Unsteady Fluid Flow Research Articles

Transient MHD Flows Through an Exponentially Accelerated Isothermal Vertical Plate with Viscous Dissipation and Heat Source Embedded in a Porous Medium

In this article, an unsteady free convection flow of an incompressible viscous fluid past an exponentially accelerated isothermal vertical plate in the presence of the viscous dissipation and heat source is observed. The problem is governed by coupled nonlinear partial differential equations. Dimensionless equations of the problem have been solved numerically by the Galerkin finite element method. The effect of magnetic parameter M, Grashof number Gr, Eckert number Ec, time and an acceleration parameter ‘a’ on velocity, temperature fields are investigated through graphs. Skin friction coefficient is derived, discussed numerically.

Comparison of Adomian Decomposition Method with Differential Transformation Method for Unsteady MHD Flow and Heat Transfer Over a Stretching/Shrinking Permeable Sheet with Ohmic Heating

In this paper, two semi-analytical techniques were implemented to solve a two-dimensional unsteady MHD fluid flow and heat transfer through a stretching/shrinking permeable sheet with ohmic heating and viscous dissipation. The governing flow equations in PDE form were reduced to ordinary differential equations using appropriate similarity transformation. We obtained approximate expressions for the velocity and temperature profiles. Comparative results obtained employing Adomian decomposition method and differential transformation method were benchmarked against a numerical solution using Keller box scheme. Our findings revealed that the approximate analytical solution obtained using DTM is more dependable with fast convergence, highly accurate with minimal calculations and computationally convenient. However, the requirement of Adomian polynomials to tackle the nonlinear terms in ADM makes its execution sometimes cumbersome and difficult.

Numerical Study of Natural Convection Flow in Rectangular Cavity with Viscous Dissipation and Internal Heat Generation for Different Aspect Ratios

Numerical simulations have been performed to investigate the influence of constant volumetric heat generation and viscous dissipation on the unsteady natural convection flow of an incompressible Newtonian fluid contained in a rectangular cavity. The left vertical wall of the cavity is cooled, while the right vertical wall is heated, and the bottom and top walls are adiabatic. A numerical technique based on the implicit finite difference method (IFDM), along with an upwind finite difference scheme and an iterative successive over relaxation (SOR) technique, is employed to solve the governing equations numerically. The effect of physical parameters, namely the modified Rayleigh number (103≤Ra≤107), aspect ratio (1≤A≤4), Prandtl number (Pr=0.7, 1.0, 6.2, 15), volumetric internal heat generation parameter (Qλ=0, 1), and Eckert number (0≤Ec≤10−6), on the streamlines and isotherms are discussed graphically. Variations of maximum stream function, as well as average and local Nusselt number, are also discussed. The results show that the increase in Eckert number from 0 to 10−4 causes the average heat transfer to decrease, while Pr=0.71, Ra=104, and Qλ=0. Additionally, the average heat transfer decreases as the cavity width increases from 1 to 4, while Pr=0.71, Ra = 5×104, Ec=10−6 and Qλ=1. The results of the numerical model used here are in excellent accord with earlier findings.

Unsteady incompressible laminar boundary layer: time and space variable molecular viscosity

The subject of this work is two approaches to describe the laminar unsteady flow of an incompressible fluid in the boundary layer. In the first approach, the viscosity of the fluid and the acceleration with which the plane is set in motion are considered constant. In essence, this is Rayleigh's problem. The solution obtained on the basis of these assumptions asymptotically converges to the well-known self-similar Stokes solution. It is important that the solutions of Stokes and Rayleigh asymptotically at large values of time correspond to the disappearance of shear stresses between the liquid and moving plane after acceleration. A paradox emerges the equations derived by Stokes to describe internal friction indicate the absence of the same friction between a moving body and fluid. Since research using the calculus of variation methods revealed that the molecular viscosity inside the stationary boundary layer should depend on the distance to the moving surface, the corresponding non-steady problem was considered. As a result, as before for the steady case, solutions describing both non-gradient and gradient flows of incompressible fluid in the boundary layer are obtained. The asymptotic analysis of the transition to steady flow testifies the consistency of these solutions. For the case of non-gradient flow, a comparison of the classical solution with the solution corresponding to the extreme fluid flow rate carried by the moving surface is made. It is shown that according to the solution obtained on the basis of the calculus of variation approach, the shear stress on the surface does not disappear anywhere after the motion becomes steady but, as expected, acquires a constant value. The research methods are purely theoretical and the results are analyzed by comparison with available theoretical and experimental data and compliance with the fundamental laws of physics, in particular the law of conservation of energy. These methods are based on the construction of analytical mathematical models, which are differential equations in partial derivatives supplemented with appropriate physical initial and boundary conditions. In addition, Euler's differential equations for the extreme of functional theory are used (in this paper, this is the extreme of fluid flow rate across the cross-section of the boundary layer). When solving these equations, the well-known Fourier method of variable separation is used. Arbitrary functions of time arising during partial integration (by one of the variables – the spatial coordinate) are determined from the conditions of asymptotic convergence of the solutions of non-steady problems to the corresponding solutions of steady problems. Conclusions. The presented results are of fundamental importance for understanding the physics of the flow around aircraft parts, as they indicate the contradiction of the existing idea of the reversibility of direct and inverse problems: the motion of a body in a still fluid and the flow of a fluid around an immobile body.

Unsteady flows of micropolar fluids parallel to the axis of an annular domain with a porous layer

Transient flows of micropolar fluids through circular domains are investigated. The flow domain has two annular regions. The outer region is clean, while the inner region contains a porous medium. The analytical solutions in closed forms for the linear and angular velocities in both regions are determined using the Laplace transform and finite Hankel integral transform under the assumptions of the continuity of the velocities, stresses, and couple stresses on the interface. The obtained solutions are new in the literature and can generate solutions for some particular cases of filtration processes involving polymeric fluids with additives or other fluids that show similarities to micropolar fluids. Effects of various parameters on the fluid motion have been investigated by numerical simulations and graphical illustrations.

Unsteady MHD flow of a fractional second grade fluid in a channel passing through a porous medium subject to a time-dependent motion of the bottom plate

The velocity of an unsteady flow of a viscous fluid of the second-grade MHD-type enclosed between two parallel side walls perpendicular to a plate was obtained by applying the integral transformation. The fluid is required to move by the plate, which over time [Formula: see text] subjected the fluid to shear stress. The solutions satisfy the given equation as well as the boundary and initial conditions, and they were separated into two types: steady state and transient state. Furthermore, through [Formula: see text], we are able to recover the results found in the literature for motion across an infinite plate. Graphs depict the effect of the side walls and the time it takes to reach the steady state. The solutions are shown in graphs and discussed physically to examine the impact of different flow parameters. It is found that the fluid velocity decreases with an increasing fractional parameter [Formula: see text] and second-grade parameter [Formula: see text]. Also, it is noticed that the fluid velocity decreases with increasing values of Reynolds number and effective permeability. Numerous industrial products, including honey, paints, varnishes, coffee, chocolate and jelly, use this type of fluid flow concept.

Unsteady flow of micropolar fluid on a magnetized sheet: Effects of magnetic and microrotation parameters on wall couple stress and skin friction

AbstractIn this study, we investigate the unsteady flow of a micropolar fluid past a magnetized stretchable/shrinkable sheet. Our research aims to analyze the effects of magnetic field, moving slit, and various parameters on the velocity, magnetic, and microrotation profiles of the fluid. By applying the Blasius–Rayleigh–Stokes variable, we derive ordinary differential equations from the partial differential equations that define the problem. We solve the transformed set of equations using the shooting method and obtain dual solutions. Our findings indicate that skin friction decreases with increasing values of the microrotation parameter and magnetic interaction parameter. We also observe that the magnetic interaction parameter enhances the microrotation of molecules. Overall, our study provides valuable insights into the behavior of unsteady flows in micropolar fluids and sheds light on the impact of various parameters on dual solutions.

Unsteady reduced order model with neural networks and flight-physics-based regularization for aerodynamic applications

Numerical simulation of unsteady fluid flow plays an important role in several areas of the aeronautical industry. Since high-fidelity computational fluid dynamics simulations could be prohibitive in terms of computational cost, data-driven reduced order models become a suitable alternative for efficiently predicting flow variables as long as the accuracy of such models is comparable to that obtained by the full order model counterpart. This is especially important for iterative design purposes, where a few target variables must be evaluated on a large number of possible parameters. Therefore, we propose a neural network based methodology to develop an unsteady reduced order model of the subsonic/transonic flow field on 2D aerodynamic profiles trained on high-fidelity computational fluid dynamics data. For the purpose of dimensionality reduction, either proper-orthogonal decomposition or autoencoders are employed. For the regression task, a gated recurrent unit neural network is used to map an unsteady Schroeder multi-sine signal of angle of attack along with its first and second time-derivatives to the solution of surface variables, such as coefficients of pressure and friction. In order to shed light on the inner workings of data-driven methods so it could be employed in the aircraft design process, we introduce a flight-physics-based regularization term to incorporate information about the calculation of integral coefficients, like drag and lift, into the machine learning training workflow. Using our method, airfoil flow variables of interest can be predicted at a fraction of the cost of classical methods without any considerable accuracy loss. We also provide a comparison between reduction methods and we show evidence that supports the use of the proposed flight-physics-based regularization for building unsteady reduced order models based on machine learning.

Chemical reaction on Unsteady MHD Convection Flow of Second grade fluid over an unbounded perpendicular absorbent plate

ABSTRACT We discuss in this paper the chemical reaction impacts on complimentary convectively flow of the gelatinous secondary graded fluid past a countless vertical porous plate underneath the effects of uniform transversal magnetic field. Time reliant penetrability as well as fluctuating suction are also explored. The prevailing equations are resolved with the regular perturbation method for the small amplitudes of the permeability. The solutions for the velocities, temperature as well as concentrations have been obtained computationally; in addition, behaviour is also explored. The skin fiction, the Nusselts number as well as Sherwood numbers are also found in addition to those behaviour computationally conferred. It is concluded that the velocity is reduced with enhancement in the intensity of the magnetic field and Prandtl number whereas it is enhanced by the ever-increasing thermal Grashofs number. The magnitude of the temperature of the flow field diminished with increase in the Prandtl number, heat source parameter. The concentration of the flow field is reduced by a rise into the Schmidt number and chemical reaction parameters.

Natural convective heat transfer and fluid flow in a porous medium filled corrugated enclosure: Effect of discrete heat sources

AbstractIn this work, we investigate the two‐dimensional unsteady natural convective fluid flow problem in a porous‐corrugated enclosure with a fixed sinusoidal heated upper wall. The corrugations of the enclosure are discretely heated while vertical walls are maintained isothermally cold. Subject to where the heat sources are located, five different cases are taken into consideration. The vorticity–streamfunction equations are discretized using a transformation‐free higher order compact approach, and the hybrid BiCGSTAB technique is used to solve the system of algebraic equations that derives from the numerical discretization. To validate our findings, we first compare them to previously published numerical and experimental data. The numerically simulated outcomes are then examined over a variety of essential parameters, such as the Darcy (10−5 ≤ Da ≤ 10−1), Rayleigh (103 ≤ Ra ≤ 106), and Prandtl (0.1 ≤ Pr ≤ 10) numbers. Symmetric and asymmetric fluid flow phenomena are observed. Asymmetric flow phenomenon can be caused by miscible or non‐miscible movements of lighter fluids by heavier fluids, or almost exclusively by nonuniform buoyancy‐driven forces caused by density variations that have arisen because of variations in fluid temperature. The averaged Nusselt value for Case 1 and Case 5 exhibits the highest percentage ratio. The thermal boundary layer is strongly affected by compression, dispersion, suppression, the zone of stratification, and the outweighing of isotherms. The simulated results are visualized by stream functions, isotherms, local and averaged Nusselt number plots.

Analysis of blood flow of unsteady Carreau-Yasuda nanofluid with viscous dissipation and chemical reaction under variable magnetic field

Blood flow analysis through arterial walls depicts unsteady non-Newtonian fluid flow behavior. Arterial walls are impacted by various chemical reactions and magnetohydrodynamic effects during treatment of malign and tumors, cancers, drug targeting and endoscopy. In this regard, current manuscript focuses on modeling and analysis of unsteady non-Newtonian Carreau-Yasuda fluid with chemical reaction, Brownian motion and thermophoresis under variable magnetic field. The main objective is to simulate the effect of different fluid parameters, especially variable magnetic field, chemical reaction and viscous dissipation on the blood flow to help medical practitioners in predicting the changes in blood to make diagnosis and treatment more efficient. Suitable similarity transformations are used for the conversion of partial differential equations into a coupled system of ordinary differential equations. Homotopy analysis method is used to solve the system and convergent results are drawn. Effect of different dimensionless parameters on the velocity, temperature and concentration profiles of blood flow are analyzed in shear thinning and thickening cases graphically. Analysis reveals that chemical reaction increases blood concentration which enhance the drug transportation. It is also observed that magnetic field elevates the blood flow in shear thinning and thickening scenarios. Furthermore, Brownian motion and thermophoresis increases temperature profile.

Dynamics of gyrotactic microorganisms for chemically reactive magnetized 3D Sutterby nanofluid flow comprising non-uniform heat sink-source aspects

This presents a theoretical and computational evaluation of the unsteady 3D Bioconvection flow of Sutterby fluid, which has non-linear nonlinear radiation features as well as gyrotactic microorganisms, illuminating the novelty of the work. Furthermore, the influences of magnetic field, activation energy, chemical reactions, mixed convection and non-uniform heat sink-source are likewise indebted. Boundary layer theory is entreated to progress the elementary PDEs designed for microorganism field, momentum, nanoparticles concentration and energy also then condensed to the extremely nonlinear ODEs through the variable’s transformation. Numerical solutions for the existing investigation are obtained by bvp4c method in MATLAB software. Numerical calculations intended for Sherwood number, density number of microorganism and wall heat transfer are correspondingly accompanied. The graphic illustrations for exemplifying features of diverse embryonic parameters on dimensionless measures are designated systematically. It is fascinating to observed that the concentration as well as microorganism field is progressed for developed approximations of the bioconvection Rayleigh number and the magnetic parameter. The temperature of the fluid develops as a implied reaction to the magnetic parameter, the radiation parameter, Biot number and temperature ratio parameter.

Unsteady flow of hybrid fluid via peristaltic pumping in wavy micro-channel under electric and magnetic field effects: An application of Hall device and slip boundary

Aim of study In the current analysis, the blood is used as a viscoelastic fluid and manipulated with an electromagnetic field because of its magnetic features. Furthermore, blood is considered as a non-Newtonian fluid that is productive in nano- and micro-scales transport. To study the performance of hybrid fluids, a selection of nanofluids is examined with a Jeffrey fluid (blood) which is doped with [Formula: see text] and [Formula: see text] nanoparticles. Mathematical formulation The long wavelength assumption, lubrication theory and Debye–Huckel linearization are employed. Analytical solutions of flow equations are implemented in Mathematica by using integration technique. The impacts of considered parameters on the flow are computed. Combined influence of Hall device, momentum, and thermal slips is observed on various flow features. Outcomes Magnitude of the velocity goes on decreasing by increasing magnetic and viscoelastic parameters. The wavy behavior is predicted in the graphs of pressure gradient due to the complex nature of peristaltic walls. Enhancing the viscoelastic effects and concentration of nanoparticles results in reduction of magnitude of the pressure gradient. Heat transfer of hybrid fluid is larger in steady state flow as compared to the unsteady state. The heat source/sink parameter has remarkable impacts on enhancement of heat transfer phenomena of viscoelastic hybrid fluid. Applications The present investigation is relevant to electromagnetic hybrid liquid micropump manufactures and emerging nano-physiological technologies.

Unsteady Fluid Flow in a Darcy–Brinkman Porous Medium with Slip Effect and Porous Dissipation

In this paper, the significance of slip situations in the appearance of a porous medium and frictional heating on unsteady fluid flow through a porous medium has been explored. The numerical solutions of the differential equation representing fluid flow through a porous material, including slip effects, are presented. We have obtained a nonlinear ordinary differential equation using a similarity transformation. Under velocity and thermal slip conditions, the Maple packages were used to numerically solve the resulting set of nonlinear problems. Both the velocity and temperature increase when the Brinkman viscosity ratio parameter [Formula: see text] increases. The effects of the nondimensional parameters on the governing flow velocity and temperature are examined with graphical profiles. The implications of relevant parameters on dimensionless temperature, velocity, local Nusselt number and skin friction coefficient are shown and explained. For various flow quantities of interest, the fluctuation of parameters is investigated, and the results are given in the system of graphs and tables.

Numerical study on unsteady heat transfer and fluid flow in a closed cylinder of reciprocating liquid hydrogen pumps

Modeling and optimization of liquid hydrogen (LH2) pumps require accurate in-cylinder heat transfer correlations. However, the applicability of existing correlations based on gas mediums to LH2 remains to be verified. In this paper, the unsteady heat transfer and fluid flow in a closed LH2 pump cylinder are numerically studied by adopting the gas spring model. The phase shifts and temperature distribution in the closed pump cylinder are investigated. LH2 is less affected by in-cylinder heat transfer and has a more uniform temperature distribution compared to nitrogen gas, while a low-temperature zone appears near the piston face at 120 rpm. Finally, the validity of Lekic's correlation in predicting the heat flux of the LH2 compression process in the closed pump cylinder is verified, and the efficiency decrement versus rotational speed is analyzed based on the correlation. This work would be useful for selecting a proper in-cylinder heat transfer model for predicting the thermodynamic process in reciprocating LH2 pumps.

Nonlinear Dynamics of Perturbations of a Plane Potential Fluid Flow: Nonlocal Generalization of the Hopf Equation

In this paper, we analytically study the two-dimensional unsteady irrotational flow of an ideal incompressible fluid in a half-plane whose boundary is assumed to be a linear sink. It is shown that the nonlinear evolution of perturbations of the initial uniform flow is described by a one-dimensional integro-differential equation, which can be considered as a nonlocal generalization of the Hopf equation. This equation can be reduced to a system of ordinary differential equations (ODEs) in the cases of spatially localized or spatially periodic perturbations of the velocity field. In the first case, ODEs describe the motion of a system of interacting virtual point vortex-sinks/sources outside the flow domain. In the second case, ODEs describe the evolution of a finite number of harmonics of the velocity field distribution; this is possible due to the revealed property of the new equation that the interaction of initial harmonics does not lead to generation of new ones. The revealed reductions made it possible to effectively study the nonlinear evolution of the system, in particular, to describe the effect of nonlinearity on the relaxation of velocity field perturbations. It is shown that nonlinearity can significantly reduce the relaxation rate by more than 1.5 times.

Flow Field and Pressure Loss Characteristics at Rotary Drillstring Joints

A thorough understanding and accurate calculation of the annulus pressure losses are paramount to drilling design and construction. However, due to the influence of the drillstring rotation and the abrupt dimensional variation at the joint, it is difficult to calculate the pressure loss by theoretical analysis in the annulus at the drillstring joints. Considering the geometric nonlinearity of drillstring joints and the unsteady flow of annular fluid caused by pipe rotation, based on the turbulence model k − ε , the flow field characteristics demonstrate the annulus pressure losses at the drillstring joint are studied by numerical simulation. Simulation results indicate that drillstring rotation speed, annular gap, and eccentricity greatly influence flow field and pressure losses at drillstring joints. The annular pressure loss would increase with the decrease of the annular gap and eccentricity but decrease with the increase of the drillstring rotation rate. The investigation method and results would help guide the design of drilling hydraulic parameters.

Numerical simulation of mass and heat transport phenomena of hydromagnetic flow of Casson fluid with sinusoidal boundary conditions

AbstractA magnetic field might interact with its surroundings, influencing chemical and physical processes in materials processing, heat exchangers, and other scientific study. Therefore, a computational study of non‐Newtonian (Casson) free convective MHD unsteady fluid flow has been highlighted in this article with mass and heat transit property through a vertical infinite porous plate. A sinusoidal boundary conditions as well as chemical reaction and thermal radiation have been considered. Using a collection of nondimensional variables, the flow related equations are also turned into nondimensional form. The EFDM algorithm is employed in order to arrive at a numerical solution via Compaq Visual Fortran. The reliability of the numerical solution has been confirmed using stability testing and convergence analysis. The whole system is convergent when the values of Prandtl number and Lewis number are greater than or equals to 0.075 and 0.025, respectively. A visual depiction of the impact of the pertinent factors on dimensionless velocity, temperature, and concentration profiles are displayed through graphical representation as well as with tabular representation. It has been inspected that when the magnetic component is regarded, it greatly affects the heat transfer factors of Casson nanofluid and the heat also rises when Eckert number, heat source and radiation parameter accelerate. It is also found that the Sherwood number is increased as the impact of chemical reaction parameter and the Lewis number, also the skin friction is decreased as the influence of porosity term got accelerated. The comparison of the current findings with the data that were previously published serves as the final stage in validating the present study.

Fractional Analysis of Unsteady Slip Flow of Viscous Fluid Confined to the Boundaries of an Annulus Driven by Exponentially Decaying/Growing Time-Dependent Pressure Gradient

Fractional Analysis of Unsteady Slip Flow of Viscous Fluid Confined to the Boundaries of an Annulus Driven by Exponentially Decaying/Growing Time-Dependent Pressure Gradient

Analysis of chemical, ion slip, and thermal radiation effects on an unsteady magnetohydrodynamic dusty fluid flow with heat and mass transfer through a porous media between parallel plates

BackgroundInvestigating the dusty fluids flow attracted substantial attention in latest years because of their widespread utility within several industrial applications, including polymer technology, gas cooling systems, combustion, petroleum industry, and transport processes. The current article is dedicated to inspect the flow with mass transfer and heat of an unsteady Magneto-hydrodynamic dusty fluid. Consequently, impacts of chemical and thermal radiation, Joule, ion slip, Hall, and viscous dissipation toward heat and mass transferring and fluid flows are provided.ResultsNumerical solution of the controlling partial differential equations was performed. The temperature, velocity, and distribution of concentration for the particle and fluid phases were inspected under the influences of various physical parameters and their discussion was supplemented with diagrams.ConclusionsThe findings specify that these parameters have a significantly governed the solutions. The thermal radiation denotes efficiency enhancement of temperature distribution.