effects of positive and negative squeeze numbers on heat and mass transfer flow are opposite. Moreover, the thermophoresis parameter decreases as the concentration field increases. However, when the Brownian motion parameter is increased, the concentration profile gets better. Additionally, several other significant factors were examined. The results of this study can facilitate quicker and easier research and assist engineers.

Gözenekli malzeme ile doldurulmuş yatay mikrokanaldan akışkan akışında kesirli zaman türevi

Fractional time derivative is considered in the description of the unsteady fluid flow through a horizontal microchannel filled with porous material. The resultant governing equations were solved using the Laplace transform technique and the method of undetermined coefficient in the Laplace domain. The Riemann-sum approximation approach was then utilized to obtain the solution in the time domain. The results were then simulated and presented as line graphs utilizing MATLAB (R2015b) to study the effects of the parameters involved in the fluid flow.

Unsteady MHD Free Convection Flow of a Second Grade Casson Fluid with Ramped Wall Temperature

The present study delves into the analysis of unsteady free convection flow involving a non-Newtonian Casson fluid adjacent to an infinitely tall vertical plate. The primary objective of this article is to examine the flow behaviour of a second-grade Casson fluid under varying critical parameters. The plate exhibits a gradual increase in wall temperature and is situated within a porous medium. The governing equations are transformed into a dimensionless form, using non dimensionless variables. The method of Laplace transform (MOLT) is employed to derive accurate solutions for the temperature and velocity within the flow field. To enhance comprehension of the issue, The impact of different physical parameters on the flow field has been examined through the utilization of graphs and tables. Outcome of the problem was compared with existing one which was in good agreement. The study revealed that the velocity magnitude was lower in the scenario with ramped temperature compared to the scenario with isothermal temperature. Finally, skin friction and Nusselt numbers of the present work are tabulated. The significant outcome of the present work is that the flow field for the present phenomena is same as that of the existing one in absence of radiation parameter and heat source parameter when, u(0,t)=0, β=∞.

Web Application for Mathematical Modeling of Unsteady Oil Flow in Porous Medium

Introduction. The analysis and interpretation of hydrodynamic research data are based on theoretical models and computational algorithms. Despite the demand for this topic, numerous issues related to unsteady fluid flows in oil reservoirs still require solutions. Therefore, mathematical setting of problems related to the account of unsteady fluid flow, the development of effective numerical methods and algorithms, their solution using modern web technologies are pressing. This study is aimed at developing a web application for mathematical modeling of the process of fluid filtration in single- porosity reservoirs when conducting a hydrodynamic study at a production well.Materials and Methods. To solve the problem, the methods of continuum mechanics and computational mathematics were applied. A model of oil flow in a single-porosity reservoir was presented. Python and JavaScript programming languages were used in the development of the application. The calculation results were stored in a relational database implemented using PostgreSQL tools.Results. A new web application has been developed for modeling the oil filtration process in single- porosity reservoirs. It is applicable for studying fluid dynamic processes and can be used to predict flowrates, production and calculation of optimal well operation modes.Discussion and Conclusion. The developed web application provides for building pressure and temperature fields in the reservoir near a flowing and shut-in production well and at various distances from it. This information makes it possible to urgently assess the duration of hydrodynamic studies, as well as to regulate the operation of wells. The application can be deployed in an existing network infrastructure and use all the functionality by connecting to a remote server. It is optimized for use on various platforms and has broad prospects for further development.

Analytical solution for unsteady Walters-B fluid flow by a deforming surface with acceleration using OHAM based package BVPh2.0

Current study aims at simulating fluid flow due to a deformable heated surface in an otherwise static viscoelastic fluid obeying Walters-B model. Velocity of the surface is supposed to grow as time from its initiation of motion progress. Simulations in this work are based on the assumption of quadratic surface temperature distribution. Temperature rise attributed to the frictional heating effect is accounted for in the analysis. By choosing appropriate base functions, homotopy solutions are developed for reasonably large values of material fluid parameter. Reliability of the analytical results is established by computing averaged squared residual of the system. The contributions of the surface acceleration and elasticity on the boundary layer formation are enlightened through the plots of velocity components and temperature. Skin friction measuring the stress experienced by the surface is evaluated and examined under different controlling parameters. The paper also presents a numerical solution using NDSolve of MATHEMATICA in a special case of steady flow, and such solution agrees very well with the corresponding homotopy solution.

Dual solutions for the two-dimension copper oxide with silver (CuO–Αg) and zinc oxide with silver (ΖnO–Αg) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip

PurposeThis paper aims to present dual solutions for the two-dimension copper oxide with silver (CuO–Ag) and zinc oxide with silver (ZnO–Ag) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip.Design/methodology/approachThe governing partial differential equations for the two dust particle phases are reduced to the pertinent ordinary differential equations using a similarity transformation. Closed-form analytical solutions for the reduced skin friction and reduced Nusselt number, as well as for the velocity and temperature profiles, were presented, both graphically and in tables, under specific non-dimensional physical parameters such as the suction parameter, Prandtl number, slip parameter and shrinking parameter, which are also presented in both figures and tables.FindingsThe results indicate that for the shrinking flow, the wall skin friction is higher in the dusty fluid when compared with the clear (viscous) fluid. In addition, the effect of the fluid–particle interaction parameter to the fluid phase can be seen more clearly in the shrinking flow. Furthermore, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable.Practical implicationsIn practice, the study of the stretching/shrinking flow is crucially important and useful. Both the problems of steady and unsteady flow of a dusty fluid have a wide range of possible applications in practice, such as in the centrifugal separation of particles, sedimentation and underground disposal of radioactive waste materials.Originality/valueEven though the problem of dusty fluid has been broadly investigated, very limited results can be found for a shrinking sheet. Indeed, this paper has succeeded to obtain analytically dual solutions. The stability analysis can be performed by following many published papers on stretching/shrinking sheets. Finally, the critical values and plotting curves for obtaining single or dual solution are successfully presented.

Efficient numerical scheme for studying dual-phase chemical reactions in unsteady Sisko fluid flow with relaxation times

This research article investigated the effects of dual-phase chemical reactions on the unsteady flow of Sisko fluid. Utilizing Caputo's fractional derivatives, the model captured the fractional behavior of the fluid and integrated relaxation times to reflect the viscoelastic nature of the Sisko fluid. The model also considered unequal diffusivities of the chemical species. The resulting equations were discretized using the finite difference method, complemented by the L1 algorithm. Our simulations underscored how memory parameters, β and γ, significantly shaped the concentration trajectories by emphasizing the impact of past flow behaviors. Moreover, the study identified the heterogeneous reaction parameter and the diffusion coefficients ratio as critical determinants in the reaction dynamics, underscoring their role in the system's behavior. This study illuminates the intricate matrix of relationships in the realm of chemical reactions and viscoelastic fluid flow, offering valuable insights for fields ranging from chemical processing to environmental remediation.

Unsteady Casson fluid flow on MHD with an internal heat source

The present paper investigates the heat transfer features of a viscous fluid in an unsteady incompressible Casson fluid flow through a porous medium with an internal heat source under the influence of a magnetic field. A Casson fluid passes through the given porous medium using Darcy model. The study involves simulating the flow using mathematical models based on conservation laws and similarity transformations. The resulting highly nonlinear coupled ordinary differential equations are solved using the Bernoulli wavelet numerical approach. The study utilizes graphical tools to illustrate the flow behaviour under different physical factors, including the effect of the internal heat source. The normalization of the flow behaviour by the magnetic field suggests that it could potentially be used to control various flows. The study finds that various physical parameters which affects the velocity and temperature profiles of the fluid.

Conjugate Heat Transfer Evaluation of Turbine Blade Leading-Edge Swirl and Jet Impingement Cooling With Particulate Deposition

Abstract Internal cooling structures for gas turbine engines are becoming more complicated to push the hot gas temperature as high as possible, which, however, allows particulates drawn into the coolant air to be more readily to deposit within these passages and thus greatly affect their flow loss and thermal performance. In this study, internal swirl cooling and jet impingement cooling subjected to particulate deposition were evaluated and compared using a conjugate heat transfer method, with an emphasis on the thermal effects of the insulative deposits. To accomplish the goal, an unsteady conjugate mesh morphing simulation framework was developed and validated, which involved particle tracking in an unsteady fluid flow, particle–wall interaction modeling, conjugate mesh morphing of both fluid and solid domains, and a deposit identification method. The swirl and the jet impingement cooling configurations modeled the internal cooling passage for the leading-edge region of a turbine blade and were investigated in a dust-laden coolant environment at real engine conditions. Coupling effects between the dynamic deposition process and the unsteady flow inside the two cooling channels were examined and the insulative effects of the deposits were quantified by comparing the temperatures on the external and internal surfaces of the metal channel walls, as well as on the deposit layers. Results demonstrated the ability of the newly developed, unsteady conjugate simulation framework to identify the deposits from the original bare wall surface and to predict the insulation effects of the deposits in the dynamic deposition process. The dust almost covered the entire impingement channel, while deposits were only seen in the vicinity of the jets in the swirl channel. Despite this, a dramatical decrease of convection heat transfer was found in the swirl channel because the swirling flow was sensitive to the interruption of the deposits. In contrast, the deposits improved the heat transfer rate in the impingement channel. When the thermal effects of the deposit layer were taken into account, the wall temperatures of both two cooling geometries were substantially elevated, exceeding the allowable temperature of the metal material. Due to the denser deposit coverage, the impingement channel wall had a greater temperature increase than the swirl channel. In terms of flow loss, the presence of the deposits inhibited the swirl intensity by interrupting the swirling flow and thus reduced the friction loss, whereas the pressure loss was improved by the deposits in the impingement cooling.

A parametric study on the analysis of thermosolutal convection for magneto-hydrodynamics dependent viscous fluid

This article explores the influence of Joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The impact of thermal radiation is also considered. The effects of mass and heat transfer on the squeezing flow of Newtonian fluids are observed and modelled using the four fundamental governing equations of fluid flow: the mass equation, momentum equation, concentration equation, and energy equation. Using the appropriate similarity transformations, the resultant non-linear partial differential equations are then transformed into ordinary differential equations. The analytical strategy is developed using the homotopy analysis method to obtain the series solution. The influence of several physical parameters, including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter, and the Schmidt number, on the velocity profile, energy, and concentration are also discussed through graphs. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also found that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y- and z-axis, whereas the velocity field along the x-axis exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution. Further, graphs and tables are presented to illustrate an error analysis.